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

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

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

4. Scalar control of induction machine
Given a load T– characteristic, the steady-state speed can be changed by altering the T– of the motor:
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
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
Lower speed  slip higher
Low efficiency at low speed

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

7. If Φag is constant  Te α slip frequency
Variable voltage, variable frequency – Constant V/f
If Φag is constant  Te α slip frequency
(regardless of the synchronous
frequency)

8. Approximates constant air-gap flux when Eag is large
Variable voltage, variable frequency – Constant V/f
How do we make constant ?
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

9. Characteristic with constant
Variable voltage, variable frequency – Constant V/f
Characteristic with constant

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

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

12. Constant V/f – open-loop : Power converters
Variable voltage, variable frequency
Constant V/f – open-loop : Power converters +
Vdc  IM
3-phase
supply
Uncontrolled
Diode rectifier
Crow bar
circuit
3-phase VSI with
PWM control
Power flow only in one direction
Transistor will be switched on when capacitor voltage increases beyond allowable during dynamic braking
Power flow in both direction

13. Constant V/f – open-loop : Power converters
Variable voltage, variable frequency
Constant V/f – open-loop : Power converters +
Vdc  IM
Let’s assume we have 415 V (rms)
Assuming output of rectifier is
In actual the value is lower if LC filter is used to remove the AC components.
Peak fundamental phase voltage for ma =1:
Therefore RMS of fundamental line-line voltage is
With overmodulation, this can be increased to (0.78)587 = 458V

14. Constant V/f – open-loop
Variable voltage, variable frequency
Constant V/f – open-loop
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2, Lr=Ls= H, Lm = , J = kgm2 , Load: k2

15. Constant V/f – open-loop
Variable voltage, variable frequency
Constant V/f – open-loop
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2, Lr=Ls= H, Lm = , J = kgm2 , Load: k2
constant_vhz_withoutBoost/Signal Builder : Group 1
Signal 1 50 40 30 20 10
0.5 1
1.5 2
2.5 3
3.5
Time (sec) 15

16. Constant V/f – open-loop
Variable voltage, variable frequency
Constant V/f – open-loop
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2, Lr=Ls= H, Lm = , J = kgm2 , Load: k2 16

17. Constant V/f – open-loop
Variable voltage, variable frequency
Constant V/f – open-loop
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2, Lr=Ls= H, Lm = , J = kgm2 , Load: k2
With almost no rate limiter 17

18. Constant V/f – open-loop
Variable voltage, variable frequency
Constant V/f – open-loop
Simulation example: 415V, 50Hz, 4 pole, Rs = 0.25, Rr = 0.2, Lr=Ls= H, Lm = , J = kgm2 , Load: k2
With 628 rad/s2 18

19. Constant V/f – open-loop low speed problems
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems
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

20. Constant V/f – open-loop low speed problems (i) voltage boost
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (i) voltage boost
Torque deteriorate at low frequency – hence compensation commonly performed at low frequency
In order to truly compensate need to measure stator current – seldom performed

21. Constant V/f – open-loop low speed problems (i) voltage boost
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (i) voltage boost
With voltage boost of Irated*Rs
Torque deteriorate at low frequency – hence compensation commonly performed at low frequency
In order to truly compensate need to measure stator current – seldom performed

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

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

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

25. Constant V/f – open-loop low speed problems (ii) Constant Im
Variable voltage, variable frequency
Constant V/f – open-loop low speed problems (ii) Constant Im
From per-phase equivalent circuit,
Current is controlled using current-controlled VSI
The problem of stator impedance drop is solved
Dependent on rotor parameters – sensitive to parameter variation

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

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

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

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

30. Constant V/f – poor speed regulation: (i) slip compensation
Variable voltage, variable frequency
Constant V/f – poor speed regulation: (i) slip compensation
How is the slip frequency calculated ? +
Vdc 
Idc
INV
Pdc= VdcIdc
Pmotor,in= Pdc – Pinv,losses
Pmotor,in
Stator Copper
lossess
Stator Core
losses
ROTOR
STATOR
Pair-gap 30

31. Constant V/f – poor speed regulation: (i) slip compensation
Variable voltage, variable frequency
Constant V/f – poor speed regulation: (i) slip compensation
How is the slip frequency calculated ?
Pair-gapc = Tesyn
Te =  Pair-gap/syn
For constant V/f control, 31

32. Constant V/f – poor speed regulation: (ii) closed-loop speed
Variable voltage, variable frequency
Constant V/f – poor speed regulation: (ii) closed-loop speed
Require speed encoder
Increase complexity 32

33. INDUCTION MOTOR DRIVES
Speed control : Constant V/Hz
Example
A 4–pole, 3-phase, 415V, 50 Hz IM has a rated torque and speed of 20 Nm and 1450 rpm respectively. The motor is supplied by a 3-phase PWM-VSI using a constant V/Hz control method. It is used to drive a load with TL–ω characteristic given by TL = Kω2. The load torque demand is such that it equals the rated torque of the motor at the rated motor speed.
i) Find the constant K in the TL–ω characteristic of the load.
What are the synchronous and motor speeds at point A and point B of the TL-ω characteristic (See figure)?
If it is required that the starting torque equals 1.2 x rated torque of the motor, what should be the voltage and frequency applied at start–up?
If Vdc of the inverter is 630V and the switching frequency is 5 kHz, what should be the values of the amplitude modulation index and frequency modulation index of the VSI for point B?

34. INDUCTION MOTOR DRIVES
Speed control : Constant V/Hz
Trated= 20 Nm
Rated synchronous speed
1500 rpm
= rad/s
Rated speed
1450 rpm
= rad/s
Rated slip frequency= 5.3 rad/s

35. INDUCTION MOTOR DRIVES
Speed control : Constant V/Hz
ωsyn1
ωm1
Slip frequency, ωslip1= ?

36. INDUCTION MOTOR DRIVES
Speed control : Constant V/Hz
ωsyn2
ωm2
Slip frequency, ωslip2= ?

37. INDUCTION MOTOR DRIVES
Speed control : Constant V/Hz
24Nm
Slip frequency, ωstart= ?

38. At 43 Hz, the L-L rms voltage should be
INDUCTION MOTOR DRIVES
Speed control : Constant V/Hz
(iv)
At B, ωsyn = rad/s  43 Hz
Hence mf =5000/43 = 116
At 43 Hz, the L-L rms voltage should be
Since we know that