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ENERGY CONVERSION ONE
(Course 25741)
CHAPTER SEVEN
INDUCTION MOTORS
SUMMARY
1. Induction Motor Construction
2. Basic Induction Motor Concepts
The Development of Induced Torque in an Induction Motor
The Concept of Rotor Slip
The Electrical Frequency on the Rotor
3. The Equivalent Circuit of an Induction Motor
The Transformer Model of an induction Motor
The Rotor Circuit Model
The Final Equivalent Circuit
4. Powers and Torque in Induction Motor
Losses and Power-Flow diagram
Power and Torque in an Induction Motor
Separating the Rotor Copper Losses and the Power Converted in an
Induction Motor’s Equivalent Circuit
5. Induction Motor Torque-Speed Characteristics
Induced Torque from a Physical Standpoint
The Derivation of the Induction Motor Induced-Torque Equation
Comments on the Induction Motor Torque Speed Curve
Maximum (Pullout) Torque in an Induction Motor
6. Variations in Induction Motor Toque-Speed Characteristics
Control of Motor Characteristics by Cage Rotor Design
SUMMARY
7. Starting Induction Motors
8. Speed Control of Induction Motor
Induction Motor Speed Control by Pole Changing.
Speed Control by Changing the Line Frequency.
Speed Control by Changing the Line Voltage.
Speed Control by Changing the Rotor Resistance.
9. Determining Circuit Model Parameters
The No-Load Test
The DC Test
The Locked-Rotor Test
10. Determining Circuit model parameters
No-load test/ DC test for stator resistance
Locked-Rotor test
11. Induction Generator
induction generator operating alone/ induction
Generator application
Induction motor ratings
INDUCTION MOTORS
INTRODUCTION
• It was shown how amortisseur windings on a
synchronous motor could develop a starting
torque without necessity of supplying an
external field current to them
• Amortisseur windings work so well that a motor
could be built without syn. motor’s main dc field
circuit
• A machine with only amortisseur winding is
called induction machine, because the rotor
voltage is induced in rotor windings rather than
being physically connected by wires
INDUCTION MOTORS
INTRODUCTION
• Cutaway diagram of typical large cage rotor
induction motor
INDUCTION MOTORS
INTRODUCTION
• Sketch of Cage Rotor
INDUCTION MOTORS
INTRODUCTION
• Typical wound rotors for induction motors, slip
rings & bars connecting rotor windings to slip
rings can be seen
INDUCTION MOTORS
INTRODUCTION
• Cutaway of a wound-rotor induction motor
• Note: brushes and slip rings are shown, also
rotor windings skewed to eliminate slot
harmonics
INDUCTION MOTORS
INTRODUCTION
• Distinguishing feature: no dc field current
required to run machine
• Although it is possible to use an induction
machine as either motor or generator, it has
many disadvantages as a generator & so is
rarely used as Gen.
• INDUCTION MOTOR CONSTRUCTION
• Same physical stator as syn. machine with
different rotor construction
• There are “cage rotor” & “wound rotor”
INDUCTION MOTORS
CONSTRUCTION
• A cage induction rotor consists of a series of conducting bars
laid into slots carved in face of rotor & shorted at either end by
large shorting rings
• This design is referred to as a cage rotor because of
conductors arrangement on rotor
• A wound rotor has a complete set of 3 phase windings that are
mirror images of windings on stator
• The 3 phase of rotor windings are usually Y-connected and end
of 3 rotor wires tied to slip rings on rotor shaft
• The rotor currents accessible at stator brushes, where they can
be examined & where extra resistance can be inserted into
rotor circuit
• This can be used to modify torque-speed characteristic of motor
• Wound rotor motors more expensive, & require more
maintenance due to wear associated with brushes & slip rings,
therefore wound motor induction motors are rarely used
BASIC INDUCTION MOTOR
CONCEPTS
• Its operation is basically same as amortisseur
windings on syn. motors
• Development of Induced Torque
• Again a BS is developed, which is rotating counterclockwise in Figure of  next slide
• Speed of magnetic field’s rotation is : nsync=120fe/p
• voltage induced in a rotor bar:
eind=(v x B).l
v=velocity of bar relative to magnetic field
B=magnetic flux density vector
l= length of conductor in magnetic field
BASIC INDUCTION MOTOR
CONCEPTS
• Development of Induced Torque
BASIC INDUCTION MOTOR
CONCEPTS
• relative move of rotor w.r.t. BS result in an
induced voltage in rotor bar
• Velocity of upper rotor bars w.r.t. BS is to right
• Induced voltage in upper bars is out of page,
while induced voltage in the lower bars is into
page
• This results in a current flow out of upper bars &
into lower bars
• Since rotor assembly is inductive, peak rotor
current flow produces a rotor magnetic field BR
BASIC INDUCTION MOTOR
CONCEPTS
• Induced torque in machine is:
Tind =kBR x BS
• resulting torque is counterclockwise & rotor
accelerates in this direction
• There is a finite upper limit on motor’s speed
• If induction motor’s rotor were turning at syn. Speed,
then rotor bars would be stationary relative to BS &
there would be no induced voltage eind=0 no rotor
current & BR=0  Tind=0
• Rotor will slow down, due to friction losses
• An induction motor can speed up to near-syn. Speed,
however it can never reach syn. speed
BASIC INDUCTION MOTOR
CONCEPTS
• Flowchart showing induction motor operation
BASIC INDUCTION MOTOR
CONCEPTS
• Note: in normal operation, both BR & BS rotate
together at syn. Speed nsync while rotor itself turn at a
slower s peed
• Concept of Rotor Slip
• Voltage induced in rotor bar depends on relative
speed of rotor with respect to BS
• Since behavior of induction motor depends on motor
voltage & current, it is more logical to talk about this
relative speed
• Two terms commonly used to define relative motion of
rotor & BS , “slip speed” & “slip”
• “slip speed” defined as difference between syn. Speed
& rotor speed
nslip=nsync-nm
BASIC INDUCTION MOTOR
CONCEPTS
• In which:
nslip= slip speed of machine
nsync= speed of magnetic fields
nm= mechanical shaft speed of motor
• “slip” is relative speed expressed on a per-unit
or percentage basis: s=nslip/nsync (x100%)
s= [nsync-nm] / nsync (x100%)
or in terms of angular velocity:
• s= [ωsync-ωm] / ωsync (x100%)
BASIC INDUCTION MOTOR
CONCEPTS
• If rotor turn at syn. speed  s=0
• while if rotor stationary  s=1
• all normal motor speeds fall somewhere
between those 2 limits
• mechanical speed of rotor shaft can be
expressed in terms of syn. speed & slip
• nm= (1-s)nsync or ωm=(1-s)ωsync
BASIC INDUCTION MOTOR
CONCEPTS
• Electrical Frequency on Rotor
• An induction motor works by inducing voltages
in rotor of machine & because of that
sometimes called rotating transformer
• Like a transformer, primary (stator) induces a
voltage in secondary (rotor) but :
Unlike a transformer, secondary frequency is
not necessarily same as primary frequency
• If rotor of motor locked so that can not move,
rotor will have the same frequency as stator
BASIC INDUCTION MOTOR
CONCEPTS
• on the other hand, if rotor turns at syn. Speed,
frequency on rotor will be zero
• what will rotor frequency be for any arbitrary rate of
rotor rotation ?
• at nm=0 r/min, rotor frequency fr=fe Hz, and slip s=1
• at nm=nsyn fr=0 and slip is s=0
• with any speed in between, rotor frequency is directly
proportional to difference between speed of magnetic
field nsync & speed of rotor nm
S=[nsync-nm] / nsync
• rotor frequency can be expressed as :
fr=s fe
BASIC INDUCTION MOTOR
CONCEPTS
•
•
•
•
•
•
alternative forms of last expression:
fr=[nsync-nm] / nsync . fe
since : nsync=120 fe/p 
fr= (nsync-nm)p/(120fe) fe
fr= p/120 (nsync-nm)
Example: A 208 V, 10 hp, 4 pole, 60 Hz, Y
connected induction motor has a full-load slip of
5 percent
• (a) what is syn. Speed of motor?
BASIC INDUC. MOTOR CONCEPTS
….EXAMPLE:
• (b) what is rotor speed of this motor at rated
load?
• (c) what is rotor frequency of this motor at rated
load?
• (d) what is shaft torque of this motor at rated
load?
BASIC INDUCTION MOTOR
CONCEPTS
• SOLUTION:
(a) nsync=120 fe/p=120x60/4=1800 r/min
(b) nm=(1-s) nsync =(1-0.05)(1800)=1710 r/min
(c) fr=s fe = 0.95 x 60=3 Hz
or fr=p/120 (nsync-nm)=4/120 (1800-1710)=3 Hz
• (d) Tload = Pout/ωm=
[10 x 746]/[1710 x 2π x 1/60]= 41.7 N.m
shaft load torque in English units: Tload=5252 P/n
where T is in lb-feet , P in hp, and nm r/min
Tload=5252 x 10 / (1710) = 30.7 lb . ft
EQUIVALENT CIRCUIT OF AN
INDUCTION MOTOR
• Basis of an induction motor is on induction of
voltage & current in its rotor (Transformer
Action)
• equivalent circuit of an induction motor is very
similar to equivalent circuit of a transformer
• “induction motor” is called a “singly excited”
machine (opposed to “doubly excited” syn.
machine)
since power is supplied to only “stator circuit”
EQUIVALENT CIRCUIT OF AN
INDUCTION MOTOR
• Since an induction motor does not have an
independent field circuit, its model will not contain an
internal voltage source such as internal generated
voltage EA in a syn. Machine
• The equivalent circuit of induction motor can be
derived from a knowledge of “transformers” and from
what already know about “variation of rotor frequency”
with speed in induction motors
• The induction motor model developed by starting with
transformer model, and then realizing variable rotor
frequency & other induction motor effects
EQUIVALENT CIRCUIT OF AN
INDUCTION MOTOR
• Transformer Model of an Induction Motor
• Per-phase equivalent circuit of an induction
motor
TRANSFORMER MODEL of
INDUCTION MOTOR
• As shown there is certain resistance & self inductance
in primary (stator) windings which must be
represented in equivalent circuit of machine
• Stator resistance called R1 & stator leakage reactance
called X1
• These appear right at input to machine model
• Flux in machine is the integral of applied voltage E1
• Curve of magneto-motive force versus flux,
(magnetization curve) compared to similar curve for
power transformer (next slide)
TRANSFORMER MODEL of
INDUCTION MOTOR
• Magnetization curve of induction motor
TRANSFORMER MODEL of
INDUCTION MOTOR
• Note: slope of induction motor’s magneto-motive
force-flux curve is much shallower than curve of a
good transformer
• because there is an air gap in an induction motor
which greatly increase reluctance of flux path &
therefore reduces coupling between primary &
secondary windings
• Higher reluctance caused by air gap means a higher
magnetizing reactance XM in equivalent circuit will
have a much smaller value (larger susceptance BM)
than its value in an ordinary transformer
TRANSFORMER MODEL of
INDUCTION MOTOR
• Primary internal stator voltage E1 coupled to
secondary ER by an ideal transformer with an
effective turns ratio aeff
• Effective turns ratio aeff easy to determined for a
wound-rotor motor
• ratio of conductors per phase on stator to
conductors per phase on rotor, modified by any
pitch & distribution factor differences
• It is rather difficult to determine aeff clearly in
cage of a case rotor motor because there are
no distinct windings on cage rotor
TRANSFORMER MODEL of
INDUCTION MOTOR
• In either case there is an effective turns ratio for motor
• Voltage ER produced in rotor in turn produces a
current flow in shorted rotor (or secondary) circuit of
machine
• Primary impedance & magnetization current of
induction motor are very similar to corresponding
components in a transformer equivalent circuit
• Induction motor equivalent circuit differs from
transformer equivalent circuit primarily in effects of
varying rotor frequency on rotor voltage ER and
secondarily in rotor resistance RR and jXR
ROTOR CIRCUIT MODEL
• A voltage induced in rotor windings when 3
phase voltage applied to stator windings
• The greater the relative motion between rotor &
stator magnetic fields, the greater the resulting
rotor voltage & rotor frequency
• The largest relative motion occurs when rotor is
stationary, called locked-rotor or blocked-rotor
condition
• So largest voltage & rotor frequency are
induced in rotor at that condition (locked rotor)
ROTOR CIRCUIT MODEL
• Smallest voltage (0 V) and frequency (0 Hz) occur
when rotor moves at same speed as stator magnetic
field (having no relative motion)
• magnitude & frequency of induced voltage in rotor at
any speed between these extremes is proportional to
the slip of motor
• If magnitude of induced rotor voltage at locked-rotor is
ER0 magnitude at any slip :
ER=s ER0
frequency of induced voltage: fr=sfe
rotor has both resistance & reactance; RR a constant
(except for ski effect) , reactance affected in a
complicated way by slip
ROTOR CIRCUIT MODEL
• reactance of an induction motor rotor depends
on: inductance of rotor & frequency of voltage
and current in rotor
• XR=ωr LR = 2π fr LR (realizing : fr=sfr) 
XR=2πsfeLR=s XR0 (XR0:blocked-rotor reactance)
• Resulted equivalent circuit of rotor: