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23 October 2013 L.N Tripathy 1
Principle of Operation Three phase winding in stator when
get supply produce rotating magnetic
field [or flux] of Constant magnitudebut rotating at synchronous speed
This rotating magnetic field induce emf
in rotor circuit and current start flowingin rotor circuit as rotor is shortCircuited.
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C0nt.. The torque is produced on the rotor due to
interaction of two fields. As per Lenzs law ,under the influence of this
toque the rotor start rotating in samedirection to catch the rotating magnetic field.The relative speed between rotating magneticfield and the rotor is called slip speed.
Note:- The rotor rotate near synchronousspeed but can not attend the synchronousspeed. So induction motor is called
Asynchronous motor.
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23 October 2013 L.N Tripathy 3
Slip of Induction Motor[ ] [ ]
[ ]
[ ][ ] 100
%
s
s
s
s
Synchronous speed N Rotor Speed NSlip s
Synchronous Speed NN N
sN
Slip is Always expressed as percentage
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23 October 2013 L.N Tripathy 4
Frequency of Stator current &
Rotor current Stator current frequency is same as
supply frequency f
Rotor induced emf frequency or Rotorcurrent frequency= sf
Where
s is the slip
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23 October 2013 L.N Tripathy 5
Rotor frequency & Production
of steady torque. At stand still rotor induce voltage frequency fr
= stator induced voltage frequency fe orsupply frequency.
When rotor rotate the relative motionbetween stator flux and rotor conductorinduces voltages of frequency fr
fr = sfe called the slip frequency in
the rotor.Note:- wound rotor [Not squirrel cage] can be
used as frequency changer.
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23 October 2013 L.N Tripathy 6
CondAt stand still rotor frequency = stator
frequency fe [s=1]. So the field
produced by rotor current rotate assame speed as stator field and steadystarting torque is produced. It tends to
turn the rotor in the direction ofrotation of stator induced field.
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23 October 2013 L.N Tripathy 7
Cont.. Note:- The operating speed is never
equal to synchronous speed if it equal
to synchronous speed the rotorconductor will be stationary w.r.t statorfield[ relative speed is zero] no current
will be induced in rotor and hence notorque is produced.
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23 October 2013 L.N Tripathy 8
Cond When rotor rotate in the direction of
stator field the frequency of rotor
currents is sfe and they will produce arotating flux wave which will rotate atsns w.r.t rotor in the forward direction.
With respect to stator the speed of theflux produced by rotor current is
sns+n=sns+ns(1-s) = ns
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23 October 2013 L.N Tripathy 9
Cond Rotor current produce an air-gap flux which
rotate at synchronous speed w.r.t stator.
So the stator field and rotor field arestationary to each other and produce thesteady torque.
Torque for any mechanical rotor speed otherthan synchronous speed is calledasynchronous torque
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23 October 2013 L.N Tripathy 10
Power Stages of Induction
Motor Stator Input
Stator Iron & Copper loss
Rotor Input
Rotor Copper loss
Mechanical power Developed
Windage and friction loss
Rotor Output
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23 October 2013 L.N Tripathy 11
Equivalent Circuit of Induction
Motor V1 = E2 + I1(R1+jX1) --------- (1)
V1= Stator line to neutral Voltage
E2
= Counter emf ( Line to neutral) generated byresultant air gap flux
I1 = Stator current
R1 = Stator effective resistance
X1= stator leakage reactance.
Ic= Core loss component of current
Im = Magnetizing component of current.
I=Exciting current
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23 October 2013 L.N Tripathy 12
Stator equivalent circuit for a polyphase
induction motor.
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23 October 2013 L.N Tripathy 13
Rotor equivalent circuit for a polyphaseinduction motor at slip frequency.
Z2s = E2s/I2s = R2 + JsX2
R2 = Reffered rotor resistancesX
2
= Reffered rotor leakagereactance at slip frequency
Z2s = Slip frequency rotorLeakage Impedance
E2s = s E2 Assuming stator
& rotor have same numberof turns per phaseI2= I2s
I2 = Load current.
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23 October 2013 L.N Tripathy 14
Cond.. sE2/I2=Z2s=R2+jsX2
Dividing by s
Z2 = E2/I2 = R2/s + jX2
Z2 impedance of stationary rotor whichappear across the load terminal
R2/s represents the combine effect ofshaft load and rotor resistance.
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23 October 2013 L.N Tripathy 15
Single-phase equivalent circuit for apolyphase Induction motor.
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Alternative form of equivalent circuit.
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Equivalent circuits with the core-lossresistance Rc neglected
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23 October 2013 L.N Tripathy 18
Analysis of Equivalent Circuit.
2 22
2
2 2
2 222 2 2
2
2 2
( ) (2)
(3)
( )
1( )
(1 )
gap ph
rotor ph
mech gap rotor ph ph
mech ph
mech gap
rotor gap
RP n I
s
P n I RR
P P P n I n I Rs
sP n I R s
P s P
P sP
----------(4)
----------------------(5)
------------------------ (6)
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23 October 2013 L.N Tripathy 19
Power developed Inductionmotor
2 2
2
(1 ) (7)
( ) (8)
(9)
(10)
mech m mech s mech
phgapmechmech
m s s
shaft mech rotor
shaft
shaft mech rotor
m
P T s T
R
n IPP sT
P P P
PT T T
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23 October 2013 L.N Tripathy 20
Torque-speed Characteristic
s
ph
t
tmech
s
ph
s
gap
m
MechMech
EnK
Where
s
R
XsR
KT
jXsREI
sRInPPT
2
2
2
2
2
2
2
22
22
2
2
2
,
)/(
)/(
/
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23 October 2013 L.N Tripathy 21
Torque-speed Characteristic
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Operating mode of InductionMotor
Motoring Mode : 1s0
Generating Mode :s1
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23 October 2013 L.N Tripathy 23
Power Stages of InductionMotor
Stator Input
Stator Iron & Copper loss
Rotor Input
Rotor Copper loss
Mechanical power Developed
Windage and friction loss
Rotor Output
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23 October 2013 L.N Tripathy 24
Losses in induction motorLosses in 3-Phase Induction Motor
Fixed losses Variable Losses
Core loss Brush friction lossIn wound rotor
Bearing and frictionloss
Windageloss
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23 October 2013 L.N Tripathy 25
Variable loss
Variable losses
Stator Ohmic
loss
Rotor Ohmic
loss
Brush contactLoss for slip ringmotor
Stray load
loss
Fixed loss= Power input at no load-(stator I2R loss).Fixed loss can be determined by no load test of Induction Motor.Stray load losses is difficult to determine it is assumed when efficiencyIs calculated.
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23 October 2013 L.N Tripathy 26
Rotor current and rotor power
2 2
2 2
2 2
2 2
2
2 2
2 2
22
stand still= R
any slip per phase rotor leakage impedance = R ( )
phase rotor current at stand still =R
per phase rotor current at any slip(s) is I =R
Rotor leakageimpedance at X
At sX
Eper
X
sE
2 2
2 2( )sX
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23 October 2013 L.N Tripathy 27
Rotor power
2
2
-1 22
2
g
2 2 2
2 22
2 2 2 2
2 2 2 2
If rotor current lag the rotor voltage an angle
Power factor = Cos ,
= tan ( )
phase power input to rotor = Air gap Power = P
/R ( ) (R / ) ( )
g
sX
R
Per
P E I Cos
R R sCossX s X
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23 October 2013 L.N Tripathy 28
Cont..
22 2 2 2 2
2 2
2 2
22 2
2 2
2 2
2
2 2
g
2 2 2 2
2 2 2 2 2 2 2 2
2 2
2 2 2 2
/
(R / ) ( )
/
(R / ) ( )
/
P can be written as
/ /
1( )
(1 )
g
g
g
g
g
g g g
R sP E I Cos E I
s X
EP I R s
s X
P I R s
P I R s I R s I R I R
sP I R I R
s
P sP s P
Pg = (Rotor ohmic loss)+( Internal mechanical power devolved in rotor)
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23 October 2013 L.N Tripathy 29
Cont..
Rotor Ohmic loss = s(Power input torotor)
Internal mechanical power Developedby rotor Pm =I2
2R2(1-s)/s=(1-s)Pg Pm=(1-s)(Power input to Rotor)
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23 October 2013 L.N Tripathy 30
Starting of Induction Motor.
Direct on line starting
Stator resistor(or reactor starting)
Auto Transformer Starting
Star- Delta Starting
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23 October 2013 L.N Tripathy 31
Direct-On- Line Starting.
2 222
2
2 2 22
2
2
2
( )1
( )
( ) ( )
( )
( )
stest st
flefl fl
fl
fl
st st
st st
fl fl
RI
T I
SRT IIs
I effective stator Turns I Effective Rotor Turns
I I Effectiverotor to stator turn ratio
I I Effective rotor to stator turn ratio
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23 October 2013 L N Tripathy 32
Cond..
2
1
1
1
1
2
est st fl
efl fl
sc
st sc
est scfl
efl fl
T Is
T I
VIZ
VOn Direct switching I I
Z
T Is
T I