Revised October 6, EEL 3211 ( 2008, H. Zmuda) 6. Induction Motors 1

Transcription

1 Induction Motors Revised October 6, 008 EEL 311 ( 008, H. Zmuda) 6. Induction Motors 1

2 Induction Motors: We just learned how damper or amortisseur windings on a synchronous motor could develop a starting torque without the necessity of supplying an external current to the field winding. This idea works so well that a motor can be made without the synchronous motors main field windings at all. A machine with only amortisseur windings is called an induction machine. These machines are called induction machines because the rotor voltage, and hence the rotor current and rotor magnetic field is induced in the rotor windings instead of being physicaly connected by wires. EEL 311 ( 008, H. Zmuda) 6. Induction Motors

3 Induction Motors: The distinguishing feature of an induction machine is that no DC field current is required to run the machine. Although an induction machine can be used as either a motor or a generator, it has many problems when used as a generator and so these are rare. For this reason, when studying induction machines are really studying induction motors. An induction motor is called a singly excited machine (as opposed to a doubly excited machine) because power is applied only to the stator. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 3

4 Induction Motors: An induction motor has the same physical stator as a synchronous machine but with a different rotor construction. There are two different types of induction motor rotors. 1. A squirrel cage induction motor rotor consists of conducting bars laid into slots carved in the face of the rotor and shorted at either end by end rings or shorting rings (see picture next page).. A wound rotor that has a complete set of three phase windings that are mirror images of the windings on the stator. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 4

5 Al or Cu bars End Rings Squirrel Cage Rotor EEL 311 ( 008, H. Zmuda) 6. Induction Motors 5

6 EEL 311 ( 008, H. Zmuda) 6. Induction Motors 6

7 Laminated Stator Pole End Rings Shaft Laminated Fe Squirrel Cage Rotor Embedded Al or Cu bars EEL 311 ( 008, H. Zmuda) 6. Induction Motors 7

8 X X X Applied AC Voltage EEL 311 ( 008, H. Zmuda) 6. Induction Motors 8

9 Induction Motors: A wound rotor that has a complete set of three phase windings that are mirror images of the windings on the stator. The three phases of the rotor windings are usually Y-Connected, and the ends of the three-phase wires are tied to slip rings on the motor s shaft. The rotor windings are accessed through brushed riding on the slip rings. Such a rotor arrangement is more expensive, requires maintenance, and hence is rarely used. We will not consider wound rotors any further in this course. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 9

10 Induction Motors Basic Operation: Operation is basically the same as that of synchronous motors with amortisseur (damper) windings. There are a few specific terms that go along with induction motors. As before, a three-phase set of voltages is applied to the stator, and a three-phase set of currents thus flows. These currents produce a stator sao magnetic field edb S rotating oa in acounterclockwise ecoc wsedirection. The speed of the magnetic field rotation as previously found is: n m 10 f electrical P, P poles, n rev/min m EEL 311 ( 008, H. Zmuda) 6. Induction Motors 10

11 Induction Motors Induced Torque: As the rotating magnetic field passes over the rotor bars it induces a voltage in them equal to: e ind vrel B B B S Rotor (Stator not shown) EEL 311 ( 008, H. Zmuda) 6. Induction Motors 11

12 Induction Motors Induced Torque: The motion of the rotor relative to the stator that produces the induced voltage. e v B ind rel B S v rel Current out of page Rotor (Stator not shown) EEL 311 ( 008, H. Zmuda) 6. Induction Motors 1 v v rel Current into page

13 Induction Motors Induced Torque: But since the rotor is inductive, current lags the induced voltage B S I R Maximum induced current Rotor (Stator not shown) EEL 311 ( 008, H. Zmuda) 6. Induction Motors 13

14 Induction Motors Induced Torque: This rotor current produces its own magnetic field B R. B S I R B R Rotor Only (Stator not shown) EEL 311 ( 008, H. Zmuda) 6. Induction Motors 14

15 Induction Motors Induced Torque: kb B The resulting torque is counterclockwise: ind R S B S B R Rotor Only (Stator not shown) EEL 311 ( 008, H. Zmuda) 6. Induction Motors 15

16 Induction Motors Induced Torque: Note how the maximum motor speed is the synchronous speed. If the motor however was tuning at synchronous speed then the relative velocity between the rotor and stator would be zero. With zero relative velocity, e ind vrel B, ind kbr BS v 0 e 0 I 0 B 0 0 rel ind R R ind and the rotor would slow down due to friction. But then the relative velocity would no longer be zero and the rotor would once again accelerate. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 16

17 Induction Motors Rotor Slip Consequently the motor will speed up to near synchronous speed but never actually reach it. Note also that both the rotor and stator magnetic fields rotate together at synchronous speed n sync, while the rotor itself always turns at a slower speed. This scalled rotor slip. In a synchronous motor, the voltage induced in a rotor bar depends on the speed of the rotor relative to the magnetic fields. The speed of an induction motor depends on the rotor voltage and current. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 17

18 Induction Motors Rotor Slip The difference between the synchronous speed (the speed of the magnetic fields) in an induction motor and the rotor speed is known as the slip speed n slip. n n n slip sync m The notion of slip s is the slip speed on a per-unit basis: nslip nsync nm nm s s 1 n 1 m s n n n n sync sync sync If the motor is tuning at synchronous speed then s = 0. If the motor is stationary then s = 1. sync EEL 311 ( 008, H. Zmuda) 6. Induction Motors 18

19 Induction Motors Rotor Slip Miscellaneous relationships: s n n sync m sync m n sync sync n 1s n 1s m sync m sync EEL 311 ( 008, H. Zmuda) 6. Induction Motors 19

20 Electrical Frequency of the Rotor The induction motor operates by inducing voltages and currents in the rotor and as such can be viewed as a rotating transformer. The stator serves as the primary, The rotor serves as the secondary, BUT the secondary frequency is not necessarily the same as the primary frequency (unlike a transformer). EEL 311 ( 008, H. Zmuda) 6. Induction Motors 0

21 Electrical Frequency of the Rotor If the rotor is locked and cannot move, the frequency of the rotor current will be the same as that in the primary. If the rotor turns at synchronous speed, the frequency of the rotor current will be zero. What is the rotor frequency for any other speed of rotor rotation? EEL 311 ( 008, H. Zmuda) 6. Induction Motors 1

22 Electrical Frequency of the Rotor s n n f f n f sync m sync m sync sync n 0 f f, s 1 m r e n n f 0, s 0 m sync r f sf r e EEL 311 ( 008, H. Zmuda) 6. Induction Motors

23 Electrical Frequency of the Rotor 10 f n e sync nm n, f sf f P n sync r e e sync nsync n fr 1 0 fe P m f e P 1 0 f n n r sync m Notation: f r denotes the electrical frequency of the rotor, while f m is its mechanical frequency. This is why it s smart to use n m (in rpm) for mechanical speeds and f r (in hertz for electrical frequency). EEL 311 ( 008, H. Zmuda) 6. Induction Motors 3

24 Circuit Model (per Phase) for the Induction Motor Because of the transformer-like operation, the model for the induction motor will be essentially that of the circuit model for a transformer. Because the induction motor is a single excited machine (no power applied to a field circuit), the model will not have an internally generated voltage E A as we had in the synchronous (doubly excited) ed) machine. To develop the model for the induction motor, let s start with the transformer model and go from there. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 4

25 Circuit Model (per Phase) for the Induction Motor Recall the transformer model from Note Set 3: RP jx P R S jx S N N jx M R C P S IDEAL EEL 311 ( 008, H. Zmuda) 6. Induction Motors 5

26 Circuit Model (per Phase) for the Induction Motor I I 1 Stator Leakage R1 jx 1 I I R jx R V P I M jx M R C E E 1 a eff E E R R R IDEAL Magnetizing Reactance (much smaller than that of a good transformer because...) EEL 311 ( 008, H. Zmuda) 6. Induction Motors 6

27 Circuit Model (per Phase) for the Induction Motor Magnetizing Reactance: Transformer Induction Motor Y EEL 311 ( 008, H. Zmuda) 6. Induction Motors 7

28 Circuit Model (per Phase) for the Induction Motor Note how the slope of the motor s flux-mmf curve is much shallower that that of a good transformer. This is because of the presence of an air gap in the motor, not present in a transformer, which greatly increases the reluctance of the flux path and thereby reducing the coupling between primary and secondary. The higher reluctance means that a higher magnetizing current is needed to obtain a given flux level. This results in a much smaller value of X M than in an ordinary transformer. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 8

29 Circuit Model (per Phase) for the Induction Motor The major difference between the model of the induction motor and that of a transformer is due the difference in frequency between the primary and the secondary. How do we model this? In general for an induction motor, a voltage is applied to the stator windings inducing a voltage in the rotor windings. The greater the relative motion between the rotor and stator magnetic field, the greater the resulting rotor voltage and rotor frequency, since e v B f n n l, ind rel r sync m P 10 EEL 311 ( 008, H. Zmuda) 6. Induction Motors 9

30 Rotor Model The largest relative motion occurs when the rotor is locked or stationary. The largest voltage and rotor frequency occur under this condition. The smallest voltage (zero) and frequency (zero) occur when the rotor turns at the same speed as the stator magnetic field yielding no relative motion. The magnitude of the induced voltage and rotor frequency at any speed between these extremes is directly proportional to the rotor slip: E se, f s sf R LR r e Locked Rotor EEL 311 ( 008, H. Zmuda) 6. Induction Motors 30

31 Rotor Model The rotor resistance is essentially constant, independent of slip. The rotor reactance is not. I R jx R s E R se ~ RL R R EEL 311 ( 008, H. Zmuda) 6. Induction Motors 31

32 Rotor Model X s L f s L For a rotor inductance L R, R R R r R but f s sf r e thus X s s L sf L R R R e R s f L sx e R LR Locked Rotor Reactance EEL 311 ( 008, H. Zmuda) 6. Induction Motors 3

33 Rotor Model I R E R se ~ RL jsx jx s LR R R R EEL 311 ( 008, H. Zmuda) 6. Induction Motors 33

34 Rotor Model Note that the rotor current is: I R s E se E R R R jxr s RR jsxlr R s R R Z s Req, jx LR s R LR LR It is thus possible to model all of the rotor effects due to varying rotor speed as being caused by a varying resistance supplied by a constant voltage source E LR. jx LR EEL 311 ( 008, H. Zmuda) 6. Induction Motors 34

35 Rotor Model Final Rotor Model: I R jx LR ~ s E LR R R Note that at very low slip the resistive term will dominate and the rotor current will vary linearly with slip. At high slip, the inductor dominates, and the rotor current approaches a steadystate current. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 35

36 Final Equivalent Circuit for Induction Motor All rotor quantities referred back to the stator side. I 1 R 1 jx 1 I jaeff X LR jx V I M jx R a M C E eff 1 R s R R EEL 311 ( 008, H. Zmuda) 6. Induction Motors 36

37 Equivalent Circuit for Induction Motor The rotor resistance R R and locked rotor reactance X LR are very difficult to determine for induction motors as is the effective turns ratio a eff. Fortunately, it is possible to take measurements that give R and X even though R R, X LR, and a eff remain unknown. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 37

38 Power and Torque in an Induction Motor I 1 jx R1 jx 1 Z eq E V jx M R C 1 R s V Z R jx R jx R s jx eq 1 1 C M I 1 EEL 311 ( 008, H. Zmuda) 6. Induction Motors 38

39 Power and Torque in an Induction Motor V Zeq R jx RC jx M R s jx I 1 R jx 1 1 R jx 1 1 R1 jx1 G R jx R s jx C M R s jx 1 1 R jx C jb M 1 1 R s jx C M EEL 311 ( 008, H. Zmuda) 6. Induction Motors 39

40 Power and Torque in an Induction Motor Losses: P 3V I in T L P StatorCopperLoss t P P CoreLosses P P AirGap RotorCopperLoss P Friction and WindageLoss Stray and Misc. Losses P out load mechanical P converted induced mechanical EEL 311 ( 008, H. Zmuda) 6. Induction Motors 40

41 Power and Torque in an Induction Motor Losses: I 1 jx R1 jx 1 Z eq Stator Copper Losses V jx M R C E E 1 R s Core Losses V Zeq R1 jx1 I 1 G C jb M 1 1 R s jx EEL 311 ( 008, H. Zmuda) 6. Induction Motors 41

42 Power and Torque in an Induction Motor Losses: Stator Copper Losses: PSCL 3I R 1 1 Core Losses: P 3E R Core 1 C Power in Air Gap: PAG Pin PSCL PCore Looking at the model, the only place for the air gap power to be consumed is in the resistor R /s, thus P AG 3I R s EEL 311 ( 008, H. Zmuda) 6. Induction Motors 4

43 Power and Torque in an Induction Motor Losses: The actual resistive losses in the rotor are: P 3I R RCL R R But the power is unchanged when transferred across an ideal transformer. Thus this rotor copper loss can also be expressed as: PRCL 3I R The electrical power converted to mechanical power is thus, P P P conv. AG RCL EEL 311 ( 008, H. Zmuda) 6. Induction Motors 43

44 Power and Torque in an Induction Motor: Converted Power: P P P conv. AG RCL R 3 I 3 I R s 1 3 I R 1 s 1 s s 3IR EEL 311 ( 008, H. Zmuda) 6. Induction Motors 44

45 Power and Torque in an Induction Motor: Note: R 1 PAG 3 I 3 I R s s PRCL 3I R 1 P P, P s sp AG RCL RCL AG Therefore the lower the slip, the lower the rotor losses. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 45

46 Power and Torque in an Induction Motor: Note also that if the rotor is not turning, s = 1, and the air gap power is entirely consumed by the rotor. Clearly if the rotor is not turning, the mechanical output tpower is zero. Also, P P P conv. AG RCL P P AG AG sp 1 s If the friction, windage, and miscellaneous losses are known then, AG out conv. F & W misc. P P P P EEL 311 ( 008, H. Zmuda) 6. Induction Motors 46

47 Power and Torque in an Induction Motor: Induced Torque: ind Recall: m 1s conv. AG 1 P P s and P conv. sync m P P 1 s conv. AG P ind 1 s AG m sync sync ind P AG sync EEL 311 ( 008, H. Zmuda) 6. Induction Motors 47

48 Power and Torque in an Induction Motor: Also notice that we can separate the rotor copper losses and the power converted in the equivalent circuit. P P P P s. 1 conv AG RCL AG The power crossing the air gap is partly consumed in the rotor copper losses and the rest is converted to mechanical power to drive the shaft. Recall that the air gap power was found as P AG 3I while the rotor loss was found to be R s P RCL I R EEL 311 ( 008, H. Zmuda) 6. Induction Motors 48

49 Power and Torque in an Induction Motor: Thus, P P P conv. AG RCL R I I R s 1 I R 1 s 1 1 s I Rconv., Rconv. R 1 R s s EEL 311 ( 008, H. Zmuda) 6. Induction Motors 49

50 Power and Torque in an Induction Motor: Also notice that we can separate the rotor copper losses and the power converted in the equivalent circuit. R1 jx 1 jx R Rotor Copper Loss 1 s jx M R C R s Converted EEL 311 ( 008, H. Zmuda) 6. Induction Motors 50

51 Torque-Speed Characteristics of an Induction Motor: How does the torque of an induction motor change as the load changes? How much torque can an induction motor supply at starting conditions? Hw much does the speed of an induction motor shaft drop as the load increases? All these questions can be answered with our circuit model. Recall two important results: conv. ind P m P AG sync EEL 311 ( 008, H. Zmuda) 6. Induction Motors 51

52 Torque-Speed Characteristics of an Induction Motor: Since sync is constant, if we know the air gap power, we know the induced torque. ind P AG sync The air gap power is the power crossing the gap from the stator to the rotor and is equal to the power absorbed in the resistance R /s. This power be found via simple circuit analysis. Consider just one phase for the analysis. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 5

53 Torque-Speed Characteristics of an Induction Motor: Compute the Thevenin Equivalent Circuit at the place shown below. I R1 jx jx 1 1 I V jx M R C E E 1 Z TH R s P I R s AG EEL 311 ( 008, H. Zmuda) 6. Induction Motors 53

54 Torque-Speed Characteristics of an Induction Motor: By voltage divider: ZM V TH V Z Z 1 M R jx C M V R 1 jx 1 R C jx M jr X C M V RR 1 C X1XM j RX 1 M X1 RC RC XM EEL 311 ( 008, H. Zmuda) 6. Induction Motors 54

55 Torque-Speed Characteristics of an Induction Motor: For small core losses RC V TH V XX jr X 1 M 1 M RC R1 j X1 XM RC RC V jx M R j X X 1 1 M C M RX R X X also, is often the case that 1 1 M EEL 311 ( 008, H. Zmuda) 6. Induction Motors 55

56 Torque-Speed Characteristics of an Induction Motor: To a very good approximation, Thevenin Impedance: X M VTH V X 1 X M Z R jx R jx TH 1 1 C M EEL 311 ( 008, H. Zmuda) 6. Induction Motors 56

57 Torque-Speed Characteristics of an Induction Motor: Z TH R R jx C M 1 1 jx 1 1 C jr X R C jx jrcx R jx C M M M M jr X R jx 1 1 RR X X j RX RX RX C 1 M 1 C 1 1 M C M jr X R jx C M 1 1 XMX 1 R1X RC R1 jx1 XM RC RC EEL 311 ( 008, H. Zmuda) 6. Induction Motors 57 M

58 Torque-Speed Characteristics of an Induction Motor: Using the same approximation as before, RC Z TH jx R jx M R j X X M and R X X 1 1 M Z TH X R jx M X X M EEL 311 ( 008, H. Zmuda) 6. Induction Motors 58

59 Torque-Speed Characteristics of an Induction Motor: Thus, X R X X M 1 1 Z TH R TH jx TH j 1 M 1 M X X X X M Z jx I Z TH V TH V X M X1 X M ~ R s EEL 311 ( 008, H. Zmuda) 6. Induction Motors 59

60 Torque-Speed Characteristics of an Induction Motor: Clearly, I I Z V TH Z TH V TH R s RTH jxth jx V V TH I R R TH XTH X P AG 3I R s s EEL 311 ( 008, H. Zmuda) 6. Induction Motors 60

61 Torque-Speed Characteristics of an Induction Motor: Clearly, P AG ind R 3 I s 3 V TH R R X X s PAG TH TH sync R s EEL 311 ( 008, H. Zmuda) 6. Induction Motors 61

62 Torque-Speed Characteristics of an Induction Motor: Plot ind vs. n m. Use: 3 V TH ind R RTH XTH X s P f n n 10 r sync m R s sync n 1s n 1s m sync m sync EEL 311 ( 008, H. Zmuda) 6. Induction Motors 6

63 Torque-Speed Characteristics of an Induction Motor: Plot ind vs. n m. Use: s ind n sync n R s 3 V TH R TH XTH X n sync m R s sync sync n f P n P P 60 sync sync sync sync EEL 311 ( 008, H. Zmuda) 6. Induction Motors 63

64 Torque-Speed Characteristics of an Induction Motor: Plot ind vs. n m. ind 3 V TH R R s sync RTH XTH X s 3 V TH R n nsync nm sync P n R TH R X TH X n n sync 60 sync n m sync 60 EEL 311 ( 008, H. Zmuda) 6. Induction Motors 64

65 EEL 311 ( 008, H. Zmuda) 6. Induction Motors 65

66 Observations: nm nsync ind 0 EEL 311 ( 008, H. Zmuda) 6. Induction Motors 66

67 Observations: Nearly linear between no-load and full-load This is because in this range the rotor resistance is much larger than the rotor reactance, so the rotor current, the rotor magnetic field, and the induced torque increase linearly with increasing slip s. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 67

68 Observations: Maximum possible or breakdown torque. (We ll compute this momentarily.) EEL 311 ( 008, H. Zmuda) 6. Induction Motors 68

69 Observations: The starting torque is greater than the full-load torque. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 69

70 Observations: Since ind V TH V The torque for a given slip varies as the square of the applied voltage. This is an important observation for one form of motor speed control to be discussed later. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 70

71 Observations: If the rotor is driven faster then synchronous speed, the direction of the induced torque reverses and the machine becomes a generator. If the motor is turning backwards relative to the direction of the stator magnetic fields, the motor will stop very rapidly and try to turn in the other direction. Recall that reversing the direction of magnetic field rotation is simply a matter of switching any two stator phases. This method is used to rapidly stop an induction motor and is called plugging. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 71

72 Observations: Overdriven Motor EEL 311 ( 008, H. Zmuda) 6. Induction Motors 7

73 Observations: A plot of Power and Torque P conv. m ind EEL 311 ( 008, H. Zmuda) 6. Induction Motors 73

74 Maximum, Pullout, or Breakdown Torque Since ind P AG sync Maximum torque occurs when the air gap power is maximum. The air gap power is the power consumed by R s When is this power maximum? EEL 311 ( 008, H. Zmuda) 6. Induction Motors 74

75 Maximum, Pullout, or Breakdown Torque We can t change V TH, Z TH, or X, or R. Z source Z TH jx I X M VTH V X1 XM ~ Z TH X R jx M X X M R s EEL 311 ( 008, H. Zmuda) 6. Induction Motors 75

76 Maximum, Pullout, or Breakdown Torque We can t change V TH, Z TH, or X, or R. Z source I V TH ~ R s P I R s AG EEL 311 ( 008, H. Zmuda) 6. Induction Motors 76

77 Maximum, Pullout, or Breakdown Torque P I R s AG TH V TH Z R s R s V TH R R s X X TH TH R s EEL 311 ( 008, H. Zmuda) 6. Induction Motors 77

78 Maximum, Pullout, or Breakdown Torque P P RTH R s XTH X RTH R s R s AG VTH R s RTH R s XTH X TH TH TH TH TH TH 0 R R s R R s X X R R sr s 0 R R s X X R s R X X TH TH R s Z source 0 EEL 311 ( 008, H. Zmuda) 6. Induction Motors 78

79 Maximum, Pullout, or Breakdown Torque R s Z R X X max source TH TH The slip at pullout torque is: s max R R TH XTH X 3 V TH AG max max RTH R smax XTH X P R s pullout P AG max sync EEL 311 ( 008, H. Zmuda) 6. Induction Motors 79

80 Maximum, Pullout, or Breakdown Torque 3V TH PAG R s max R R s X X TH max TH R s Z R X X max source TH TH P AG max 3V TH Z source R Z X X TH source TH 3V Z max TH source TH TH source TH source R X X Z R Z EEL 311 ( 008, H. Zmuda) 6. Induction Motors 80

81 Maximum, Pullout, or Breakdown Torque P AG max pullout 3V TH Z source TH TH source TH source R X X Z R Z 3V Z source TH Z source Z R Z P AG source TH source 3 V max 3 Z TH R sync sync source TH EEL 311 ( 008, H. Zmuda) 6. Induction Motors 81

82 Maximum, Pullout, or Breakdown Torque Since s max R Z source the slip at which h maximum torque occurs is linearly l proportional to the rotor resistance though the value of the maximum torque is independent of the value of the rotor resistance. pullout P AG max 3V Z TH R sync sync source TH EEL 311 ( 008, H. Zmuda) 6. Induction Motors 8

83 Maximum, Pullout, or Breakdown Torque Recall the plot on Slide 65: EEL 311 ( 008, H. Zmuda) 6. Induction Motors 83

84 Torque-Speed Characteristics Also recall the torque speed characteristics derived and examine its dependence on R : ind 3 TH R n nsync nm P n sync TH n sync 60 sync n m 3 V sync R TH R X X n EEL 311 ( 008, H. Zmuda) 6. Induction Motors 84

85 Torque-Speed Characteristics If we could somehow vary R we would find this kind of behavior (verify this for yourself by plotting the equation on the last slide): EEL 311 ( 008, H. Zmuda) 6. Induction Motors 85

86 Torque-Speed Characteristics If a rotor is designed with high resistance, the starting torque is quite high, but the slip is also quite high under normal operating conditions. i P P s conv. AG 1 Recall from Slide 47: The higher the slip, the smaller the fraction of air-gap power converted to mechanical power, thus the smaller the efficiency. Hence a motor with high starting torque has poor efficiency at normal operating speeds. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 86

87 Torque-Speed Characteristics Alternatively a rotor is designed with low resistance has a low starting torque and a high starting current but its efficiency at normal operating speed dis quite high. h It would be very desirable to have a motor with a high R on starting but a low R at normal speed. Large bars (small R ) near surface (small X ) Pullout torque near synchronous speed. Good efficiency. Small bars (large R ) near surface (X still small ) Pullout torque near synchronous speed. Poorer efficiency. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 87

88 Torque-Speed Characteristics The desirable feature of having a motor with a high R on starting but a low R at normal speed can actually be accomplished by taking advantage of the leakage reactance in the design of an induction i motor. Keep in mind: Mechanical Speeds: n Rotor 1 s n Stator Electrical l Frequencies: r sync f sf EEL 311 ( 008, H. Zmuda) 6. Induction Motors 88

89 Torque-Speed Characteristics An ingenious and simple way of obtaining a rotor resistance which will automatically vary with speed makes use of the fact that at standstill the rotor frequency equals the stator frequency; as the motor accelerates, the rotor frequency decreases to a very low value, perhaps p or 3 Hz at full load in a 60-Hz motor. Squirrel-cage rotors can be designed so that their effective resistance at 60 Hz is several times their resistance at or 3 Hz. The various schemes all make use of the inductive effect of the slot-leakage flux on the current distribution in the rotor bars. One way that this happens is by the skin effect. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 89

90 Skin Effect: Gives depth of penetration into a (real) conductor as a function of frequency as 1 f Io value at surface I z I o z I e 1 Ie o z Perfect Conductor Current flows entirely on the conductor surface. Real Conductor Current penetrates into the conductor. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 90

91 Skin Effect: Current distribution due to skin effect. The higher the frequency the more the current flows on the conductor surface giving a smaller effective area and hence a larger R. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 91

92 Torque-Speed Characteristics Leakage Resistance Skin Depth: 1 f Resistance: R A EEL 311 ( 008, H. Zmuda) 6. Induction Motors 9

93 Torque-Speed Characteristics Leakage Resistance d w w 1 f EEL 311 ( 008, H. Zmuda) 6. Induction Motors 93

94 Torque-Speed Characteristics Leakage Resistance A wd d A A w d eff w w 1 f EEL 311 ( 008, H. Zmuda) 6. Induction Motors 94

95 Torque-Speed Characteristics Leakage Resistance Cu Cu R, Aeff w d 4 A R A AC eff A wd wd R DC Aeff wd4 1 1 wd 4 A f f EEL 311 ( 008, H. Zmuda) 6. Induction Motors 95

96 Torque-Speed Characteristics - Leakage Resistance EEL 311 ( 008, H. Zmuda) 6. Induction Motors 96

97 Torque-Speed Characteristics - Leakage Resistance EEL 311 ( 008, H. Zmuda) 6. Induction Motors 97

98 Torque-Speed Characteristics Leakage Reactance: Recall that the reactance X in an induction motor equivalent circuit is the rotor s leakage reactance referred back to the primary. (See Slide 3, 36) X aeff XLR The leakage reactance is due to the rotor flux lines that do not couple with the stator windings. The farther away a rotor bar (or part of a rotor bar) )is from the stator, t the greater its leakage reactance. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 98

99 Torque-Speed Characteristics Leakage Reactance: If the squirrel cage bars are placed close to the surface of the rotor, the leakage reactance will be small (X will be small). If the rotor bars are placed deep in the surface of the rotor, the leakage will be greater and X will be larger. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 99

100 Torque-Speed Characteristics Consider a squirrel-cage rotor having deep, narrow bars: X Low Leakage (X small) X Leakage inductance for the bottom portion of the bar is greater than that of the top portion because Large Leakage the bottom experiences has less flux linkage. (X large) EEL 311 ( 008, H. Zmuda) 6. Induction Motors 100

101 Torque-Speed Characteristics Because of the variation in the reactance, under ac conditions the current in the low-reactance upper layers will be greater than that in the high-reactance h lower layers. As a result, the current will be forced toward the top of the slot, and the phase of current in the upper layers will lead that of the current in the lower ones. This non-uniform current distribution results in an increase in the effective bar resistance. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 101

102 Torque-Speed Characteristics Low X More current here High X Rotor Bar Current distribution is uniform for f ~ 0 (Low R ) Less current here Current distribution for f > 0. Note how the current is forced to the top reducing the effective area and thus increasing R for low speeds (large f r ). EEL 311 ( 008, H. Zmuda) 6. Induction Motors 10

103 Torque-Speed Characteristics The result is that the current in the low-reactance upper layers will be greater than that in the high-reactance lower layers. As a result, the current will be forced toward the top of the slot, and the phase of current in the upper layers will lead that of the current in the lower ones. This non-uniform current distribution results in an increase in the effective bar resistance and a smaller decrease in the effective leakage inductance of the bar. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 103

104 Torque-Speed Characteristics Consequently a squirrel-cage rotor with deep bars can be readily designed to have an effective resistance at stator frequency (corresponding to rotor standstill conditions) several times greater than its dc resistance. As the motor accelerates, the rotor frequency decreases and therefore the effective rotor resistance decreases, approaching its dc value at small slips. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 104

105 Torque-Speed Characteristics An alternative way of attaining similar results is the double-cage arrangement shown on the next slide. The squirrel-cage winding consists of two layers of bars shortcircuited by end rings. The upper bars are of smaller crosssectional area than the lower bars and consequently have higher resistance. As before, the inductance of the lower bars is greater than that of the upper ones. At standstill, EEL 311 ( 008, H. Zmuda) 6. Induction Motors 105

106 Torque-Speed Characteristics Double Cage Rotor Design An alternative way of attaining similar results is the double-cage design: Top Bar (High R ) Bottom Bar (Low R ) EEL 311 ( 008, H. Zmuda) 6. Induction Motors 106

107 Torque-Speed Characteristics At standstill, when rotor frequency equals stator frequency, there is relatively little current in the lower bars because of their high reactance; the effective resistance of the rotor at standstill is then approximately equal to that of the high-resistance upper layer. At the low rotor frequencies corresponding to small slips, however, reactance effects become negligible, and the rotor resistance then approaches that of the two layers in parallel. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 107

108 Torque-Speed Characteristics The upper bars are of smaller cross-sectional area than the lower bars and consequently have higher resistance. The inductance of the lower bars is greater than that of the upper ones because of the flux crossing the slot between the two layers. The difference in inductance can be made quite large by properly proportioning the constriction in the slot between the two bars. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 108

109 Summary: By use of double-cage and deep-bar rotors, squirrel-cage motors can be designed to have the good starting characteristics resulting from high rotor resistance and, at the same time, the good running characteristics resulting from low rotor resistance. Induction motors generally fall into four types: Class A: Normal Starting Torque, Normal Starting Current, Low Slip Class B: Normal Starting Torque, Low Starting Current, Low Slip Class C: High Starting Torque, Low Starting Current Class D: High Starting Torque, High Slip EEL 311 ( 008, H. Zmuda) 6. Induction Motors 109

110 EEL 311 ( 008, H. Zmuda) 6. Induction Motors 110

111 Starting Induction Motors and Speed Control Clearly, by their very nature, inductions motors tend to be self starting. Electronics is used to limit the starting current. The speed can be somewhat controlled with line voltage. Another method of speed control uses power electronic circuits to vary the line current. Read Section 7.77 and 7.8 for a discussion on these topics. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 111

112 Determination of Circuit Model Parameters We still need to determine: R1, R, X1, X, and X M For a real motor. From Slide 50: R jx jx 1 1 R R Rotor Copper Loss jx R M R C 1 s s Converted EEL 311 ( 008, H. Zmuda) 6. Induction Motors 11

113 Determination of Circuit Model Parameters DC Stator Resistance I DC I 1, Rated A R 1 R 1 V DC V R 1 R 1 V DC I DC Motor (No-Load) EEL 311 ( 008, H. Zmuda) 6. Induction Motors 113

114 Determination of Circuit Model Parameters No-Load Test Measures rotational losses and provides magnetization current. 1. The motor spins freely, so the only loads are the friction i and windage losses.. All P conv in this motor is consumed by mechanical losses. 3. The slip is very small. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 114

115 Determination of Circuit Model Parameters No-Load test Measures rotational losses and provides magnetization current. I A Wattmeter A Variable Voltage Variable Frequency V Wattmeter A I B Motor (No-Load) Three-Phase Source Wattmeter A I C (spins freely) EEL 311 ( 008, H. Zmuda) 6. Induction Motors 115

116 Determination of Circuit Model Parameters No-Load Test I 1 I 0 R1 jx 1 jx R I M s s jx M R C R s 1000R 1s 1s R R, R X s s EEL 311 ( 008, H. Zmuda) 6. Induction Motors 116

117 Determination of Circuit Model Parameters No-Load Test I 1 R 1 jx 1 jx M R C 1 s R s R F W & EEL 311 ( 008, H. Zmuda) 6. Induction Motors 117

118 Determination of Circuit Model Parameters No-Load Test I 1 R 1 jx 1 jx M R C R 1 s s EEL 311 ( 008, H. Zmuda) 6. Induction Motors 118

119 Determination of Circuit Model Parameters No-Load Test The input power measured by the meters must equal the losses in the motor. The rotor copper losses can be neglected since I is extremely small since the slip is so small. The (known) stator copper losses are, PSCL 3I R 1 1 So the input power must equal, Pin PSCL Pcore PF & W Pmisc Rotational Losses EEL 311 ( 008, H. Zmuda) 6. Induction Motors 119

120 Determination of Circuit Model Parameters No-Load Test I 1 R 1 jx 1 X R R M C 1 s s jx M R C R 1 s s The current needed d to establish a magnetic field is quite large because of the large reluctance of its air gap, hence the reactance X M will be much smaller than the resistances in parallel with it. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 10

121 I Determination of Circuit Model Parameters No-Load Test 1,noload V R 1 jx 1 jx M R C R X R R M 1 s s C 1 s s The power factor will be small and lagging, and most of the voltage drop will be across the inductors. Thus, V Z in X 1 X I 1, noload EEL 311 ( 008, H. Zmuda) 6. Induction Motors 11 M

122 Determination of Circuit Model Parameters Locked-Rotor Test Equivalent to a short circuit transformer test. I A A Wattmeter Variable Voltage Variable Frequency A I B V Wattmeter Motor (Rotor Locked) Three-Phase Source A I C Wattmeter EEL 311 ( 008, H. Zmuda) 6. Induction Motors 1

123 Determination of Circuit Model Parameters Locked-Rotor Test With the rotor blocked, the current is adjusted to be that at full-load (approximately). The voltage, current, and power to the motor are measured. Since the rotor is not moving, the slip s = 1. Hence R /s = R and R is quite small. For a locked rotor, X is also quite small, and the model can be approximated as... EEL 311 ( 008, H. Zmuda) 6. Induction Motors 13

124 Determination of Circuit Model Parameters Locked-Rotor Test R1 jx 1 jx neglect R jx M R C these s R X R jx C M R R jx EEL 311 ( 008, H. Zmuda) 6. Induction Motors 14

125 Determination of Circuit Model Parameters Locked-Rotor Test I 1,locked rotor R1 jx 1 jx V R s R EEL 311 ( 008, H. Zmuda) 6. Induction Motors 15

126 Determination of Circuit Model Parameters Locked-Rotor Test A major problem with this test is that although the stator frequency equals the line frequency, the rotor frequency is different. Under normal operating conditions, the slip for most motors is on the order of a few percent, so that the rotor frequency is in the range of 1 3 Hertz. When the rotor is locked, then the rotor frequency equals the line frequency. Particularly, difficulties are encountered with variable resistance rotors. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 16

127 Determination of Circuit Model Parameters Locked-Rotor Test This is why a variable frequency source is used. A typical compromise is to use a test frequency that is 5% or less than the rated frequency. At lower than normal operating frequency, the inductive reactances are smaller, so the voltage level l needs to be adjusted d so as not to exceed maximum current ratings. IEEE standards carefully guideline the actual test procedure. Nevertheless, great care must be used when using this test. EEL 311 ( 008, H. Zmuda) 6. Induction Motors 17

128 Determination of Circuit Model Parameters Locked-Rotor Test For a given test voltage and frequency, the power meter gives: P 3 V I cos in T L the locked-rotor power factor is PF cos P in 3 VI 3 T L The magnitude of the impedance is Z V V T locked rotor I 1 3I L EEL 311 ( 008, H. Zmuda) 6. Induction Motors 18

129 Determination of Circuit Model Parameters Locked-Rotor Test Thus (recall Slide 3): Z Z R jx locked rotor RL RL RL Z RL cos j Z RL sin R R R R R R RL 1 RL 1 X X X (At the test frequency) RL 1 EEL 311 ( 008, H. Zmuda) 6. Induction Motors 19

130 Determination of Circuit Model Parameters Locked-Rotor Test Thus (recall Slide 3): X X X L L L RL 1 testt RL test t 1 X L L L X X RL rated RL rated 1 1 X L L, X L L X RL rated 1 rated rated RL RL test L1 L test ftest RL f rated f test X X 1 EEL 311 ( 008, H. Zmuda) 6. Induction Motors 130 X f X RL

131 Determination of Circuit Model Parameters Locked-Rotor Test Unfortunately there is no way to isolate X 1 and X. In practice, the following rule is generally observed: Rotor Type X 1 and X vs. X LR X 1 X Class A 0.5 X LR 0.5 X LR Class B 0.4 X LR 0.6 X LR Class C 03X 0.3 X LR 07X 0.7 X LR Class D 0.5 X LR 0.5 X LR EEL 311 ( 008, H. Zmuda) 6. Induction Motors 131

132 Induction Motor Examples See Slide Set 6a EEL 311 ( 008, H. Zmuda) 6. Induction Motors 13