AC Machine Stator
‘b’ phase axis
1200
1200 ‘a’ phase axis
1200
‘c’ phase axis
induction motor 1
Currents int different
t
phases of AC Machine
01 12
Amp
t0 t1 t2 t3 t4
1 Cycle time
induction motor 2
MMF Due to ‘a’ phase current
1
0.8 Axis of phase a
t0
0.6
0.4
t01
0.2
Fa 0 a’ a
a’
-0.2 t12
-0.4
-0.6
t2
-0.8
-1
-90 -40 10 60 110 160 210 260
Space angle (theta) in degrees
induction motor 3
a Fc RMF(Rotating Magnetic Field)
c
’ b’ 1.5
Fa F t = t 0= t 4
1
Fa F
b c 0.5 Fc
a’ Fb 0
Fb
-0.5
t = t 0 = t4 -1
-1.5
-93 10 113 216
F Space angle () in degrees
Fb a Fc Fb a
b’ a
c’ b’ b’
Fca c
’ ’
b c
F b c b c
a’ Fc a’ Fc a’ Fb
t = t1 t = t2 t = t3
induction motor 4
F
RMF(Rotating Magnetic Field)
-Analogy with DC machines
The salient field structure in DC
machines is mimicked along with speed
in an AC machines by a multiphase (2 or
more) winding. The number of poles are
determined by winding distribution and is
independent of the number of phases.
The rotational speed is determined by the supply frequency and
the number of poles, such that an observer in air-gap counts same
number of poles per second, meaning the more the number of poles
the slower the machine will run and vice-versa.
induction motor 5
Induction Motor
day in the low and medium horsepower range
ction
ble using V/f or Field Oriented Controllers
tors in areas where traditional DC Motors
mining or explosive environments
g on motor construction: Squirrel Cage
ost of them run with a lagging power factor
induction motor 6
Squirrel Cage Rotor
induction motor 7
Slip Ring Rotor
•The rotor contains windings similar to stator.
•The connections from rotor are brought out using slip rings that
are rotating with the rotor and carbon brushes that are static.
induction motor 8
induction motor 9
induction motor 10
Torque Production in an Induction Motor
•In a conventional DC machine field is stationary and the
current carrying conductors rotate.
•We can obtain similar results if we make field structure
rotating and current carrying conductor stationary.
•In an induction motor the conventional 3-phase winding
sets up the rotating magnetic field(RMF) and the rotor
carries the current carrying conductors.
•An EMF and hence current is induced in the rotor due to
the speed difference between the RMF and the rotor,
similar to that in a DC motor.
•This current produces a torque such that the speed
difference between the RMF and rotor is reduced.
induction motor 11
Slip in Induction Motor
•However, this speed difference cannot become zero because that
would stop generation of the torque producing current itself.
•The parameter slip ‘s’ is a measure of this relative speed difference
ns n s 120 f1
s n s ; p # of poles
n p
s s
where ns,s,f1 are the speeds of the RMF in RPM ,rad./sec and
supply frequency respectively
n, are the speeds of the motor in RPM and rad./sec respectively
•The angular slip frequency and the slip frequency at which voltage
is induced in the rotor is given by
N2
2 s , f 2 sf1 , E2 s s E1 N1 Stator turns N 2 Rotor turns
N1induction motor 12
Induction motor Equivalent Circuit
induction motor 13
Relation between air-gap, gross mechanical
power and rotor copper loss
Pag : Pmech : P2 1 : 1 s : s
Pmech
Internal efficiency = 1 s
Pag
Implies lower the slip higher is the induction motor efficiency
induction motor 14
Approximate Equivalent Circuit
•Assumes negligible magnetizing current
• Note Rc has been removed.
The sum of core losses and the windage and friction loses are treated
as constant. This is because as speed increases rotor core loss
decreases (lower f2) but windage and frictionloses increase.With
decrease of speed the converse is true. Thus the sum is constant at
any speed and is termed as rotational loss.
induction motor 15
IEEE Equivalent Circuit
•Assumes 30-50% magnetizing current and drop across R1+jX1 not
negligible
• As before, the sum of core losses and the windage and friction loses are
treated as constant.
induction motor 16
Thevnin’s equivalent of the
IEEE Equivalent Circuit
• This is done by applying Thevenin’s theorem and treating the rotor
side as load
Xm
Vth K thV1 , Rth K th2 R1 , X th X 1 , K th
X m X1
induction motor 17
Determining equivalent circuit parameters
Uses no-load test and blocked rotor tests to determine them
induction motor 18
Performance Characteristics(1)
R2
Pmech Tmech mech I 22 (1 s ) Pag (1 s );
s
4f1
mech (1 s ) syn ; syn p
Pmech Pag
Tmech
mech syn
induction motor 19
Performance Characteristics(2)
Pmech Pag 1 '2 R2'
Tmech I2
mech syn syn s
1 Vth2 R2'
Tmech
syn ( Rth R2' / s ) 2 ( X th X 2' ) 2 s
induction motor 20
Performance Characteristics(3)
Case 1: s small (close to zero )
R2'
Then Rth
s
R2'
and X th X 2'
s
1 Vth2
Tmech s
syn ( R2 )
'
Tmech s
induction motor 21
Performance Characteristics(4)
Case 2: s l arg e(close to one)
R2'
Then Rth X th X 2'
s
1 Vth2 R2'
Tmech
syn ( X th X 2' ) s
1
Tmech
s
induction motor 22
Performance Characteristics(5)
Combining case 1 and 2 the approximate torque speed characteristics
would look approximately like:
Tmech
Tmax
nm ns Speed (n)
induction motor 23
Performance Characteristics(6)
How to obtain Tmax? By differentiating the following equation
with respect to s and equating it to zero.
1 Vth2 R2'
Tmech
syn ( Rth R2' / s) 2 ( X th X 2' ) 2 s
One can obtain the following:
1 Vth2
Tmax
2 syn R R 2 ( X X ' ) 2
th th th 2
2
1 Vth2 p Vth 1
( small R1 )
2 syn ( X th X 2 ) 2 1 ( Lth L2 )
' '
R2'
Slip at maximum torque = sTmax
[ Rth2 ( X th X 2' ) 2 ]
induction motor 24
Performance Characteristics(7)
(Speed Control)
Speed control by varying Speed control by varying
rotor resistance (vary supply voltage and frequency
Tmax by varying sTmax) (Vth/1)
(inefficient) induction motor
(efficient) 25
Performance Characteristics(8)
Also using
1 Vth2 R2'
Tmech
syn ( R2' / s) 2 ( X th X 2' ) 2 s
and
R2'
sTmax
( X th X 2' )
for small R1 one can write the following:
Tmax sT2max s 2
Tmech 2 sTmax s
induction motor 26
Performance Characteristics(9)
induction motor 27
Different modes of IM operation
induction motor 28
Different modes of IM operation
induction motor 29
Speed control of SRIM with ext. resistors
induction motor 30
Applications of SRIM
induction motor 31
Wind Power applications of SRIM
induction motor 32
induction motor 33
