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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)