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PowerPoint Slides
to accompany
Electric Machinery
Sixth Edition
A.E. Fitzgerald
Charles Kingsley, Jr.
Stephen D. Umans
Chapter 6
Polyphase Induction
Machines
6-0
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6.1 INTRODUCTION TO POLYPHASE INDUCTION MACHINES
Two types of motor:
Squirrel-Cage
6-1
Wound Rotor
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6.1 INTRODUCTION TO POLYPHASE INDUCTION MACHINES
How does an induction motor work?
1. Apply AC three-phase current to stator winding to produce rotating
magnetic field.
2.
Rotating magnetic field induces voltages in rotor windings resulting
with rotor currents.
3.
Then, rotor currents will create rotor magnetic field.
4.
Constant speed stator magnetic field will drag rotor magnetic field.
ns: Synchronous speed (the speed
of stator rotating field in rpm).
120
ns 
fs
p
ns
n
6-2
n : Rotor speed (rpm).
SLIP: It is defined as the difference
between synchronous speed and the
rotor speed divided by synchronous
speed.
ns  n
s
ns
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6.1 INTRODUCTION TO POLYPHASE INDUCTION MACHINES
The speed of rotor magnetic field with respect to rotor is
nr  ns  n  s ns
The relative motion of stator flux and the rotor conductors induces
voltages of frequency (fr is called slip frequency)
f r  s fe
The rotor speed
n  (1  s) ns
Mechanical angular velocity
6-3
m  (1  s) s
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6.1 INTRODUCTION TO POLYPHASE INDUCTION MACHINES
Breakdown torque
6-4
Typical induction-motor torque-speed curve for constant-voltage,
constant-frequency operation.
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6.2 CURRENTS AND FLUXES IN POLYPHASE INDUCTION
MACHINE
Developed rotor winding of an induction motor with its flux-density and mmf
waves in their relative positions for (a) zero and (b) nonzero rotor leakage
reactance.
6-5
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6.2 CURRENTS AND FLUXES IN POLYPHASE INDUCTION
MACHINE
Reactions of a
squirrel-cage rotor
in a two-pole field.
Figure 6.6
6-6
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6.3 INDUCTION MOTOR EQUIVALENT CIRCUIT
Stator equivalent circuit for a polyphase induction motor.
Counter emf generated by the resultant air-gap flux
6-7
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6.3 INDUCTION MOTOR EQUIVALENT CIRCUIT
Rotor equivalent circuit for a polyphase induction motor at slip
frequency.
Iˆ2s  Iˆ2
Eˆ 2s  s Eˆ 2
Eˆ 2 R2
Z2 

 j X2
s
Iˆ2
6-8
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6.3 INDUCTION MOTOR EQUIVALENT CIRCUIT
Single-phase equivalent circuit for a polyphase induction motor.
Models the combined
effect of rotor resistance
and shaft load
6-9
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6.3 INDUCTION MOTOR EQUIVALENT CIRCUIT
Alternative form of equivalent circuit.
Electromechanical power is
equal to the power delivered
to this resistance
6-10
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6.4 ANALYSIS OF THE EQUIVALENT CIRCUIT
Pgap 
2
n ph I 2 
R2 

 s 
Pmech  Pgap  Protor 
Protor  s Pgap
Protor  n ph I 22 R2
1 s 
2
n ph I 2 R2 

 s 
Pmech  (1  s) Pgap
Pmech  mTmech
Pmech is not the net power but it includes the losses such as friction, windage.
Output power and torque from the shaft is
Pshaft  Pmech  Prot
6-11
Tshaft 
Pshaft
m
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6.5 TORQUE AND POWER BY USE OF THEVENIN’S THEOREM
(a) General linear network and (b) its equivalent at terminals ab by
Thevenin’s theorem.
6-12
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6.5 TORQUE AND POWER BY USE OF THEVENIN’S THEOREM
Equivalent circuits with the core-loss resistance Rc neglected.


j Xm
ˆ
ˆ

V1,eq  V1 
 R1  j ( X 1  X m ) 
6-13
Z1,eq
j X m ( R1  j X 1 )

R1  j ( X 1  X m )
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6.5 TORQUE AND POWER BY USE OF THEVENIN’S THEOREM
Induction-motor equivalent circuits simplified by Thevenin’s theorem.
Iˆ2 
Tmech
6-14
Vˆ1,eq
Z1,eq  j X 2  R2 s
2


n
V
1
ph 1,eq ( R2 s )


2
2
s  ( R1,eq  ( R2 s))  ( X 1,eq  X 2 ) 
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Induction-machine torque-slip curve showing braking,
motor, and generator regions.
Figure 6.14
6-15
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The End of This Chapter
6-16
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Computed torque, power, and current curves
for the 7.5-kW motor in Examples 6.2 and 6.3.
Figure 6.15
6-17
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Inductionmotor torqueslip curves
showing
effect
of changing
rotor-circuit
resistance.
Figure 6.16
6-18
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Electromechanical torque vs. speed for the wound-rotor
induction motor of Example 6.4 for various values of the
rotor resistance R2.
Figure 6.17
6-19
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Deep rotor bar and
slot-leakage flux.
Figure 6.18
6-20
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Skin effect in a copper rotor bar 2.5 cm deep.
Figure 6.19
6-21
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Double-squirrelcage rotor bars
and slot-leakage
flux.
Figure 6.20
6-22
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Typical torquespeed curves for
1800-r/min
general-purpose
induction motors.
Figure 6.21
6-23
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Connections of a one-step starting autotransformer.
Figure 6.22
6-24
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Interconnected
induction and
synchronous
machines
(Problems 6.7
and 6.8).
Figure 6.23
6-25
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Induction-motor equivalent
circuits simplified by
Thevenin’s theorem.
Figure 6.13
6-26