the stator winding are supplied with balanced three-phase ac voltage, which produce induced voltage...
TRANSCRIPT
The stator winding are supplied with balanced three-phase AC voltage, which produce induced voltage in the rotor windings. It is possible to arrange 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 speed s , which is defined by :
ps
2
ωs is syncronous speed [rad/sec] Ns is syncronous speed [rpm] p is numbers of polesω is the supply frequency [rad/sec] f is the supply frequency [Hz] Nm is motor speed
Stator
Three-phasewindings
RotorAir gap
T
Rotor windings
Three-phasesupply
ms
p
fNs
120
or
Stator
Three-phasewindings
RotorAir gap
T
Rotor windings
Three-phasesupply
ms
The rotor speed or motor speed is : )1( Ssm
Where S is slip, as defined as : S
mSS
Or
S
mS
N
NNS
The motor speed
Equivalent Circuit Of Induction MotorEquivalent Circuit Of Induction Motor
Stator
Three-phasewindings
RotorAir gap
T
Rotor windings
Three-phasesupply
ms
Stator Air gap motor
Vs
Is
Im Ir’
Xs Xr’Rs
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
Xm is magnetizing reactance
Rm is Core losses as a reactance
Performance Characteristic of Induction Motor
Stator copper loss :
Stator Air gap motor
Vs
Is
Im Ir’
Xs Xr’Rs
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 :
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
PT
s
g
S
g P
S
SP
)1(
)1(or
m
dd N
PT
2
60or
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 :
)( 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
)( 222ssm 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 Xr’Rs
RmXm
Rr’/s
Stator Air gap rotor
Vs
Ii
Im Ir’
Xs Xr’Rs
Rr’/s
PiPo
Is=Ir’
Xm
Performance Characteristic of Induction Motor
)(
)()(
''
''
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 Xr’Rs
Rr’/s
PiPo
Is=Ir’
Xm
The rotor current is :
2
1
2'
2'
'
rsr
s
sr
XXS
RR
VI
2'
2'
2'3
rsr
ss
srd
XXS
RRS
VRT
Stator Air gap rotor
Vs
Ii
Im Ir’
Xs Xr’Rs
Rr’/s
PiPo
Is=Ir’
Tmax
Smax
Tst
Td
S=0s
Ns
S=1
TL
S=Smm
NmNm =0
Tm=TL
Operating point
Torque – speed Characteristic
Tmax
Smax
Tst
S=0s
Ns
S=1
S=Sm
Nm =0
ss =0s
-Tmax
-Smax
S=-1 S=2
Forwardregeneration
Forwardmotoring
Reverseplugging
smsm
sm
Torque
Three region operation :
1. Motoring :
2. Regenerating :
3. Plugging :
10 S
0S
21 S
Starting speed of motor is m = 0 or S = 1,
Performance Characteristic of Induction Motor
Starting torque of motor is :
2'
2'
2'3
rsr
ss
srst
XXS
RR
VRT
Slip for the maximum torque Smax can be found by setting : 0dS
Td d
So, the slip on maximum torque is :
212'2
'
max
rss
r
XXR
RS
2'2
2
max
2
3
rssss
s
XXRR
VT
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
VT
Where the slip of motor s = - Sm
2'
2'
2'3
rsr
ss
srd
XXS
RRS
VRT
Speed-Torque Characteristic :
2'
2'
S
RRXX rsrs
2'
2'3
rss
srd
XXS
VRT
2'
2'3
rss
srst
XX
VRT
For the high Slip S. (starting)
So, the torque of motor is :
And starting torque (slip S=1) is :
sr
rs RS
RXX
'2'
rs
sd R
SVT
'
3 2
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 :
212'2
'
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
Tmax
S=0s
Ns
S=1
TL
Nm =0
Td
Vs1Vs Vs2> >
12
Tst
Tst1
Tst2
Stator Voltage Control
Controlling Induction Motor Speed by Adjusting The Stator Voltage Td
IMAC
VariableVoltageSources
Vs
Stator airgap
rotor
Ii
Im Ir’
Xs Xr’Rs
Rr’/s
PiPo
Is=Ir’
Vs
2'
2'
2'3
rsr
ss
srd
XXS
RRS
VRT