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The stator winding are supplied with balanced three-phase AC voltage,

which produce induced voltage in the rotor windings. It is possible toarrange the distribution of stator winding so that there is an effect of

multiple poles, producing several cycle of magnetomotive force (mmf) or

field around the air gap.

The speed of rotation of field is called the synchronous speedws , which

is defined by :

ps

ww

2

s is syncronous speed [rad/sec]Ns issyncronousspeed [rpm]

p is numbers of poles

is the supply frequency [rad/sec]

f is the supply frequency [Hz]

Nm is motor speed

Stator

Three-phase

windings

RotorAir gap

w T

Rotor windings

Three-

phase

supply

mws

w

p

f

Ns

120

or

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Stator

Three-phase

windings

RotorAir gap

w T

Rotor windings

Three-phase

supply

mws

w

The rotor speed or motor speed is : )1( Ssm ww

Where S is slip, as defined as :S

mSSw

ww Or

S

mS

N

NNS

The motor speed

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Equivalent Circuit Of Induction Motor

Stator

Three-phase

windings

RotorAir gap

w T

Rotor windings

Three-

phasesupply

mws

w

Stator Air gap motor

Vs

Is

Im Ir

Xs XrRs

RmXm

Rr/s

Where :

Rs is resistance per-phase of stator winding

Rr is resistance per-phase of rotor winding

Xs is leakage reactance per-phase of the

winding stator

Xs is leakage reactance per-phase of the

winding rotor

Xmis magnetizing reactance

Rm is Core losses as a reactance

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Performance Characteristic of

Induction Motor

Stator copper loss :

Stator Air gap motor

Vs

Is

Im Ir

Xs XrRs

RmXm

Rr/s

sscus RIP 23

'2')(3 rrcur RIP Rotor copper loss :

m

s

m

mc

R

V

R

VP

22

33 Core losses :

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S

RIP rrg

'

2')(3

)1()(3

'

2' SS

RIPPP rrcurgd

)1( SPP gd

-Power developed on air gap (Power fropm stator to

rotor through air gap) :

Performance Characteristic of

Induction Motor

-Power developed by motor :

or

-Torque of motor :

m

dd

PTw

s

g

S

g P

S

SP

ww

)1(

)1(or

m

dd

NPT2

60or

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mssi IVP cos3

gcusc PPP

Input power of motor :

Performance Characteristic of

Induction Motor

loadnodo PPP

gcusc

loadnod

i

o

PPP

PP

P

P

Output power of motor :

Efficiency :

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)( cuscg PPP

loadnod PP

SP

SP

P

P

g

g

g

d

1

)1(

If

and

so, the efficiency can calculated as :

Performance Characteristic of

Induction Motor

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)( 222

ssm XRX Generally, value of reactance magnetization Xm >> value Rm (core

losses) and also

So, the magnetizing voltage same with the input voltage : sm VV

Therefore, the equivalent circuit is ;

Stator Air gap motor

Vs

Is

Im Ir

Xs XrRs

RmXm

Rr/s

Stator Air gap rotor

Vs

Ii

Im Ir

Xs XrRs

Rr/s

PiPo

Is=Ir

Xm

Performance Characteristic of

Induction Motor

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)(

)()(

''

''

rsmr

s

rsmrsm

i

XXXjS

RR

S

RRjXXXX

Z

Total Impedance of this circuit is :

Performance Characteristic of

Induction Motor

Stator Air gap rotor

Vs

Ii

Im Ir

Xs XrRs

Rr/s

PiPo

Is=Ir

Xm

The rotor current is :

2

1

2'

2'

'

rsr

s

sr

XXS

RR

VI

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2'

2'

2'3

rsr

ss

srd

XXS

RRS

VRT

w

Stator Air gap rotor

Vs

Ii

Im Ir

Xs XrRs

Rr/s

PiPo

Is=Ir

Tmax

Smax

Tst

Td

S=0ws

Ns

S=1

TL

S=Smwm

NmNm =0

Tm=TLOperating point

Torque speed Characteristic

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Tmax

Smax

Tst

S=0

ws

Ns

S=1

S=Sm

Nm =0

wsws =0ws

-Tmax

-Smax

S=-1 S=2

Forward

regenerationForward

motoring

Reverse

plugging

wswm

wswm

wswm

Torque

Three region operation :

1. Motoring :

2. Regenerating :

3. Plugging :

10 S

0S

21 S

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Starting speed of motor is wm= 0 or S = 1,

Performance Characteristic of

Induction Motor

Starting torque of motor is :

2'

2'

2'

3

rsr

ss

srst

XXS

RR

VRT

w

Slip for the maximum torque Smaxcan be found by setting : 0dSTd d

So, the slip on maximum torque is :

2

12'2

'

max

rss

r

XXR

RS

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2'2

2

max

2

3

rssss

s

XXRR

VT

w

Performance Characteristic of

Induction Motor

Torque maximum is :

And the maximum regenerative torque can be found as :

2'

2

2

max

2

3

rssss

s

XXRR

V

T w

Where the slip of motor s = - Sm

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2'

2'

2'3

rs

r

ss

srd

XXS

RRS

VRT

w

Speed-Torque Characteristic :

2

'2'

S

RRXX rsrs

2'2'3

rss

srd

XXS

VRT

w

2'2'3

rss

srst

XX

VRT

w

For the high Slip S. (starting)

So, the torque of motor is :

And starting torque (slip S=1) is :

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sr

rs

RS

RXX

'2'

rs

sd

R

SVT

'

3 2

w

For low slip S region, the motor speed near unity or synchronous

speed, in this region the impedance motor is :

So, the motor torque is :

21

2'2

'

max

rss

r

XXR

RS

And the slip at maximum torque is :

The maximum motor torque is :

2'

2'

2'3

rsr

ss

srd

XXS

RRS

VRT

w