INDUCTION MOTOR steady-state model

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INDUCTION MOTORsteady-state model

• SEE 3433
• MESIN ELEKTRIK

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• Construction

Stator windings of practical machines are
distributed
Coil sides span can be less than 180o
short-pitch or fractional-pitch or chorded
winding
If rotor is wound, its winding the same as stator
Stator 3-phase winding Rotor squirrel cage /
wound
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4

• 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
?
MMF closer to sinusoidal - less harmonic
contents
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• Construction

The harmonics in the mmf can be further reduced
by increasing the number of slots e.g. winding
of a phase are placed in 12 slots
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• Construction

In order to obtain a truly sinusoidal mmf in the
airgap

• the number of slots has to infinitely large

• conductors in slots are sinusoidally distributed

In practice, the number of slots are limited it
is a lot easier to place the same number of
conductors in a slot
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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

This is the excitation current which is
sinusoidal with time
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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

0
t 0
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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

i(t)
t
t1
F(?)
t t1
?
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

i(t)
t
t2
F(?)
t t2
?
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

i(t)
t
t3
F(?)
t t3
?
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

i(t)
t
t4
F(?)
t t4
?
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

i(t)
t
t5
F(?)
t t5
?
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

i(t)
t
t6
F(?)
t t6
?
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

i(t)
t
t7
F(?)
t t7
?
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

i(t)
t
t8
F(?)
t t8
?
2?
?
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• Combination of 3 standing waves resulted in
  ROTATING MMF wave

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Frequency of rotation is given by
p number of poles f supply frequency
known as synchronous 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 to produce 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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Induced voltage
Flux density distribution in airgap Bmaxcos ?

Sinusoidally distributed flux rotates at ?s and
induced voltage in the phase coils
Maximum flux links phase a when ?t 0. No flux
links phase a when ?t 90o
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Induced voltage

?a ? flux linkage of phase a
?a N ?p cos(?t)
By Faradays law, induced voltage in a phase coil
aa is
Maximum flux links phase a when ?t 0. No flux
links phase a when ?t 90o
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Induced voltage
In actual machine with distributed and
short-pitch windinds induced voltage is LESS than
this by a winding factor Kw

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Stator phase voltage equation Vs Rs Is
j(2?f)LlsIs Eag Eag airgap voltage
or back emf (Erms derive previously) Eag k f
?ag
Rotor phase 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 N1/N2
The rotor parameters referred to stator are

• rotor voltage equation becomes
• Eag (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 Pm
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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
This torque expression is derived based on
approximate equivalent circuit
A more accurate method is to use Thevenin
equivalent circuit
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Power and Torque
Tem
Pull out Torque (Tmax)
Trated
?r
0
?rated ?syn
sTm
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