chapter 6 induction motors - uidaho.eduinduced torque in an induction motor • the induced torque...

1

Chapter 6

Induction Motors

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

The Development of Induced Torque in an Induction

Motor

2

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

magnetic field BR lagging rotor current by 90o. Interaction between BR and BS produces a

torque in the machine.


The Concept of Rotor Slip

3

• Slip speed is defined as the difference between

synchronous speed and rotor speed:

slip speed of the machine

speed of the magnetic field

rotor mechanical speed

slip

slip sync m

slip

sync

m

slip sync m

sync syn

n n n

Where n

n

n

n n ns

n nc


The Equivalent Circuit of an Induction Motor

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

Figure 6-7

Figure 6-9 Rotor Circuit Model Figure 6-10 Rotor Circuit Model

Stator Circuit Model Rotor Circuit Model

The Equivalent Circuit of an Induction Motor

5

R1 = Stator resistance/phase

X1 = Stator leakage reactance/phase

R2= Rotor resistance referred to stator/phase

X2 = Rotor leakage reactance referred to stator/phase

Figure 6-12

The per-phase equivalent circuit of an induction motor. Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

• 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.


Figure 6-13

The power-flow diagram of an induction motor

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Power Flow and Losses of an Induction Motor


Power and Torque in an Induction Motor

• The input impedance of the motor is given by

The only element in the equivalent circuit where the air-gap

power can be consumed is in the resistor R2/s, therefore,

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1 1 1

3

eq 1 1 m 2 2

in f 1 1

AG in SCL core

2

SCL 2 1

Z = R + jX + (jX ) R + jX

IZ

P V I Cos

P = P - P - P

P = 3 I R

eq

VI

2 2

23

AG

RP I

s


Zeq = (R1+jX1)+(Rc)||(jXm)||(R2/s+jX2)

Pin = 3VϕI1 cos(1)

1

• The power converted from electrical to mechanical form,

Pconv, is given by

• The output power can be found as

• The induced torque is given by the equation

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2

2 23

(1 )

conv AG RCL

RCL

conv AG

P P P

P I R

P s P

&

out conv F W miscP P P P

2 2

2

(1 )

(1 )

3

conv AG AG

ind

m sync sync

ind

sync

P s P P

s

RI

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

10


Induced Torque in an Induction Motor

• The induced torque in an induction motor was to be

• 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.

16

conv AG

ind

m sync sync

P P RI

s

2 2

2

3


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


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M

TH

1 1 M

M 1 1

TH TH TH

1 1 M

TH

2

TH 2 TH 2

TH

2 2 2

TH 2 TH 2

2

AG TH 2

ind 2 2

sync sync TH 2 TH 2

jX=

R + j(X + X )

jX (R + jX )Z = R + jX =

R + j(X + X )

=R + R /s+ j(X + X )

VI =

R + R /s + X + X

P 3V R /s= =

R + R /s + X + X

V V

VI


Figure 6-19

A typical induction motor torque-speed characteristic curve


Maximum (Pullout) Torque in an Induction Motor

20

2

AG TH 2

ind 2 2

sync sync TH 2 TH 2

ind

2

max 22

TH TH 2

2

TH

max22

sync TH TH TH 2

P 3V R /s= =

R + R /s + X + X

d= 0

ds

Rs =

R + X + X

3V=

2w R + R + X + X

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

while the corresponding maximum torque is independent of R2


2sync

Figure 6-22

The effect of varying rotor resistance on the torque-speed characteristic of a wound-rotor

induction motor.


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= 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.

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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).


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eq 1 M

1,nl

VZ = X + X

I

in SCL core F&W misc SCL rot

2

SCL 1,nl 1

2

rot in 1,nl 1

P = P + P + P + P = P + P

P = 3I R

P = P - 3 I R

• The rotational losses of the motor are

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

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


Figure 6-54

The circuit for a dc resistance test.

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• 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.

DC

1

DC

VR =

2I


Figure 6-55

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

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• The Locked-Rotor (or Blocked-Rotor) Test: to obtain R2,

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


• The locked-rotor reactance at test frequency, X’LR, is

obtained from

32

T

LR

1 L

in

LR

T L

'

LR LR LR LR

V VZ = =

I 3 I

PCos =

3V I

Z = R + jX ZLR

'rated

LR LR 1 2

test

fX = X = X + X

f

LR 1 2 2R = R + R R

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

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


chapter 6 induction motors - uidaho.eduinduced torque in an induction motor • the induced torque...

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