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CHAPTER 3
IDUCTIO MOTOR
3.1 ITRODUCTIO TO IDUCTIO MOTOR
3.2 COSTRUCTIO
3.2.1 TYPES OF ROTOR
a. SQUIRREL-CAGE ROTOR
b. WOUND ROTOR
3.2.2 STATOR
3.3 PRODUCTIO OF ROTATIG MAGETIC FIELD
3.4 PRICIPLE OF OPERATIO
3.5 SLIP AD SYCHROOUS SPEED
3.6 PER PHASE EQUIVALET CIRCUIT
3.7 POWER FLOW DIAGRAM
3.8 IDUCTIO MOTOR TESTS
3.8.1 NO LOAD TEST/ RUNNING LIGHT TEST
3.8.2 BLOCKED/LOCKED ROTOR TEST
3.8.3 DC RESISTANCE TEST
3.9 EFFICIECY
3.10 TORQUE EQUATIO
3.10.1 MECHANICAL TORQUE
3.10.2 MAXIMUM TORQUE
3.10.3 STARTING TORQUE
3.11 STARTIG METHOD AD SPEED COTROL
3.11.1 USING PRIMARY RESISTORS
3.11.2 USING STAR-DELTA STARTER
3.11.3 USING AUTO TRANSFORMER
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3.1 ITRODUCTIO TO IDUCTIO MOTOR
Definition of Induction:
The process by which an electromotive force is produced in a circuit by varying the
magnetic field linked with the circuit.
Induction motors are the most commonly used electric motors.
Although it is possible to use an induction machine as either a motor or a generator, it has
many disadvantages and low efficiency as a generator and so is rarely used in thatmanner. The performance characteristics as a generator are not satisfactory for most
applications.
For this reason, induction machines are usually referred to as induction motors.
AC current supplied to the stator winding produces a flux through the air gap that induces
currents in the rotor windings.
Rotor receives electric power by induction in exactly the same way as thesecondary of 2 winding transformer.
Can be treated as a rotating transformer, one in which primary winding isstationary (stator) but the secondary is free to rotate (rotor).
Most appliances, such as washing machines and refrigerators, use a single-phaseinduction machine
For industrial applications, the three-phase induction motor is used to drivemachines
Advantages
Very simple and extremely rugged Low cost and very reliable Requires minimum of maintenance
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Disadvantages
Speed cannot be varied without sacrificing some of its efficiency. Speed decreases with increase in load
3.2 COSTRUCTIO
A machine is called induction machines because the rotor voltage (which produces the
rotor current and the rotor magnetic field) is induced in the rotor windings instead of
being physically connected by wires.
The distinguishing feature of an induction machine is that no DC field current is required
to run the machine.
Although it is possible to use an induction machine as either a motor or a generator, it has
many disadvantages as a generator and so is rarely used in that manner. For this reason,
induction machines are usually referred to as induction motor.
Two sets of electromagnets are formed inside any motor. In an AC induction motor, one
set of electromagnets is formed in the stator because of the AC supply connected to the
stator windings. The alternating nature of the supply voltage induces an Electromagnetic
Force (EMF) in the rotor (just like the voltage is induced in the transformer secondary) as
per Lenzs law, thus generating another set of electromagnets; hence the name
induction motor. Interaction between the magnetic field of these electromagnets
generates twisting force, or torque. As a result, the motor rotates in the direction of the
resultant torque.
An induction motor consists of two main parts: stator and rotor. It has the same
physical stator as a synchronous machine but with different rotor construction. There are
two types of induction motor rotors that can be placed inside the stator, i.e. squirrel-cage
rotor and wound rotor.
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3.2.1 TYPES OF ROTOR
a) Squirrel-Cage Rotor
Squirrel-cage rotor, as shown below, 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.
Fig. 3.0: Example of Squirrel-Cage Rotor
The rotor is cylindrical and is made of conducting bars short circuited at both ends It is also known as brushless induction motor. It is more rugged and since there are no brushes it is safer in combustible
environment.
b) Wound Rotor
Wound rotor, as shown below has a complete set of three-phase windings similar to
stator windings. Usually, it is Y-connected and the rotor coils are tied to the slip rings.
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Fig. 3.1: Wound Rotor
The rotor is cylindrical and is made up of a three phase windings with terminalsbrought out to slip rings
Wound rotor induction motors are also known as a slip-ring motors This type is the more complicated of the two type but it has a higher starting
torque and is more controllable
3.2.2 STATOR
The stator is made up of several thin laminations of aluminum or cast iron. They are
punched and clamped together to form a hollow cylinder (stator core) with slots as shown
in Fig. 3.2. Coils of insulated wires are inserted into these slots. Each grouping of coils,
together with the core it surrounds, forms an electromagnet (a pair of poles) on the
application of AC supply.
The number of poles of an AC induction motor depends on the internal connection of thestator windings. The stator windings are connected directly to the power source.
Internally they are connected in such a way, that on applying AC supply, a rotating
magnetic field is created.
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Fig. 3.2: A Typical Stator
3.3 PRODUCTIO OF ROTATIG MAGETIC FIELD
When a three phase stator winding is connected to a three phase voltage supply, three
phase currents will flow in the windings which induce three-phase flux in the stator. This
flux will rotate at a speed called as synchronous speeds
. The flux is called as rotating
magnetization field. The mathematical equation is given as:
p
f120
s= where =f the supply frequency
=p no. of poles in the
machine/motor
The currents that flows in the stator are spaced 120 each other. Graphical representation
is shown in Fig. 3.3.
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Fig. 3.3: 3-Phase Current
( ) tsinitimR =
( ) ( )= 120tsinitimY
( ) ( )+= 120tsinitimB
3.4 PRICIPLE OF OPERATIO
When a three phase current flow in a three-phase winding, rotating magnetic field (flux)
will be produced. The flux has constant magnitude and is distributed in sinusoidal form.
This flux will induce voltage in the rotor conductor by Flemings Right Hand Rule. By
Faradays Law, if the rotor winding is short-circuited, rotor current will flow in it. The
reaction between rotor current and stator flux causes the rotor to rotate in the same
direction as the stator flux.
An induction motor with 2 poles can be taken to explain this phenomena. Conductor A
will be located under north pole while conductor B will be located under south pole as
illustrated in Fig. 3.4. The flux rotates in the clock-wise direction (towards the right).lf
the flux is taken as the reference, the conductors A and B are likely to move to the left.
Then, from the Right Hand Fleming, voltage or current will be induced as shown in
Fig. 3.5.
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Fig. 3.4: Conductor A is located under north pole and conductor B is located under south pole
Fig. 3.5: Right Hand Fleming Fig. 3.6: Ampere Right Hand Rule
The same process happens to conductor B.
As shown in Fig. 3.6, when current flows in the rotor circuit, flux will be induced and the
direction is anti-clock-wise. This is called Ampere Right Hand Rule. The interaction
between flux produced by the rotor current and the rotating flux will induce torque on the
rotor conductor that acts to the right. This torque causes the rotor to rotate clockwise. The
illustration is shown in Fig. 3.7.
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Fig. 3.7: Interaction between Rotor Current Flux and Rotating Flux
Conclusion:
Rotating field will cause the rotor to rotate at the same direction as the stator flux. The
torque direction is independent upon the conductor position. Torque direction is always
the same as the flux rotation.
At the time of starting the motor, rotor speed = 0. The rotating magnetic field will cause
the rotor to rotate from 0 speeds to a speed that is lower than the synchronous speed. If
the rotor speed is equal to the synchronous speed, there will be no cutting of flux and
rotor current equals zero. Therefore, it is not possible for the rotor to rotate ats
.
3.5 SLIP AD SYCHROOUS SPEED
Slip is defined as the difference between synchronous speed (magnetic fields speed) and
rotor speed:
s
rs
s
= .. (3.0)
where: =s
synchronous speed in rev/min.
=r
rotor speed in rev/min.
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From Eqn. 3.0, the rotor speed can be derived as ( )s1sr = . Slip can also be
represented in percent. When the rotor move atrn rev/sec (rps), the stator flux will
circulate the rotor conductor at a speed of ( )rs
nn per second. Therefore, the frequency
of the rotor emf,r
f is written as:
( )pnnfrsr
=
sf=
where:
=s slip
=f supply frequency.
The rotor therefore runs at a speed slightly less than the synchronous speed the difference
being called slip speed.
Slip speedrs
=
3.6 PER PHASE EQUIVALET CIRCUITThe per-phase equivalent circuit of a three-phase induction motor is just like a single
phase transformer equivalent circuit. The difference is only that, the secondary winding is
short-circuited unlike in the transformer it is open-circuited as a load is to be connected
later. The per-phase equivalent circuit is illustrated in Fig. 3.8 below.
Fig. 3.8: Per-Phase Equivalent of 3-Phase Induction Motor.
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The per-phase equivalent circuit referred to the stator winding is shown in Figure 742.
This equivalent circuit is categorized into two types: [i] actual equivalent circuit and [ii]
approximate equivalent circuit.
Fig. 3.9: Per-Phase Equivalent Circuit Referred to Stator Winding.
From the equivalent circuit;
=1
I Stator phase current. :2o1
III +=
= Stator line current (for stator Y-connection)
=3
IL , where =
LI stator line current (for stator: - connection)
=2
I Rotor current referred to stator winding
=oI No-load current, mco III +=
=c
I Core current
=m
I Magnetizing current
For approximate equivalent circuit;
2o1 III +=
mco III +=
( )
c
phs
cR
EI = ;
( )
m
phs
mjX
EI = ;
( )
( )121
2
phs
2
XXjRs
R
EI
++
+
= ... (3.1)
This model is normally used for analysis purposes for simplicity.
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3.7 POWER FLOW DIAGRAM
Power flow diagram is actually a flow of power right from the input to the output.
Fig. 3.10: Power Flow Diagram
Fig. 3.10 shows the power flow diagram while Fig. 3.11 illustrates the components that
involve in the power losses calculation.
Fig. 3.11: Components Involved in Power Flow Diagram
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From the circuit shown in Fig. 3.11, the power equations can be derived as follows:
[i] SCL occurs ats
R , then ( ) s
2
2 RI3SCL= . (3.2)
[ii] RCL occurs atR2
'RR = , then ( ) 2
2
2 RI3RCL= . (3.3)
[iii]m
P occurs at ( )s1s
R2 , then ( ) ( )s1
s
RI3P 2
2
2m = . (3.4)
[iv] RIPoccurs ons
R2 , then : ( )
s
RI3RIP 2
2
2= . (3.5)
From Eqn. (3.2...3.5), we can derive the power equations in terms of slip and power,
then:
From Eqn. 3.4 : ( ) ( )s1s
RI3P 22
2m = = ( )
s
s1RCL = ( )s1RIP (3.6)
From Eqn. 3.5 : ( )s
RI3RIP 2
2
2= =
( )s1P
m
=
s
RCL (3.7)
From these equations, we do not need to recalculatem
P andRIP, if RCL is known
provided that the value for slip is known.
The input power comes from the stator input, then:
cosIV3cosIV3PphphLLin
==
WhereLV and
LI are line voltage and line current respectively.
phV and
phI are phase voltage and phase current respectively.
is the angle between voltage and current.
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3.8 IDUCTIO MOTOR TESTS
The equivalent circuit of an induction motor is a very useful tool for determining the
motors response to change in load. There are three tests that are normally being carried
out for a 3-phase induction motor, namely:
i) No load test/ running light testii) Blocked/Locked rotor test
iii) DC resistance test [ this is optional: used to determine stator resistance ]
3.8.1 O LOAD TEST/ RUIG LIGHT TESTThe test set-up is shown in figure below. In this test, the motor is running at rated voltage
and no-load is connected to the motor. Readings are taken on the stator part are:
LV : line to line stator voltage
LI : stator line current
LP : 3-phase input power
Fig. 3.12: Test Set-Up for No Load Test
CBAL IIII ++=
From this test, we can determine the value ofCR and mX . This is corresponding to the
measurement as shown in figure below.
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Fig. 3.13: Equivalent Circuit of Induction Motor
Calculation ofC
R and mX
LL
L
L
LLL
L
L
oc
s
IV
Pcos
cosIV3
PP
3
VE
=
==
=
From phasor diagram shown below,
Fig. 3.14: Phasor Diagram from No-Load Test
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LLC
LLm
cosII
sinII
=
=
m
L
m
C
L
C
I
VX
I
VR
=
=
3.8.2 BLOCKED/LOCKED ROTOR TEST
In this test, the rotor is locked (not moving). The set-up is shown on figure below.
Fig. 3.14: Test Set-Up for Blocked Rotor Test
Power, voltage and current readings are taken.
BRP : Blocked rotor power
BRI : Line current
BRV : Line voltage
From this test, we can determine the value of RBRand XBR.
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rSBR
2
BR
2
BRBR
BR
BR
BR
2
BR
BR
BR
BR
2
BR
BR
BR
'RRR
RZX
I
VZ
IPR
RI3
PP
+=
=
=
=
==
The value rR' of can be calculated if sR is known from the DC test.
3.8.3 DC RESISTACE TESTThis test is performed to determine stators resistance sR . There are two possible
connections: Y or connection.
Fig. 3.15: DC Resistance Test (Y-Connection)
dcs
dcs
dc
dc
RR
RRIV
2
1
2
=
==
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Fig. 3.15: DC Resistance Test (-Connection)
dcs
sdc
dc
s
ss
dc
dc
RR
RR
RR
RR
I
V
2
3
3
2
3
)(2
=
=
==
Exercise 2.5
The results of no-load and blocked rotor tests for a three-phase induction motor are:
o-load test: VL-L = 220V
Pin = 1000W
IL = 20A
P = 400W
Blocked rotor test: VL-L = 30V
Pin = 1500W
IL = 50A
Calculate the per-phase parameters of the approximate equivalent circuit by assuming the
stator are connected in Y.
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3.9 EFFICIECY
Efficiency for any electrical machine is defined as:
+
==
in
in
in
out
P
lossesTotalP
P
P (3.8)
One thing should be noted that theout
P is actually the output from the rotor or motor itself
while the input power comes from the stator.
3.10 TORQUE EQUATIO
Torque equation can be derived from the power equation that is expressed in mechanical
formula and electrical formula. These two formula can be equated together to obtain its
relationship in terms of circuit parameters.
Basic power equation is given as;
TP= where60
2= (speed in rad/sec)
= Speed in rev/min (rpm)
=T Torque in Nm
Then torque,
2
P60T;Torque
= . (3.9)
Eqn. 3.9 is the general formula for torque equation. This formula can be employed to
calculate the output and mechanical torque by some formula modification.
For mechanical torque :2
P60T@T mmmech
= .. (3.10)
For output torque :2
P60T outo
= .. (3.11)
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3.10.1 MECHAICAL TORQUE ( mT )The mechanical torque is sometimes called the induced torque. The mechanical torque
can be also expressed in terms of circuit parameters.
( ) ( ) mr
mr22
2m T
60
T2s1
s
RI3P
===
where =r
speed of the rotor and
=r
The rotor speed in rad/s
( ) ( )( ) ( )
( )( )
s
2
2
2
s
2
2
2
r
22
2
ms
RI3s1ss1RI3
s1s
RI3
T
=
=
=
But,( )
( )121
2
phs
2
XXjRs
R
EI
++
+
= ; so ,( )
( )22
1
2
phs
2
XRs
R
EI
+
+
=
Substitute ( )
( )22
1
2
phs2
XRs
R
EI
+
+
= , into the mechanical torque, mT equation,
Thus,
( )
( )( )[ ]
( )
+
+
=
+
+
=2
2
1
2
s
2
2
phs
s
2
2
2
2
1
2
phs
m
XRs
R
s
RE3
s
R
XRs
R
E3
T
.. (3.12)
By simplifying the above equation, therefore, the formula for the mechanical torque, mT is
( )[ ]( ) ( )[ ]22
12
2
s
2
phs
msXsRR
sRE3T
++==
.. (3.13)
where21
XXX +=
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Fig. 3.16: Motor Torque vs Slip(Speed)
Eqn. 3.13, if we draw on themT versus s on the graph will be appeared as in Fig. 3.16.
From the torque-speed characteristics (Fig. 3.16.) it is observed that;
stT : The torque required by the motor to start. Also called as initial torque.
maxT : The max torque for the motor. Also called as stalling or pull-out torque.
maxS : The slip at
maxT
LT : No-load torque.
FLT : Full-load torque.
s : Synchronous speed.
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3.10.2 MAXIMUM TORQUE ( maxT )
To obtainmaxT , differentiate the mT to obtain maxs ,
From the same curve, the max point can be obtained by differentiating Eqn. 3.13.
0ds
dTm = :
To obtain max torque, then, yield:
( ) 221
2
max
XR
Rs
+
=
Substitutemax
s into Eqn. 3.13, we get:
( )[ ]
( ) ( )( )[ ]2211
s
2
phs
max
XRR
1
2
E3T
++==
(3.14)
3.10.3 STARTIG TORQUE ( stT )
Starting torque can be derived from Eqn. 3.13 with slip, 0.1s =
At starting, 0r= , therefore, 1=
=
s
rss
As a result, the equation of the starting torque, stT is
( )[ ]( )[ ]22
12
2
s
2
phs
stXRR
RE3T
++==
(3.15)
Fig. 3.17 represents the relationship between torque and slip/speed with varyingR .
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3.11.1 USIG PRIMARY RESISTORS
The purpose is to apply a reduced voltage across the motor terminals so that the initial
current is reduced. However, it should be noted that EI and 2ET .
By using the primary resistors, the applied voltage per phase can be reduced by factor of
x.
scst xIT = and scst IxT 2=
ff
f
sc
f
st
f
f
sc
f
f
st
f
st
saxsI
Ix
T
T
sI
xIs
I
I
T
T
22
2
2
22
=
=
=
=
This method is useful for smooth starting small machine. The circuit used for this type of
method is shown below.
Fig. 3.18: Starting of Induction motor using primary resistors
3.11.2 USIG STAR-DELTA STARTER
This method is used for delta-connected motors. It consists of 2-way switch, which
connects the motor in star for starting and delta for normal running, as shown in figure
below.
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At starting, when star-connected, the voltage is reduced by3
1. Hence, the torque
developed is reduced by3
1. This method is cheap and effective provide the starting
torque required does not exceed 1.5 full-load torque. This method is used for machine
tools, pumps and motor-generators.
Fig. 3.19: Starting of Induction motor using star-delta starter
3.11.3 USIG AUTO TRASFORMERThis method can be both for star and delta connected motors. At starting, a reduced
voltage is applied across the motor terminals. When the speed is about 80%, the
autotransformer is cut-off and full supply voltage is applied. The circuit used for this type
of method is shown in figure below.
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Fig. 3.19: Starting of Induction motor using autotransformer
Let the tapping of the transformation ratio = k
ff
fL
stf
fL
st
fL
st saksI
Iks
I
I
T
T 222
2
2
=
=
=