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Induction Motors
Induction Motors
Chapter Six
A. Basic Principles
1. The stator of an induction motor contains the field.
It contains 3 phases, P poles, a sinusoidal mmf and
flux distribution which rotate at a speed
120
=
2. The rotor contains the armature windings. The rotor
may be one of two types 1. wound rotor 2. caged rotor.
The caged rotor has windings consisting of conducting
bars embedded in slots in the rotor iron and shortcircuited at each end by conducting rings.
The Development of Induced Torque in an Induction Motor
= ( x )
= ()
= () ∙ 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.Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
= !"(# )
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Induction Motors
Induction Motors
B. Three Phase Induction Motor Characteristics
1. Suppose we now apply 3 phase currents to the
stator field. The stator flux will now rotate at
$%&'
synchronous speed ( = )
(
2. Suppose further, that the rotor () ) is turning
slower than synchronous speed, such that it is
slipping backward at *( = + − )
3. Define slip (s) as relative motion on a percentage
basis,
"=
-./0 12
-./0
B. Three Phase Induction Motor Characteristics
4. Notice that
) = (1 − ")+
3) = (1 − ")3+ 5. With the rotor now turning at high speed, the
electrical voltages and currents in the rotor are still
generated by the relative motion between the rotor
conductors and the stator flux. The rotor currents and
voltages have an electrical frequency of
45 = − )
= "
%6
7&
= "3 where
"3 is the frequency of the currents in the stator.
5 = "
{Hz}
x 100%
Induction Motors
Induction Motors
B. Three Phase Induction Motor Characteristics
Even though the rotor is not turning at synchronous
speed, the rotor flux is still locked to the stator flux,
hence the rotor flux does rotate at synchronous speed.
To see this note that the speed of the rotor field is the
sum of the (rotor speed) + (speed of the rotor field
w.r.t. the rotor).
) + " = 1 − " + " = rotor speed slip speed of rotor
%6
7&
sync. speed
C. Ex 6.1 .. A 208V, 10 Hp, 4 pole, 60 Hz, Y connected
induction motor has a full load slip of 5 percent.
a) What is the synchronous speed of the motor?
=
$%&'9
:
=
$%&∙7&
;
= 1800=>?
b) What is the rotor speed at full load?
) = 1 − " = 0.95 1800 = 1710=>?
c) What is the rotor frequency at full load?
5 = "
= 0.05 60 = 3FG
d) What is the shaft torque at full load?
4LMMN )
HIJ 10F> ∙ (746
F>
=
=
= 41.7P?
2O
3)
1710 =N? ∙ ( )
60
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Induction Motors
D. Equivalent Circuit of an Induction Motor
Per phase equivalent Y
Induction Motors
E.
Equivalent Circuit of an Induction Motor
The rotor circuit
The magnitude and frequency of the induced rotor
voltage is directly proportional to the slip.
Q = " ∙ Q& where Q& is the max. voltage for s =1.
Q$ = =?L=RMLM!=S!MLTT=LMU
V
Q = UVWU"W!UL=R=!M!=!MLT
L'' = WMMV="=LM!
Induction Motors
E. Equivalent Circuit of an Induction Motor
For a rotor inductance X , the reactance is given by
Y = 2O
5 X = 2O"
X = " 2O
X = "Y&
whereY& is the reactance at s =1.
Z[
[ \]^[
= Q
_ + `"Y&
Q&
=
_
+ `Y&
"
=
Induction Motors
E. Equivalent Circuit of an Induction Motor
It is now possible to treat all effects of varying rotor speed
by using a varying rotor impedance
a,c =
+ `Y&
In this view, the rotor
voltage is a constant ERO ,
and the rotor current vs.
speed is shown.
ERO is at same frequency
as the of stator .
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Induction Motors
E. Equivalent Circuit of an Induction Motor
The Final Eqv. circuit: If the effective turns ratio of the
induction motor is ‘L'' ′.
So,
Q$ = Q = L'' Q&
And the rotor current becomes
% =
L''
The Transformer Model 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
s = slip
And the rotor impedances as “seen” from the stator
become
a% = L% '' (
Let
_% = L% '' _
[
+ `Ye )
and Y% = L% '' Ye
The per-phase equivalent circuit of an induction motor ‘seen’ from the stator.
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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
F. Power Flow and Losses of an Induction Motor
Power and Torque in an Induction Motor
• The input impedance of the motor is given by
_%
ac = _$ + `Y$ + (_f | `Yh ||( + `Y% )
"
S∅
$ =
= $ < # $
ac
= 3S∅ $ cos # $
nfo = 3$ % _$
The power-flow diagram of an induction motor
H5 = 3Q$ % /_
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• The power at the air gap is
Prs = Ptu − Pvwx − Pyz{| = 3%
% _%
"
• The induced torque is given by the equation
τind =
• The power converted from electrical to mechanical form,
Pconv, is given by
Pco n v = P A G − PR C L
2
2
PR C L = 3 I R 2
Pco n v = (1 − s ) P A G
τind =
Pconv
ωm
=
(1− s)PAG PAG
=
(1− s)ωsync ωsync
R 
I22  2 
ωsync  s 
3
• The output power can be found as
Pout = Pconv − PF &W − Pmisc
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Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
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