induction motor

1. INDUCTION MOTOR
Scalar Control
(squirrel cage)
MEP 1523
ELECTRIC DRIVES

2. Scalar control of induction machine:
Control of induction machine based on steady-state
model (per phase SS equivalent circuit):
Rr’/s
+
Vs
–
Rs
Lls Llr’
+
Eag
–
Is Ir’
Im
Lm

3. Scalar control of induction machine
r
s
Trated
Pull out
Torque
(Tmax)
Te
s
sm
rated
rotor
TL
Te
Intersection point
(Te=TL) determines the
steady –state speed

4. Given a load T– characteristic, the steady-state speed
can be changed by altering the T– of the motor:
Scalar control of induction machine
Pole changing
Synchronous speed change with
no. of poles
Discrete step change in speed
Variable voltage (amplitude),
frequency fixed
E.g. using transformer or triac
Slip becomes high as voltage
reduced – low efficiency
Variable voltage (amplitude),
variable frequency
Using power electronics converter
Operated at low slip frequency

5. Variable voltage, fixed frequency
0 20 40 60 80 100 120 140 160
0
100
200
300
400
500
600
Torque
w (rad/s)
Lower speed  slip higher
Low efficiency at low speed
e.g. 3–phase 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

6. Variable voltage, variable frequency
At low slip
Constant V/f operation

7. Variable voltage, variable frequency – Constant V/f
If Φag is constant  Te α slip frequency

8. f
V
f
Eag


ag

Approximates constant air-gap flux when Eag is large
Eag = k f ag
= constant
Speed is adjusted by varying f - maintaining V/f to
approximate constant air-gap flux
How do we make constant ?
ag

Variable voltage, variable frequency – Constant V/f

9. 0 20 40 60 80 100 120 140 160
0
100
200
300
400
500
600
700
800
900
Torque
50Hz
30Hz
10Hz
Variable voltage, variable frequency – Constant V/f
Characteristic with constant ag


10. Vrated
frated
Vs
f
Variable voltage, variable frequency
Constant  constant V/f
ag

Constant slope

11. Constant V/f – open-loop
VSI
Rectifier
3-phase
supply IM
Pulse
Width
Modulator
s* +
Ramp
f
C
Variable voltage, variable frequency
V
rate limiter is needed to ensure the slip
change within allowable range (e.g. rated
value)

12. Constant V/f – open-loop
Variable voltage, variable frequency
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2,
Lr=Ls= 0.0971 H, Lm = 0.0955, J = 0.046 kgm2 , Load: k2
is
To Workspace2
speed
To Workspace1
torque
To Workspace
In1Out1
Subsystem
Signal 1
Signal Builder
Scope1
Scope
Rate Limiter
Va
Vb
Vc
isd
isq
ird
speed
Vd
irq
Vq
Te
Induction Machine
In1
Out1
Out2
Out3
Constant V/Hz

13. Constant V/f – open-loop
Variable voltage, variable frequency
0 0.5 1 1.5 2 2.5 3 3.5
0
10
20
30
40
50
Signal 1
Time (sec)
constant_vhz_withoutBoost/Signal Builder : Group 1
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2,
Lr=Ls= 0.0971 H, Lm = 0.0955, J = 0.046 kgm2 , Load: k2

14. Constant V/f – open-loop
Variable voltage, variable frequency
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2,
Lr=Ls= 0.0971 H, Lm = 0.0955, J = 0.046 kgm2 , Load: k2
0 20 40 60 80 100 120 140 160
-50
0
50
100
150
200
250
300
350
400
450

15. Constant V/f – open-loop
Variable voltage, variable frequency
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2,
Lr=Ls= 0.0971 H, Lm = 0.0955, J = 0.046 kgm2 , Load: k2
0 20 40 60 80 100 120 140 160 180 200
-100
0
100
200
300
400
500
0 0.5 1 1.5
-50
0
50
100
150
200
0 0.5 1 1.5
-200
0
200
400
600
With almost no rate limiter

16. Constant V/f – open-loop
Variable voltage, variable frequency
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2,
Lr=Ls= 0.0971 H, Lm = 0.0955, J = 0.046 kgm2 , Load: k2
With 628 rad/s2
-20 0 20 40 60 80 100 120 140 160
-50
0
50
100
150
200
250
300
350
400
450
0 0.5 1 1.5
-50
0
50
100
150
200
0 0.5 1 1.5
-200
0
200
400
600

17. Problems with open-loop constant V/f
At low speed, voltage drop across stator impedance is
significant compared to airgap voltage - poor torque
capability at low speed
Solution:
(i) Voltage boost at low frequency
(ii) Maintain Im constant  stator current control
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems

18. Variable voltage, variable frequency
0 20 40 60 80 100 120 140 160 180
0
50
100
150
200
250
300
350
400
450
500
•Torque deteriorate at low frequency – hence compensation commonly
performed at low frequency
•In order to truly compensate need to measure stator current – seldom
performed
Constant V/f – open-loop low speed problems (i) voltage boost

19. Variable voltage, variable frequency
•Torque deteriorate at low frequency – hence compensation commonly
performed at low frequency
•In order to truly compensate need to measure stator current – seldom
performed
0 20 40 60 80 100 120 140 160 180
0
50
100
150
200
250
300
350
400
450
500
With voltage
boost of Irated*Rs
Constant V/f – open-loop low speed problems (i) voltage boost

20. Voltage boost at low frequency
Vrated
frated
Linear offset
Non-linear offset – varies with Is
Boost
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (i) voltage boost

21. VSI
Rectifier
3-phase
supply IM
Pulse Width
Modulator
Vboost
s*
+
+ V
Ramp
f
C
Variable voltage, variable frequency
Idc
+
Vdc
-
Constant V/f – open-loop low speed problems (i) voltage boost

22. Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (i) Constant Im
ag, constant → Eag/f , constant → Im, constant (rated)
Rr’/s
+
Vs
–
Rs
Lls Llr’
+
Eag
–
Is Ir’
Im
Lm
maintain at rated
Controlled to maintain Im at rated

23. Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (i) Constant Im
s
r
m
lr
r
lr
m I
s
R
)
L
L
(
j
s
R
L
j
I






m
r
r
r
r
r
r
s I
s
R
L
1
j
s
R
L
j
I
















• Current is controlled using current-
controlled VSI
• The problem of stator impedance drop is
solved
• Dependent on rotor parameters –
sensitive to parameter variation ,
I
1
T
1
j
1
T
j
I m
r
r
r
slip
r
slip
s
















From per-phase equivalent circuit,

24. VSI
Rectifier
3-phase
supply IM
*
+
+ |Is|
slip
C
Current
controller
s
PI
+
Variable voltage, variable frequency
r
-
Current reference generator
Tacho
Constant V/f – open-loop low speed problems (i) Constant Im

25. Constant V/f
Variable voltage, variable frequency
Poor speed regulation
Problems with open-loop constant V/f
Solution:
(i) Slip compensation
(ii) Closed-loop control

26. Constant V/f – poor speed regulation: (i) slip compensation
Variable voltage, variable frequency
T
ωr (rad/s)
ωslip1
ωr1
T1
ωr2≈ωs1*
T2
Motor characteristic
AFTER slip
compensation
ωs2*=ωs1*+ωslip1
ωslip1
ωs1*
Tload
Motor characteristic
BEFORE slip
compensation

27. Constant V/f – poor speed regulation: (i) slip compensation
VSI
Rectifier
3-phase
supply IM
Pulse Width
Modulator
Vboost
Slip speed
calculator
s*
+
+
+
+ V
Vdc Idc
Ramp
f
C
Variable voltage, variable frequency
Idc
+
Vdc
-

28. Variable voltage, variable frequency
How is the slip frequency calculated ?
Pdc= VdcIdc
Pmotor,in= Pdc – Pinv,losses
Pair-gap
Pmotor,in
Stator Copper
lossess
Stator Core
losses
ROTOR
STATOR
+
Vdc

Idc
INV
Constant V/f – poor speed regulation: (i) slip compensation

29. Variable voltage, variable frequency
How is the slip frequency calculated ?
Pair-gapc = Tesyn Te = Pair-gap/syn
For constant V/f control,
rated
,
slip
rated
,
e
slip
e
T
T


 rated
,
e
rated
,
slip
e
slip
T
T



Constant V/f – poor speed regulation: (i) slip compensation

30. Variable voltage, variable frequency
• Require speed encoder
• Increase complexity
Constant V/f – poor speed regulation: (i) closed-loop speed