Chapter 6. Induction Motors. Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Transcription

1 Chapter 6 Induction Motors 1

2 The Development of Induced Torque in an Induction Motor Figure 6-6 The development of induced torque in an induction motor. (a) The rotating stator field B S induces a voltage in the rotor bars; (b) the rotor voltage produces a rotor current flow, which lags behind the voltage due to rotor inductance; (c) the rotor current produces a magnetic field B R lagging rotor current by 90 o. Interaction between B R and B S produces a torque in the machine. 2

3 The Concept of Rotor Slip Slip speed is defined as the difference between synchronous speed and rotor speed: n n n slip sync m Where n n slip sync n m slip speed of the machine speed of the magnetic field rotor mechanical speed slip n n n s n n sync syn c slip sync m 3

4 The Equivalent Circuit of an Induction Motor Figure 6-7 Stator Circuit Model Rotor Circuit Model Figure 6-9 Rotor Circuit Model Figure 6-10 Rotor Circuit Model 4

5 The Equivalent Circuit of an Induction Motor R 1 = Stator resistance/phase X 1 = Stator leakage reactance/phase R 2 = Rotor resistance referred to stator/phase X 2 = Rotor leakage reactance referred to stator/phase Figure 6-12 The per-phase equivalent circuit of an induction motor. 5

6 Unlike a transformer, in an induction motor, due to the presence of an air gap, the magnetizing current is significant and its effect may not be ignored. However, the core-loss resistance may be removed from the equivalent circuit and its effect accounted for by including core losses in our calculations. Figure 6-8 The magnetization curve of an induction motor compared to that of a transformer. 6

7 Power Flow and Losses of an Induction Motor Figure 6-13 The power-flow diagram of an induction motor 7

8 Power and Torque in an Induction Motor The input impedance of the motor is given by Z = R + jx + (jx ) R + jx Zeq = (R1+jX1)+(Rc) (jxm) (R2/s+jX2) 1 1 m 2 2 I Z Pin P = 33VϕI1 V I Cos cos(1) in f 1 1 P = P - P - P P V eq AG in SCL core I = 3 I R 2 SCL 2 1 The only element in the equivalent circuit where the air-gap power can be consumed is in the resistor R2/s, therefore, P AG 3I 2 1 R 2 2 s 8

9 The power converted from electrical to mechanical form, P conv, is given by P P P conv AG RCL RCL conv 2 3I 2 R 2 The output power can be found as P P (1 s) P AG P P P P out conv F& W misc The induced torque is given by the equation ind ind P (1 s) P P (1 s) 3 conv AG AG m sync sync R s 2 2 I2 sync 9

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16 Induced Torque in an Induction Motor The induced torque in an induction motor was to be ind P P 3 R conv AG 2 2 I2 s m sync sync To find rotor current I 2, the stator circuit is replaced with its Thevenin equivalent circuit. Figure 6-17 Per-phase equivalent circuit of an induction motor. 16

17 Figure 6-18 (a) The Thevenin equivalent voltage of the stator circuit. (b) The Thevenin impedance. (c) The resulting simplified equivalent circuit of an induction motor 17

18 V TH 1 1 M M 1 1 Z = R + jx = TH TH TH R 1 + j(x 1 + X M ) I 2 I = 2 = V jxm R + j(x + X ) V TH = R TH + R 2 /s+ j(x TH + X 2 ) V TH jx (R + jx ) R + R /s + X + X 2 2 TH 2 TH 2 P 3V R /s 2 AG TH 2 = = ind 2 2 R + R /s + X + X sync sync TH 2 TH 2 18

19 Figure 6-19 A typical induction motor torque-speed characteristic curve 19

20 Maximum (Pullout) Torque in an Induction Motor 2 AG TH 2 = = ind 2 2 d ds max max ind s = = P 3V R /s R + R /s + X + X sync sync TH 2 TH 2 =0 R R + X 2 + X 2 TH TH 2 3V 2 2 TH 2w R + R + X + X 2sync 2 sync TH TH TH 2 2 Slip at maximum torque can be varied by changing rotor resistance while the corresponding maximum torque is independent of R 2 20

21 Figure 6-22 The effect of varying rotor resistance on the torque-speed characteristic of a wound-rotor induction motor. 21

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28 Induction Motor Testing The No-Load Test: to obtain the rotational losses and information leading to magnetizing reactance. Motor operated at rated voltage and no load. Figure 6-53 The no-load test of an induction motor. (a) test circuit. (b) the resulting equivalent circuit. Note that at no load the motor s impedance is essentially R 1 + j (X 1 +X M ). 28

29 The rotational losses of the motor are P = P + P + P + P = P + P in SCL core F&W misc SCL rot P = 3 I R 2 SCL 1,nl 1 P = P - 3 I R 2 rot in 1,nl 1 V Z = X + X eq 1 M I1,nl o The stator resistance will be obtained from the dc test. o X 1 will be obtained from the locked-rotor test. 29

30 The DC Test: to obtain stator resistance, R 1. An adjusted dc voltage is applied between two terminals of the stator circuit such that rated armature current flows. V DC R= 1 2I DC Figure 6-54 The circuit for a dc resistance test. 30

31 The Locked-Rotor (or Blocked-Rotor) Test: to obtain R 2, X 1 +X 2, and X M (using the no-load test results). Figure 6-55 The locked-rotor test for an induction motor: (a) test circuit; (b) motor equivalent circuit 31

32 The locked-rotor reactance at test frequency, X LR, is obtained from V VT Z = = LR I 3I 1 L P in Cos = LR 3 V T I L ' Z = R + jx Z LR LR LR LR LR The locked-rotor reactance at rated frequency, X LR, is f X = X = X + X f rated ' LR LR 1 2 test X 1 and X 2 are found from rule of thumb based on rotor design. R = R + R R LR

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