chapter 6 induction motors - uidaho.eduinduced torque in an induction motor • the induced torque...
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1
Chapter 6
Induction Motors
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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.
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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
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The Equivalent Circuit of an Induction Motor
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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.
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Figure 6-13
The power-flow diagram of an induction motor
7
Power Flow and Losses of an Induction Motor
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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,
8
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
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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
9
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
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10
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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
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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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18
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
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Figure 6-19
A typical induction motor torque-speed characteristic curve
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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
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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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24
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= 229 N ∙ m
(b) Tstart
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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.
28
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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29
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.
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Figure 6-54
The circuit for a dc resistance test.
30
• 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
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Figure 6-55
The locked-rotor test for an induction motor: (a) test circuit; (b) motor equivalent circuit
31
• The Locked-Rotor (or Blocked-Rotor) Test: to obtain R2,
X1+X2, and XM (using the no-load test results).
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• 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.
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