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Topic 4: Three-phase Induction (Asynchronous) Machines
Electromechanical Energy Conversion
Various devices can convert energy to mechanical energy and vice
versa. The structure of these
devices may be different depending on functions they perform.
Some devices are used for continuous
energy conversion and these are known as motor and generators.
Even though there various devices used
in the conversion of energy, but they all operate on similar
principles. In this topic, we extensively discuss
on electric machines only.
Electric Machines
Some applications such as light bulbs and heaters require energy
in electrical form while others, such
as fans and rolling mills, require energy in mechanical form.
One form of energy can be obtained from the
other form with the help of converters. Converter that is used
to translate electrical input to mechanical
output or vice versa are called electric machines.
The process of translation is known as electromechanical energy
conversion. In these machines, the
conversion is reversible. If the conversion is from mechanical
to electrical, the machine is said to act as a
generator. If the conversion is from electrical to mechanical,
the machine is said to act as a motor.
Same electric machine can be made to operate as a generator as
well as a motor. Machines are called
ac machines if the electrical system is ac and dc machines if
the electrical system is dc.
Figure 1. Electromechanical Energy Conversion
In electric machines, conversion of energy from electrical to
mechanical forms or vice versa results
from the following two electromagnetic phenomena:
1. When a conductor moves in a magnetic field, voltage is
induced in the conductor.
2. When a current-carrying conductor is placed in a magnetic
field, the conductor experiences a
mechanical force.
These two effects occur simultaneously whenever energy
conversion takes place from electrical to
mechanical or vice versa.
Basic Structure of Electric Machines
An electric machines has two major components, stator and rotor
that separated by the air gap. Fig. 2
shows the structure of electric machines. Generally, the
structure of electric machine can be divided into
two parts; stator and rotor. The Stator is referred to the
static part of the machine (the outer frame) while
the rotor is the moving part (inner frame) of the machine.
Electrical machines Electrical system Mechanical system
Energy flow Motor
Generator
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(a)
Figure 2. Structure of electric machine.
Both stator and rotor are made of ferromagnetic materials. In
most
inner periphery of the stator and outer periphery of the rotor
str
slots. Theses conductors (in the slots of stator or rotor) are
interconnected to form windings.
The winding in which voltage is induced is called the armature
winding. The winding through which a
current is passed to produce the primary source of flux is
called the field winding. Permanent magnets are
used in some machines to provide the major
The three basic electric machines are dc machines, induction
machines and synchronous machines.
Three-Phase Induction Machines
It is the most widely used machine in industry. In the induction
machines both stator and rotor
winding carry alternating currents (ac). The ac is supplied to
the stator winding directly and to the rotor
winding by induction.
Induction machine can operate both as motor and as generator.
But, this machine is extensively use
as a motor in many applications.
Construction
An induction machines consist of two main parts; stator and
rotor. There are two types of roto
squirrel-cage rotor and wound rotor.
The squirrel-cage winding consists of aluminum or copper bars
embedded in the rotor slots and
shorted at both ends by aluminum or copper end rings. This type
of rotor is the most commonly used rotor.
The wound-rotor winding has a complete set of three
Usually, it is Y-connected and the rotor coils are tied to the
slop rings.
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(b)
Structure of electric machine. (a) cylindrical machine (uniform
air gap). (b) salient pole
machine (non-uniform air gap)
Both stator and rotor are made of ferromagnetic materials. In
most machines, slots are cut on the
inner periphery of the stator and outer periphery of the rotor
structure. Conductors are placed in these
slots. Theses conductors (in the slots of stator or rotor) are
interconnected to form windings.
The winding in which voltage is induced is called the armature
winding. The winding through which a
produce the primary source of flux is called the field winding.
Permanent magnets are
used in some machines to provide the major source of flux in the
machine.
The three basic electric machines are dc machines, induction
machines and synchronous machines.
It is the most widely used machine in industry. In the induction
machines both stator and rotor
winding carry alternating currents (ac). The ac is supplied to
the stator winding directly and to the rotor
Induction machine can operate both as motor and as generator.
But, this machine is extensively use
consist of two main parts; stator and rotor. There are two types
of roto
cage winding consists of aluminum or copper bars embedded in the
rotor slots and
shorted at both ends by aluminum or copper end rings. This type
of rotor is the most commonly used rotor.
rotor winding has a complete set of three-phase windings similar
to stator winding.
connected and the rotor coils are tied to the slop rings.
(a) cylindrical machine (uniform air gap). (b) salient pole
, slots are cut on the
e. Conductors are placed in these
slots. Theses conductors (in the slots of stator or rotor) are
interconnected to form windings.
The winding in which voltage is induced is called the armature
winding. The winding through which a
produce the primary source of flux is called the field winding.
Permanent magnets are
The three basic electric machines are dc machines, induction
machines and synchronous machines.
It is the most widely used machine in industry. In the induction
machines both stator and rotor
winding carry alternating currents (ac). The ac is supplied to
the stator winding directly and to the rotor
Induction machine can operate both as motor and as generator.
But, this machine is extensively used
consist of two main parts; stator and rotor. There are two types
of rotor;
cage winding consists of aluminum or copper bars embedded in the
rotor slots and
shorted at both ends by aluminum or copper end rings. This type
of rotor is the most commonly used rotor.
phase windings similar to stator winding.
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Figure 3. Cutaway diagram of a typical (a) small (b) large
squirrel
Figure 4. Cutaway diagram of a wound
Three Modes of Operation
The induction machine can be operated in three modes: motoring,
generating and plunging. These
three modes of operation can be represented by a t
can determine several conditions such as
a) How does the torque of an induction motor change as the load
changes?
b) How much can an induction motor supply at starting
conditions?
c) How much does the speed of an induction motor drop as its
shaf
Fig. 5 and 6 provides some important information about the
operation of induction motors. The
information is summarized below:
a) The induced torque of the motor is zero at synchronous
speed
b) There is a maximum torque that cannot be exceeded.
c) The starting torque on the motor is slightly la
the motor to start. It also known as initial torque.
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Cutaway diagram of a typical (a) small (b) large squirrel-cage
induction motor.
Cutaway diagram of a wound-rotor induction motor.
The induction machine can be operated in three modes: motoring,
generating and plunging. These
represented by a torque-speed characteristic curve. From the
curve, we
can determine several conditions such as
How does the torque of an induction motor change as the load
changes?
How much can an induction motor supply at starting
conditions?
How much does the speed of an induction motor drop as its shaft
load increases?
provides some important information about the operation of
induction motors. The
The induced torque of the motor is zero at synchronous speed 0.
There is a maximum torque that cannot be exceeded.
The starting torque on the motor is slightly larger than its
full-load torque. This torque is required by
the motor to start. It also known as initial torque.
cage induction motor.
The induction machine can be operated in three modes: motoring,
generating and plunging. These
From the curve, we
provides some important information about the operation of
induction motors. The
load torque. This torque is required by
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d) During 0 , induction machine operatdirection of the rotating
magnetic field
induction machine.
e) During , induction machine operates in generating mode.
Tproduce a generating torque that is acting
the rotating magnetic field). This mode is utilizes to provide
regenerative breaking in some drive
application. To stop the drive system, the
frequency. In this process, the rotor speed is higher than
synchronous speed because of the inertia of
the drove system. As a result, the generating action of the
induction machine will cause the power
flow to reverse and the kinetic energy of the drive system will
be fed back to the supply (
mechanical power to electric power
f) During 0, induction machine operates in plugging mode.
Trotating magnetic field but will oppose the motion of the rotor.
This torque is a braking torque.
mode is utilized in drive application where the drive system is
required to stop very quickly. It
happens when the terminal ph
rotate opposite to the rotation of the rotor. The motor will
come to zero speed rapidly and will
accelerate in the opposite direction, unless the supply is
disconnected at zero speed.
Figure 5.
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induction machine operates in motoring mode. The rotor
direction of the rotating magnetic field. This is the natural
(or motoring) mode of operation of the
induction machine operates in generating mode. The induction
machi
produce a generating torque that is acting opposite to the
rotation of the rotor (or acting opposite
This mode is utilizes to provide regenerative breaking in some
drive
To stop the drive system, the synchronous speed will be reduced
by reducing the supply
frequency. In this process, the rotor speed is higher than
synchronous speed because of the inertia of
the drove system. As a result, the generating action of the
induction machine will cause the power
ow to reverse and the kinetic energy of the drive system will be
fed back to the supply (
mechanical power to electric power). The process is known as
regenerative breaking.
induction machine operates in plugging mode. The torque will be
in the direc
rotating magnetic field but will oppose the motion of the rotor.
This torque is a braking torque.
mode is utilized in drive application where the drive system is
required to stop very quickly. It
ase sequence is changed suddenly, the rotating magnetic field
will
rotate opposite to the rotation of the rotor. The motor will
come to zero speed rapidly and will
accelerate in the opposite direction, unless the supply is
disconnected at zero speed.
A typical torque-speed characteristic curve
rotor will rotate in the
. This is the natural (or motoring) mode of operation of the
he induction machine will
(or acting opposite
This mode is utilizes to provide regenerative breaking in some
drive
by reducing the supply
frequency. In this process, the rotor speed is higher than
synchronous speed because of the inertia of
the drove system. As a result, the generating action of the
induction machine will cause the power
ow to reverse and the kinetic energy of the drive system will be
fed back to the supply (converting
). The process is known as regenerative breaking.
ill be in the direction of
rotating magnetic field but will oppose the motion of the rotor.
This torque is a braking torque. This
mode is utilized in drive application where the drive system is
required to stop very quickly. It
ase sequence is changed suddenly, the rotating magnetic field
will
rotate opposite to the rotation of the rotor. The motor will
come to zero speed rapidly and will
accelerate in the opposite direction, unless the supply is
disconnected at zero speed.
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Figure 6. A torque-speed characteristic curve showing the
extended operating ranges
Principles of Operation
If the stator windings are connected to a three
voltages in the rotor windings produce rotor currents that
interact with the air gap field to produce torque.
The rotor, if free to do so, will then start rotating.
According to Lenzs law, the rotor rotates in the direction of
the rotating field
speed between the rotating field and the rotor winding decrease.
The rotor will eventually reach a steady
state speed that is less than the synchronous speed gap. The
revolution per minutes (rpm) of the
where the supply frequency in Hz number of pole
It is obvious that at there will be no induced voltage and
current in the rotor circuit and hence no torque. During this
state, there will be no cutting of flux and rotor current equals
zero. Therefore, it is
not possible for the rotor to rotate at synchronous speed.
The different between the rotor speed and the synchronous speed
of the rotating field is called the
slip speed or slip rpm and is defined as
The slip is defined as the relative speed expressed on a
perrepresented by
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speed characteristic curve showing the extended operating
ranges
If the stator windings are connected to a three-phase supply and
the rotor circuit is closed, the induced
oduce rotor currents that interact with the air gap field to
produce torque.
The rotor, if free to do so, will then start rotating.
According to Lenzs law, the rotor rotates in the direction of
the rotating field such that
speed between the rotating field and the rotor winding decrease.
The rotor will eventually reach a steady
that is less than the synchronous speed at which the stator
rotating field rotates in the air revolution per minutes (rpm) of
the synchronous speed of this rotating magnetic flux is
frequency in Hz
there will be no induced voltage and current in the rotor
circuit and hence
there will be no cutting of flux and rotor current equals zero.
Therefore, it is
at synchronous speed.
The different between the rotor speed and the synchronous speed
of the rotating field is called the
and is defined as
the relative speed expressed on a per-unit or sometimes as
percentage basis.
speed characteristic curve showing the extended operating
ranges
phase supply and the rotor circuit is closed, the induced
oduce rotor currents that interact with the air gap field to
produce torque.
such that the relative
speed between the rotating field and the rotor winding decrease.
The rotor will eventually reach a steady-
at which the stator rotating field rotates in the air
of this rotating magnetic flux is
(4.1)
there will be no induced voltage and current in the rotor
circuit and hence
there will be no cutting of flux and rotor current equals zero.
Therefore, it is
The different between the rotor speed and the synchronous speed
of the rotating field is called the
(4.2)
unit or sometimes as percentage basis. It
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(4.3)
From Eq. (4.3), the rotor speed can be derived as
1 (4.4)
The radian per second (rad/s) of rotor speed is
1 (4.5)
where synchronous speed in rad/s The frequency of the induced
voltage and current in the rotor circuit will correspond to this
slip rpm, because this is the relative speed between the rotating
field and the rotor winding. The rotor frequency can
be expressed as
(4.6)
Example 1
A three-phase 460 V, 100 hp, 60 Hz, four-pole induction machine
delivers rated output power at a slip of
0.05. Determine
a) Synchronous speed and motor speed.
b) Frequency of the rotor current.
c) Slip rpm.
Equivalent Circuit
The per-phase equivalent circuit of a three-phase induction
motor is similar to a single-phase
equivalent circuit of a transformer. The only difference is that
the secondary winding of an induction motor
is short-circuited.
stator circuit rotor circuit
Figure 7. The per phase circuit of induction motor
The value of variable resistance of rotor / can be replaced by
two resistors in series. From Eq. (4.7), the equivalent circuit of
three-phase induction motor can be drawn as Fig. 6.
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" + $ % (4.7)
Figure 8. The complete circuit of induction motor per-phase with
rotor having two resistors in series
The equivalent circuit per phase referred to stator of induction
motor is illustrated in Fig. 9. This circuit
is similar to equivalent circuit per phase of transformer
referred to the primary side.
Figure 9. The equivalent circuit per-phase referred to stator of
induction motor
The circuit of Fig. 9 can be simplified to an approximate
equivalent circuit to allow a simple calculation
to be performed to calculate the currents in the circuit as
shown in Fig. 9.
Figure 10. Approximate per-phase equivalent circuit of induction
motor referred to stator
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Power Flow Diagram or Losses in Induction Motor
An induction motor can be described as a rotating transformer.
Its input is from the three-phase
supply. The secondary (rotor) winding of an induction motor is
shorted, so no electrical output exists.
Instead, the output will be mechanical. The flow of power from
the input to the output is shown below.
Figure 11. The overall power in induction motor
Power flow diagram is normally represented as a fish bone, where
it illustrates the power flow in the
machine from the input part into the output part. The branches
indicate the losses that present in the
machine.
Figure 12. Power flow diagram of induction motor
The losses of Fig. 12 is corresponding with the approximate
circuit as shown in Fig. 10.
+
Es
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I1 I2 RsjXs
RrjXr
IIc Im
Rc jXm Rr (1-s)/s
Figure 13. All losses obtained from approximate circuit
Motor input (Pin)
Stator copper and core loss (PSCL &
Pc)
Air gap power (PAG) or rotor
input power (RIP)
Rotor copper loss (PRCL)
Mechanical power (Pm) or power
converted (Pconv)
Windage, friction, stray losses and etc
(P)
Motor output (Pout)
Pin Pout
PSCL PRCL Pc P
PAG/RIP Pm/Pconv
PSCL PRCL
Pc
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From the above circuit, the following power equations can be
derived.
& 3|)||+| cos 3|01||+1| cos 2 (4.8)
&3 4565 7"8 (4.9)
&9:1 3|+; | (4.10)
+& 3|+; | $"< % (4.11)
&":1 3|+; | ; (4.12)
&3=> 3|+; | ; $ % (4.13)
&=?@ &3=> & (4.15)
From Eq. (4.11), (4.12) and (4.13), we can obtain this
relationship.
+& A8BCD AEFG (4.16)
Example 2
A three-phase induction 100 hp, 400 V, 50 Hz 6-pole Y-connected
squirrel cage induction motor has the
following parameters refer to the stator.
Rs = 0.125 Rr = 0.095 X = 0.45 Xm = 10
If the rotational losses are 550 W, using approximate equivalent
circuit, find the following at 5% slip;
a) The line current and power factor
b) The output horsepower
c) The efficiency
Example 3
A 480 V, 50 hp Y-connected induction motor has line current 60 A
at 0.85 power factor lagging. This motor
has these following power losses
PSCL = 2 kW PRCL = 700 W P = 600 W Pc = 1800 W
Find
a) the air gap power
b) the power converted
c) the output power
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d) the efficiency
e) of the motor
Torque Equation for Induction Motor
The output power of an induction motor is in the form of
mechanical power. This mechanical power is
proportional to torque and rotational speed/angular velocity ().
There are four different torques that we
are interested to analyzed in induction motor, i.e. starting
torque, Ts, maximum torque, Tmax, mechanical
torque, Tm and output torque, To. Torque equation can be derived
from basic power equation.
& H where IJ rad/s (4.17)
Therefore, general equation for torque is define as
H A
JAI (4.18)
where T = torque in Nm
N = speed in rpm
a) Mechanical Torque
Also known as induced torque;
HK A8BCD (4.19)
b) Output Torque
Also known as shaft or load torque;
H=?@ ABLM (4.20)
c) Starting Torque
At starting, 0. Therefore, 1. Thus, equation for starting torque
is
H@ N "
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KWX "
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Figure 14. Variable-frequency speed control in induction
motor.
characteristic curve for speeds (a) below base speed, (b) above
base speed (c) for all frequencies.
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(a)
(b)
(c)
frequency speed control in induction motor. The family of
torque
characteristic curve for speeds (a) below base speed, (b) above
base speed (c) for all frequencies.
family of torque-speed
characteristic curve for speeds (a) below base speed, (b) above
base speed (c) for all frequencies.
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2. Speed control by pole changing.
In the day before modern solid-state control circuits were
commons, the stator windings of induction
motors were often constructed so that the number of poles in the
stator windings could be changed. But
now, this technique is largely outdated.
3. Speed control by changing the line voltage.
The torque developed by an induction motor is proportional to
the square of the applied voltage. This
method is sometimes used on small motors driving fans.
4. Speed control by changing the rotor resistance.
In wound-rotor induction motors, it is possible to change the
shape of the torque
inserting extra resistances into the rotor circuit of the
machine. However, inserting extra resistances into
the rotor circuit seriously reduces the efficiency of the
machine. Such method is normally used only for
short periods because of this efficiency problem.
Figure 15.
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Speed control by pole changing.
state control circuits were commons, the stator windings of
induction
motors were often constructed so that the number of poles in the
stator windings could be changed. But
ue is largely outdated.
Speed control by changing the line voltage.
The torque developed by an induction motor is proportional to
the square of the applied voltage. This
method is sometimes used on small motors driving fans.
e rotor resistance.
rotor induction motors, it is possible to change the shape of
the torque
inserting extra resistances into the rotor circuit of the
machine. However, inserting extra resistances into
educes the efficiency of the machine. Such method is normally
used only for
short periods because of this efficiency problem.
Variable-line-voltage speed control
state control circuits were commons, the stator windings of
induction
motors were often constructed so that the number of poles in the
stator windings could be changed. But
The torque developed by an induction motor is proportional to
the square of the applied voltage. This
rotor induction motors, it is possible to change the shape of
the torque-speed curve by
inserting extra resistances into the rotor circuit of the
machine. However, inserting extra resistances into
educes the efficiency of the machine. Such method is normally
used only for
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Figure 16.
Starting of an Induction Motor
Squirrel-cage induction motors are frequently started by
connecting them directly across the supply
line (self-start). A large starting current of the order of 500
to 800 percent of full
the line. This initial excessive current wil
the same line. Also, if a large current flows for a long time it
may overheat the motor and damage the
insulation. In such a case, reduced-voltage starting must be
used.
1. Using primary resistors
The purpose is to apply a reduced voltage across the motor
terminals so that the initial current is
reduced. This method is useful for smooth starting small
machine.
S
S
S
Three-phase Supply
Figure 17. Starting of induction motor using primary
resistor
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Speed control by varying the rotor resistance
cage induction motors are frequently started by connecting them
directly across the supply
start). A large starting current of the order of 500 to 800
percent of full-load current may flow in
the line. This initial excessive current will effect the
operation of other electrical equipment connected to
the same line. Also, if a large current flows for a long time it
may overheat the motor and damage the
voltage starting must be used.
The purpose is to apply a reduced voltage across the motor
terminals so that the initial current is
reduced. This method is useful for smooth starting small
machine.
IM
R
R: running contactsS: starting contactsStart: S closed , R
openRun: S open , R closedR
R
Starting of induction motor using primary resistors
cage induction motors are frequently started by connecting them
directly across the supply
load current may flow in
l effect the operation of other electrical equipment connected
to
the same line. Also, if a large current flows for a long time it
may overheat the motor and damage the
The purpose is to apply a reduced voltage across the motor
terminals so that the initial current is
running contactsstarting contacts
R openR closed
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2. Using star-delta starter
This method is used for delta-connected motors. It consists of
two-way connects the motor in star for
starting and delta for normal running.
At starting, when star-connected, the voltage is reduced by 1/3.
Hence, the developed torque is reduced by 1/3. This method is cheap
and effective provided the starting torque required does not exceed
1.5 full-load torque. This method is used for machine tools, pumps
and motor-generators.
Figure 18. Starting of induction motor using star-delta
starter
3. Using auto transformer
This method can be both for star and delta connected motors. At
starting, a reduce voltage is applied
across the motor terminals. When the speed is about 80%, the
autotransformer is cut-off and full supply
voltage is supplied.
S S
R
S S
R
S S
R
IM
R: running contacts
S: starting contacts
Start: S closed, R open
Run: S open, R closed
Three-phase
Supply
Figure 19. Starting of induction motor using auto
transformer
4. Using solid-state voltage controller for starting
A solid-state voltage controller can also be used as a
reduces-voltage starter. The controller can
provide smooth starting. This arrangement can also be used to
control the speed of the induction motor.
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IMThree-phase
Supply
Figure 20. Starting of induction motor using solid-state voltage
controller