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AC DRIVES
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INDUCTION MOTOR
steady-state model
(squirrel cage)
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Construction
a
b
b
c
c
a
Stator 3-phase winding
Rotor squirrel cage / wound
120o120o
120o
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Construction
a
a
Single N turn coil carrying current i
Spans 180o elec Permeability of iron >> Qo all MMF drop appear in airgap
U
UTT
/2-T/2-T
Ni / 2
-Ni / 2
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ConstructionDistributed winding
coils are distributed in several slots
Nc for each slot
U
UTT/2-T/2-T
(3Nc
i)/2
(Nci)/2
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Construction
Distributed winding (full-pitch)
The resultant MMF is the total contribution of MMF from
each coil
Considering only the space-fundamental component,
Concentrated Distributed
Distributed space fundamental
Concentrated space fundamental
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Phase a sinusoidal distributed winding
U
U
Airgap mmf
F(U)
T 2T
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Sinusoidal winding for each phase produces space sinusoidal
MMF and flux
Sinusoidal current excitation (with frequency [s) in a phaseproduces space sinusoidal standing wave MMF
Combination of 3 standing waves resulted in MMF wave rotatingat:
f2p
2s T![
p number of poles
f supply frequency
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Rotating flux induced:
emf in stator winding (known as back emf)
Emf in rotor winding
Rotor flux rotating at synchronous frequency
Rotor current interact with flux producing torque
Rotor ALWAYS rotate at frequency less than synchronous, i.e. at
slip speed:
[sl = [s [r
Ratio between slip speed and synchronous speed known as slip
s
rss[
[[!
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Stator voltage equation:
Vs = Rs Is + j(2Tf)LlsIs + Eag
Eag airgap voltage or back emf
Eag = k fJag
Rotor voltage equation:
Er= Rr Ir+ js(2Tf)Llr
Er induced emf in rotor circuit
Er/s = (Rr/ s) Ir+ j(2Tf)Llr
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Perphase equivalent circuit
Rr/s
+
Vs
Rs LlsL
lr
+
Eag
Is
Ir
ImLm
Rs stator winding resistance
Rr rotor winding resistance
Lls stator leakage inductanceLlr rotor leakage inductance
Lm mutual inductance
s slip
+
Er/s
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We know Eg and Errelated by
@rotor voltage equation becomes
Eg = (Rr / s) Ir + j(2Tf)Llr Ir
a
s
E
E
g
r ! Where a is the winding turn ratio
The rotor parameters referred to stator are:
2
lrlr2
rrrr
a
'LL,
a
'RR,)'I(aI !!!
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Perphase equivalent circuit
Rr/s
+
Vs
Rs Lls Llr
+
Eag
Is Ir
Im
Lm
Rs stator winding resistance
Rr rotor winding resistance referred to stator
Lls stator leakage inductanceLlr rotor leakage inductance referred to stator
Lm mutual inductance
Ir rotor current referred to stator
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Power and Torque
Power is transferred from stator to rotor via airgap,known as airgap power
? As1s
'RI3'RI3
s
'RI3P r2'rr
2'r
r2'rag !!
Lost in rotor
winding
Converted to mechanical
power = (1s)Pag
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Power and Torque
Mechanical power, Pm = Tem [r
But, s[s = [s - [r [r= (1-s)[s
@Pag = Tem
[s
s
r
2'
r
s
ag
ems
'RI3PT
[!
[!
Therefore torque is given by:
2lrls2
rs
2s
s
rem
'XXs
'RR
V
s
'R3T
[!
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Power and Torque
1 0
[rs
Trated
Pull out
Torque
(Tmax)
Tem
0 [rated [s
2lrls
2
s
rm
XXR
Rs
s!
s[
!2
lrls2
ss
2
s
s
maxXXRR
V
s
3T
sm
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Steady state performance
The steady state performance can be calculated fromequivalent circuit, e.g. using Matlab
Rr/s
+
Vs
RsLls Llr
+
Eag
Is Ir
Im
Lm
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Steady state performance
Rr/s
+
Vs
Rs
Lls Llr
+
Eag
Is Ir
Im
Lm
e.g. 3phase squirrel cage IM
V = 460 V Rs= 0.25;
Rr=0.2;
Lr= Ls = 0.5/(2*pi*50) Lm=30/(2*pi*50)
f = 50Hz p = 4
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Steady state performance
-2 -1.
-1 -0.
0 0.
1 1.
2-800
- 00
- 00
-200
0
20 0
00
00
orque
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Steady state performance
0 0.1 0.2 0.3 0. 0. 0. 0. 0.8 0. 10
0. 1
0. 2
0. 3
0.
0.
0.
0.
0. 8
0.
1
fficienc
y
(1-s)