# INDUCTION MOTOR steady-state model - PowerPoint PPT Presentation

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## INDUCTION MOTOR steady-state model

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### SEE 3433 MESIN ELEKTRIK INDUCTION MOTOR steady-state model – PowerPoint PPT presentation

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Title: INDUCTION MOTOR steady-state model

1
• SEE 3433
• MESIN ELEKTRIK

2
• 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
3
(No Transcript)
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
5
• Construction

Distributed winding coils are distributed in
several slots Nc for each slot
?
MMF closer to sinusoidal - less harmonic
contents
6
• 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
7
• 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
8
• Phase a sinusoidal distributed winding

?
Airgap mmf
F(?)
?
?
2?
9
• 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
10
• 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
11
• 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?
?
12
• 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?
?
13
• 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?
?
14
• 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?
?
15
• 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?
?
16
• 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?
?
17
• 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?
?
18
• 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?
?
19
• Combination of 3 standing waves resulted in
ROTATING MMF wave

20
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21
(No Transcript)
22
Frequency of rotation is given by
p number of poles f supply frequency
known as synchronous frequency
23
• 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
24
Stator phase voltage equation Vs Rs Is
j(2?f)LlsIs Eag where Eag airgap voltage
or back emf Eag k f ?ag
Rotor phase voltage equation Er Rr Ir
js(2?f)Llr where Er induced emf in rotor
circuit Er /s (Rr / s) Ir j(2?f)Llr
25
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
26
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

27
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
28
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
29
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
30
Power and Torque
This torque expression is derived based on
approximate equivalent circuit
A more accurate method is to use Thevenin
equivalent circuit
31
Power and Torque
Tem
Pull out Torque (Tmax)
Trated
?r
0
?rated ?syn
sTm
s
1
0