Induction Motor Fundamentals
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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
f e : electrical frequency on stator
120 f e
nsync 
synchronous speed in rpm
P
nm : mechanical speed or speed of the rotor
B S : stator's magnetic field, rotates at synchronous speed
B R : rotor's induced magnetic field, rotates at synchronous
speed, follows B S at steady state
But rotor will not follow BS.
Concept of Rotor Slip
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nsync
fe
60
P/2
120 f e
 nsync 
P
f syn 

 nm  (1  s)nsync
s
f sync  f m
f sync
 m  (1  s )sync
100%
f m  (1  s ) f sync
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Rotor Electrical Frequency
f r : rotor electrical frequency
fr
: speed of B R relative to the rotor
P/2
Since BR follows BS, we have:
fr
f sync  f m 
P/2
P
P
 f r  ( f sync  f m )  sf sync  sfe
2
2
P
fr 
(nsync  nm )
120
Induction Motor Equivalent
Circuit
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Equivalent Circuit of Induction Motor (1)
stator copper loss
leakage
From Bnet
IR
E1  4.44 f e N eff  m
E R  4.44 f r N effR  m
 4.44 sf e N effR  m  sER 0
E R 0  4.44 f e N effR  m
 neff
N eff
E1


ER 0
N effR
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Equivalent Circuit of Induction Motor (2)
X R  r LR  2f r LR  2sfe LR  sX R 0
X R 0  2f e LR
ER0
ER
ER
IR 


RR  jX R
RR  jsX R 0
RR / s  jX R 0
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Equivalent Circuit of Induction Motor (3)
neff : 1
per phase equivalent circuit
2
R2  neff
RR
2
X 2  neff
X R0
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Thevinin Equivalent Circuit
Thevinin equivalent circuit
Z M  Rc // jX M 
jRc X M
Rc  jX M
Z TH  Z M //( R1  jX 1 )
ZTH  RTH  jX TH
VTH
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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Power and Torque (1)
2
R2  neff
RR
I R  neff 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
Induction Motor Torque Speed
Characteristics
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Induced Torque from Physical Standpoint (1)
Tind  kB R  B net
Tind  kBR Bnet sin 
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Induced Torque from Physical Standpoint (2)
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Induced Torque from Physical Standpoint (3)
sin 
Tind  kBR Bnet sin 
(a)  (b)  (c)  (d )
s
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Thevinin Equivalent Circuit
Thevinin equivalent circuit
Z M  Rc // jX M 
jRc X M
Rc  jX M
Z TH  Z M //( R1  jX 1 )
ZTH  RTH  jX TH
VTH
Z M ( R1  jX 1 )

Z M  R1  jX 1
ZM

V
Z M  R1  jX 1
Induced Torque Equation
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Tind 
PAG
sync
Tind 
Tind
sync[( RTH
2
3VTH
R2 / s
 R2 / s) 2  ( X TH  X 2 ) 2 ]
2
3VTH
R2 s

sync[( RTH s  R2 ) 2  ( X TH  X 2 ) 2 s 2 ]
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Torque Speed Characteristic (1)
s
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Torque Speed Characteristic (2)
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Converted Power vs Speed Characteristic
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Effect of R2
Maximum (Pullout)Torque
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Tind 
sync[( RTH
2
3VTH
R2 / s
 R2 / s) 2  ( X TH  X 2 ) 2 ]
Tind
R2
2
0
 RTH
 ( X TH  X 2 ) 2
( R2 / s)
s
smax 
Tmax 
R2
2
RTH
 ( X TH  X 2 ) 2
2
3VTH
2
2sync[ RTH  RTH
 ( X TH  X 2 ) 2 ]
has no relationship with R2 and s
Appendix - Examples
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Example 1
details in im1.m
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Example 2
details in im2.m
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Example 3
details in im3.m
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Example 4
Neglect mechanical losses.
low slip region is pretty linear
Tind2
Tind1
nm2 nm1 nsync
Tind 2 nsync  nm 2 s2


Tind1 nsync  nm1 s1
details in im4.m
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Example 5
Rc  
details in im5.m