INDUCTION MOTOR steadystate model squirrel cage

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INDUCTION MOTORsteady-state model(squirrel cage)

• MEP 1422
• ELECTRIC DRIVES

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• Construction

a
c
b
c
b
a
Stator 3-phase winding Rotor squirrel cage /
wound
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• Construction

Single N turn coil carrying current i Spans 180o
elec
Permeability of iron gtgt ?o ? all MMF drop
appear in airgap
a
a
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• Construction

Distributed winding coils are distributed in
several slots Nc for each slot
?
(3Nci)/2
(Nci)/2
?
-?/2
?
?/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,
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• Phase a sinusoidal distributed winding

?
Airgap mmf
F(?)
?
?
2?
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• Sinusoidal winding for each phase produces space
  sinusoidal MMF and flux
• Sinusoidal current excitation (with frequency ?s)
  in a phase produces space sinusoidal standing
  wave MMF
• Combination of 3 standing waves resulted in MMF
  wave rotating at

p number of poles f supply frequency
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(No Transcript)
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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

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Stator voltage equation Vs Rs Is
j(2?f)LlsIs Eag Eag airgap voltage or back
emf Eag k f ?ag
Rotor voltage equation Er Rr Ir
js(2?f)Llr Er induced emf in rotor
circuit Er /s (Rr / s) Ir j(2?f)Llr
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Perphase equivalent circuit
Llr
Ir
Lls
Rs
Vs
Eag
Er/s
Is
Rr/s
Lm
Im
Rs stator winding resistance Rr rotor winding
resistance Lls stator leakage inductance Llr
rotor leakage inductance Lm mutual
inductance s slip
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We know Eg and Er related by
Where a is the winding turn ratio
The rotor parameters referred to stator are

• rotor voltage equation becomes
• Eg (Rr / s) Ir j(2?f)Llr Ir

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Perphase equivalent circuit
Rs stator winding resistance Rr rotor
winding resistance referred to stator Lls
stator leakage inductance Llr 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
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
Therefore torque is given by
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Power and Torque
Tem
Pull out Torque (Tmax)
Trated
?r
0
?rated ?s
sm
s
1
0
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Steady state performance
The steady state performance can be calculated
from equivalent circuit, e.g. using Matlab
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Steady state performance
e.g. 3phase squirrel cage IM V 460 V Rs
0.25 ? Rr0.2 ? Lr Ls 0.5/(2pi50)
Lm30/(2pi50) f 50Hz p 4
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Steady state performance
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Steady state performance
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Steady state performance