Chapter 6 Induction Motors

Chapter 6

Induction Motors

Figure 6-6

The development of induced torque in an induction motor. (a) The rotating stator field BS 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 o magnetic field BR lagging rotor current by 90 . Interaction between BR and BS produces a torque in the machine.

The Concept of Rotor Slip

• Slip speed is defined as the difference between synchronous speed and rotor speed:

nslip n sync n m

Where nslip  slip speed of the machine

nsync  speed of the magnetic field

nm  rotor mechanical speed

n n n slip s slip  sync m nnsync sync

Figure 6-7 Stator Circuit Model Rotor Circuit Model

The Equivalent Circuit of an Induction Motor

R1 = Stator resistance/phase

X1 = Stator leakage reactance/phase

R2= Rotor resistance referred to stator/phase

X2 = Rotor leakage reactance referred to stator/phase

• 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.

Power Flow and Losses of an Induction Motor

Figure 6-13 The power-flow diagram of an induction motor

ZZeqeq = = ( R+jXR 11+jX 1)+( +(jXRc)||( m )jX R+jXm 2)||(R 2 /s+jX2)

V I1I 1 1 Z eq Pin =3 3V V Iϕ CosI1 cos( 1) in f 1 1  P = P - P - P AG in SCL core 2 PSCL = 3 I 21 R 1 The only element in the equivalent circuit where the air-gap power can be consumed is in the resistor R2/s, therefore, R PI 3 2 2 AG 2 s

Pconv, is given by

PPPconv AG RCL 2 PIR 3 RCL 22 P(1 s ) P conv AG • The output power can be found as

PPPPout conv  F& W  misc

• The induced torque is given by the equation P(1 s ) P P  conv  AG  AG ind m(1 s )  sync  sync

Induced Torque in an Induction Motor • The induced torque in an induction motor was to be

PPconv AG 3 2 R2  ind    I2     s m sync sync

• To find rotor current I2, the stator circuit is replaced with its Thevenin equivalent circuit.

Figure 6-17 Per-phase equivalent circuit of an induction motor.

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 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 17

jX VV= M TH  R1 + j(X 1 + X M )

jXM (R 1 + jX 1 ) ZTH = R TH + jX TH = R1 + j(X 1 + X M )

VTH I2 = RTH + R 2 /s+ j(X TH + X 2 ) V I= TH 2 22 RTH + R 2 /s + X TH + X 2  P 3V2 R /s  ==AG TH 2 ind 2 2 sync sync RTH + R 2 /s + X TH + X 2 

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

Maximum (Pullout) Torque in an Induction Motor

P 3V2 R /s  ==AG TH 2 ind 2 2 sync sync RTH + R 2 /s + X TH + X 2  d ind =0 ds

R2 s=max 2 2 RTH + X TH + X 2 

2 3VTH  max = 2 2 22wsync R + R + X + X  sync TH TH TH 2

• Slip at maximum torque can be varied by changing rotor resistance

while the corresponding maximum torque is independent of R2

Figure 6-22 The effect of varying rotor resistance on the torque-speed characteristic of a wound-rotor induction motor. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 21

= 229 N ∙ m

(b) Tstart

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 R1+ j (X1+XM).

• The rotational losses of the motor are

P=P +P +P +P =P +P in SCL core F&W misc SCL rot 2 PSCL = 3I 1,nl R 1 P = P - 3I2 R rot in 1,nl 1

V Zeq = X 1 + X M I1,nl

o The stator resistance will be obtained from the dc test.

o X1 will be obtained from the locked-rotor test.

• The DC Test: to obtain stator resistance, R1. An adjusted dc voltage is applied between two terminals of the stator circuit such that rated armature current flows.

VDC R=1 2IDC

Figure 6-54 The circuit for a dc resistance test.

X1+X2, and XM (using the no-load test results).

Figure 6-55 The locked-rotor test for an induction motor: (a) test circuit; (b) motor equivalent circuit

• The locked-rotor reactance at test frequency, X’LR, is obtained from V  VT ZLR = = I1 3IL

Pin CosLR = 3 VTL I ' ZLRLRLRLR = R + jX Z LR

• The locked-rotor reactance at rated frequency, XLR, is

frated ' XLR = X LR = X 1 + X 2 ftest

• X1 and X2 are found from rule of thumb based on rotor design.

RLR = R 1 + R 2 R 2