Induction Motor Introduction
and Equivalent Circuit
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Induction Machine - Introduction
A machine with only armortisseur windings is called an
induction machine.
 No DC field current is required to run the machine. Rotor
voltage is induced in the rotor windings rather than being
physically connected by wires.
 Induction machine has the same physical stator as a
synchronous machine with a different rotor construction.
Induction machines can be operated as either motors and
generator. However, they are primarily used as induction motors.
Induction machines are by far the most common type of motor
used in industrial, commercial or residential settings.
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IM Stator
Stator for a 2hp induction machine
http://www.ece.ualberta.ca/~knight/ee332/induction/basics/construction.html
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IM Rotor
Two types of rotors for induction machine:
Cage Rotor
Wound Rotor
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Cage Rotor
A cage (or squirrel-cage) rotor consists of a series of conducting bars
laid into slots carved in the face of the rotor and shorted at either end
by large shorting rings.
skewed
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Wound Rotor (1)
A wound rotor has a complete set of three phase windings usually Y-connected.
The ends of three rotor wires are tied up to slip rings on the rotor’s shaft, where
extra resistance can be inserted into rotor circuits for control.
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Wound Rotor (2)
skewed
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IM Basic Concepts
fe : electrical frequency on stator
fe
f sync 
synchronous speed in revolution/second
P/2
f sync 120 fe
nsync 

synchronous speed in rpm
P
60
nm : mechanical speed or speed of the rotor
BS : stator's magnetic field, rotates at synchronous speed
B R : rotor's induced magnetic field, rotates at synchronous
speed, follows BS at steady state
But the rotor will not follow BS.
Concept of Rotor Slip
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f syn 
n sync
 n sync
fe
60
P/2
120 f e

P

 n m  (1  s ) n sync
s
f sync  f m
f sync
  m  (1  s ) sync
 100 %
f m  (1  s ) f sync
Rotor Electrical Frequency
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f r : rotor electrical frequency
f slip
fr

: speed (rev/s) of B R relative to the rotor
P/2
Since BR follows BS, we have:
f sync  f m  f slip
f slip
 f slip  f sync  f m  sf sync
P
P
 f r  f slip  sf sync  sfe
2
2
nslip
nslip P
P

 f r  f slip 
60
2 120
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Example 1
details in im1.m
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Equivalent Circuit of Induction Motor (1)
stator copper loss
leakage
From Bnet
IR
E 1  4 . 44 f e N eff  m
E R  4.44 f r N effR  m
 4.44 sf e N effR  m  sE R 0
E R 0  4.44 f e N effR  m
 n eff
N eff
E1


ER0
N effR
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Equivalent Circuit of Induction Motor (2)
X R   r L R  2  f r L R  2  sf e L R  sX
R0
X R 0  2 f e L R
ER
IR 
R R  jX
R
ER

R R  jsX
R0
E R0

R R / s  jX
R0
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Equivalent Circuit of Induction Motor (3)
n eff : 1
per phase equivalent circuit
2
R 2  n eff
RR
2
X 2  n eff
X R0
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Thevinin Equivalent Circuit
Thevinin equivalent circuit
Z M  R c // jX
M

jR c X M
R c  jX M
Z TH  Z M //( R1  jX 1 )
ZTH  RTH  jXTH
V TH
Z M ( R1  jX 1 )

Z M  R1  jX 1
ZM
V

Z M  R1  jX 1
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Induction Motor Power Flow
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Example 2
details in im2.m
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Power and Torque (1)
2
R 2  n eff
RR
I R  n eff I 2
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Power and Torque (2)
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Power and Torque (3)
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Per Phase Equivalent Circuit with Rotor Loss and
Converted Power Separated
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Example 3
details in im3.m