Slide 1

Induction Motor – Scalar Control
By
Dr. Ungku Anisa Ungku Amirulddin
Department of Electrical Power Engineering
College of Engineering

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 2

Outline
 Introduction
 Speed Control of Induction Motors
 Pole Changing
 Variable-Voltage, Constant Frequency
 Variable Frequency
 Constant Volts/Hz (V/f) Control
 Open-loop Implementation
 Closed-loop Implementation
 Constant Airgap Flux Control
 References
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 3

Introduction
 Scalar Control - control of induction machine

based on steady-state model (per phase SS
equivalent circuit)
Rs

Is

Lls

Llr’

+

+
Vs
–

Dr. Ungku Anisa, July 2008

Ir ’

Lm
Im

EEEB443 - Control & Drives

E1

Rr’/s

–

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Slide 4

Introduction
Te
Pull out
Torque
(Tmax)

Intersection point
(Te=TL) determines the
steady –state speed

Te

TL

Trated

What if the load must
be operated here?

s

sm

1
Dr. Ungku Anisa, July 2008

rated
rotors
rotor’
0

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r
Requires speed
control of motor
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Slide 5

Speed Control of IM
 Given a load T– characteristic, the steady-state speed can be

changed by altering the T– curve of the motor
Te 

3R

s 

2

'
r

Vs

2

2

2
'
s s 

Rr 
2
   X ls  X lr  
  R s 
s 
 


 

P

4

3

f

P

1
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

Varying voltage
(amplitude)

Varying line
frequency

Pole Changing
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Slide 6

Speed Control of IM
Pole Changing
 Machines must be specially manufactured (i.e. called pole changing

motors or multi-speed motors)
 Need special arrangement of stator windings

 Only used with squirrel-cage motors
 Because number of poles induced in squirrel cage rotor will follow
number of stator poles
 Two methods:
 Multiple stator windings





stator has more than one set of 3-phase windings
only energize one set at a time
simple, expensive

 Consequent poles

 Discrete step change in speed
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 7

Speed Control of IM
Pole Changing
 Consequent poles
 single winding divided into
few coil groups
 No. of poles changed by
changing connections of coil
groups
 Change in pole number by
factor of 2:1 only

A two-pole stator winding for pole changing.
Notice the very short pitch (60 to 90) of
these windings.
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 8

Speed Control of IM
Pole Changing
 Consequent poles
 Close up view of one phase of a
pole changing winding.
 In Figure (a): the 2-pole
configuration, one coil is a north
pole and the other is a south
pole.
 In Figure (b): when the
connection on one of the two
coils is reversed, they are both
north poles, and the magnetic
flux returns to the stator halfway
between the two coils. The
south poles are called
consequent poles. Hence the
winding is now 4-pole.
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 9

Speed Control of IM
Variable-Voltage (amplitude),
Constant Frequency
 Controlled using:
 Transformer (rarely used)
 Thyristor voltage controller
 thyristors connected in anti-parallel
motor can be star or delta connected
 voltage control by firing angle control
(gating signals are synchronized to
phase voltages and are spaced at 60
intervals)
 Only for operations in Quadrant 1 and
Quadrant 3 (requires reversal of phase
sequence)
 also used for soft start of motors
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 10

Speed Control of IM
Variable-Voltage (amplitude), Constant Frequency
 Voltage can only be reduced from rated Vs (i.e. 0 < Vs ≤ Vs,rated)
 From torque equation, Te  Vs2
 When Vs , Te and speed reduces.

 If terminal voltage is reduced to bVs, (i.e. Vs = bVs,rated) :
Te 

3R

'
r

bV 

2

s

2
'
s s 

Rr 
2
   X ls  X lr  
  R s 
s 
 


Note: b  1
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 11

Speed Control of IM
Variable-Voltage
(amplitude), Constant
Frequency
 Suitable for applications

where torque demand
reduces with speed
(eg: fan and pump drives
where TL  m2)
 Suitable for NEMA Class D
(high-slip, high Rr’) type
motors
 High rotor copper loss,
low efficiency motors
 get appreciable speed
range
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

Practical
speed range
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Slide 12

Speed Control of IM
Variable Voltage (amplitude),
Constant Frequency
 Disadvantages:
 limited speed range  when
applied to Class B (low-slip) motors
 Excessive stator currents at low
speeds  high copper losses
 Distorted phase current in machine
and line (harmonics introduced by
thyristor switching)
 Poor line power factor
(power factor proportional to firing
angle)
 Hence, only used on low-power,

appliance-type motors where
efficiency is not important
 e.g. small fan or pumps drives
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 13

Speed Control of IM
Variable Frequency
 Speed control above rated (base) speed
 Requires the use of PWM inverters to control frequency of motor
 Frequency increased (i.e. s increased)
 Stator voltage held constant at rated value
 Airgap flux and rotor current decreases
 Developed torque
decreases
Te  (1/s)

 For control below

base speed –
use Constant
Volts/Hz method
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 14

Constant Volts/Hz (V/f) Control
 Airgap flux in the motor is related to the induced stator voltage

E1 :
 ag 

E1
f



Vs
f

Assuming small voltage drop
across Rs and Lls

 For below base speed operation:
 Frequency reduced at rated Vs - airgap flux saturates
(f  ,ag  and enters saturation region oh B-H curve):
- excessive stator currents flow
- distortion of flux wave
- increase in core losses and stator copper loss
 Hence, keep ag = rated flux
 stator voltage Vs must be reduced proportional to reduction in f
(i.e. maintaining Vs / f ratio)
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 15

Constant Volts/Hz (V/f) Control
 Max. torque remains almost

constant
 For low speed operation:

 can’t ignore voltage drop across

Rs and Lls (i.e. E1  Vs)
 poor torque capability
(i.e. torque decreased at low
speeds shown by dotted lines)
 stator voltage must be boosted
– to compensate for voltage
drop at Rs and Lls and maintain
constant ag

 ag 

E1
f



Vs
f

T max 

Vs

2

s

 For above base speed operation

(f > frated):

 stator voltage maintained at

rated value
 Same as Variable Frequency
control (refer to slide 13)
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 16

Constant Volts/Hz (V/f) Control
Vs

Vs vs. f relation in Constant Volts/Hz drives Boost - to

compensate for
voltage drop at Rs
and Lls

Vrated

Linear offset curve –
• for high-starting
torque loads
• employed for most
applications

Linear offset

Boost
Dr. Ungku Anisa, July 2008

Non-linear offset
curve –
• for low-starting
torque loads

Non-linear offset – varies with Is

EEEB443 - Control & Drives

frated

f
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Slide 17

Constant Volts/Hz (V/f) Control
 For operation at frequency K times rated frequency:
 fs = Kfs,rated  s = Ks,rated

(1)

(Note: in (1) , speed is given as mechanical speed)
 KV s , rated , when f s  f s , rated
 Stator voltage: V s  
 V s , rated , when f s  f s , rated

(2)

Voltage-to-frequency ratio = d = constant:
d 

Dr. Ungku Anisa, July 2008

V s ,rated

 s ,rated

EEEB443 - Control & Drives

(3)
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Slide 18

Constant Volts/Hz (V/f) Control
 For operation at frequency K times rated frequency:
Hence, the torque produced by the motor:
Te 

3R

'
r

Vs

2

s s 
R 
  K
  R s 
s 
 
'
r

2

2

 X ls

 X lr 

2





(4)

where s and Vs are calculated from (1) and (2)
respectively.

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 19

Constant Volts/Hz (V/f) Control
 For operation at frequency K times rated frequency:
The slip for maximum torque is:
'

s max  

Rr
2

Rs  K

2

 X ls

 X lr 

(5)

2

 The maximum torque is then given by:
T max 

Vs

3
2 s  R 
 s

2

Rs  K

2

2

 X ls

 X lr 

2




(6)

where s and Vs are calculated from (1) and (2)
respectively.
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 20

Constant Volts/Hz (V/f) Control
Rated (Base)
frequency

Constant
Torque Area

(below base speed)

Field Weakening Mode (f > frated)

• Reduced flux (since Vs is constant)
• Torque reduces

Constant Power Area
(above base speed)

Note:
Operation restricted
between synchronous
speed and Tmax for
motoring and braking
regions, i.e. in the
linear region of the
torque-speed curve.
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 21

Constant Volts/Hz (V/f) Control
Constant Torque Area

Constant Power Area
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Slide 22

Example
 A 4-pole, 3 phase, 400 V, 50 Hz, 1470 rpm induction

motor has a rated torque of 30 Nm. The motor is used to
drive a linear load with characteristic given by TL = K,
such that the speed equals rated value at rated torque. If
a constant Volts/Hz control method is employed,
calculate:
 The constant K in the TL - characteristic of the load.
 Synchronous and motor speeds at 0.6 rated torque.
 If a starting torque of 1.2 times rated torque is required, what

should be the voltage and frequency applied at start-up? State
any assumptions made for this calculation.
 Answers:

K = 0.195, synchronous speed = 899.47 rpm & motor speed = 881.47 rpm,
At start up: frequency = 1.2 Hz, Voltage = 9.6 V
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 23

Constant Volts/Hz (V/f) Control –
Open-loop Implementation

PWM
Voltage-Source
Inverter
(VSI)
Note: e= s = synchronous speed
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 24

Constant Volts/Hz (V/f)
Control – Open-loop Implementation
 Most popular speed control method because it is easy to

implement
 Used in low-performance applications
 where precise speed control unnecessary

 Speed command s* - primary control variable

 Phase voltage command Vs* generated from V/f relation

(shown as the ‘G’ in slide 23)
 Boost voltage Vo is added at low speeds
 Constant voltage applied above base speed

 Sinusoidal phase voltages (vabc*) is then generated from Vs* &

s* where s* is obtained from the integral of s*

 vabc* employed in PWM inverter connected to motor
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 25

Constant Volts/Hz (V/f)
Control – Open-loop Implementation
 Problems in open-loop drive operation:
 Motor speed not controlled precisely







primary control variable is synchronous speed s
actual motor speed r is less than s due to sl
sl depends on load connected to motor

r 

P



P

2
2

 m 
 s   sl 

sl cannot be maintained since r not measured



can lead to operation in unstable region of T- characteristic
stator currents can exceed rated value – endangering inverterconverter combination

 Problems (to an extent) can be overcome by:
 Open-loop Constant Volts/Hz Drive with Slip Compensation
 Closed-loop implementation - having outer speed loop with
slip regulation
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 26

Constant Volts/Hz (V/f) Control –
Open-loop Implementation
Open-loop Constant Volts/Hz Drive with Slip Compensation
- Slip speed is estimated and added to the reference speed r*
Vdc = Vd

Idc

Slip
Compensator
sl
r*
Note: e= s = synchronous speed
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 27

Constant Volts/Hz (V/f)
Control – Open-loop Implementation
Open-loop Constant Volts/Hz Drive with Slip Compensation
 How is sl estimated in the

Slip Compensator?
 Using T- curve, sl  Te
 sl can be estimated by
estimating torque where:
Te 

Pag

s



Pin  PSCL  inverter

s

(8)

Pin  V dc I dc

 sl

 Te

T
 e , rated

Dr. Ungku Anisa, July 2008

losses


 sl , rated



(7)
Note: In the figure,
slip= sl = slip speed
syn= s = synchronous speed

(9)

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Slide 28

Constant Volts/Hz (V/f) Control –
Closed-loop Implementation
Open-loop system
(as in slide 23)

Slip Controller

Note: e= s = synchronous speed
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 29

Constant Volts/Hz (V/f) Control –
Closed-loop Implementation
 Reference motor speed r* is compared to the actual speed r

to obtain the speed loop error
 Speed loop error generates slip command sl* from PI
controller and limiter
 Limiter ensures that the sl* is kept within the allowable slip
speed of the motor (i.e. sl*  slip speed for maximum torque)
 sl* is then added to the actual motor speed r to generate
synchronous speed command s* (or frequency command)
 s* generates voltage command Vs* from V/f relation
 Boost voltage is added at low speeds
 Constant voltage applied above base speed

 Scheme can be considered open loop torque control (since

T  s) within speed control loop

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 30

Constant Airgap Flux Control
 Constant V/f control employs the use of variable frequency

voltage source inverters (VSI)
 Constant Airgap Flux control employs variable frequency
current source inverters or current-controlled VSI
 Provides better performance compared to Constant V/f
control with Slip Compensation

 airgap flux is maintained at rated value through stator current

control

 Speed response similar to equivalent separately-excited dc

motor drive but torque and flux channels still coupled
 Fast torque response means:
 High-performance drive obtained
 Suitable for demanding applications
 Able to replace separately-excited dc motor drives

 Above only true is airgap flux remains constant at rated value
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 31

Constant Airgap Flux Control
 Constant airgap flux in the motor means:

 ag 

E1
2 f

Assuming small voltage drop
across Rs and Lls

 L m I m  constant

 For ag to be kept constant at rated value, the magnetising current Im

must remain constant at rated value
 Hence, in this control scheme stator current Is is controlled to
maintain Im at rated value
Controlled to maintain Im at rated
Rs

Lls

Is

Llr’

+

+
Vs

Ir ’

Lm
maintain at rated

–
Dr. Ungku Anisa, July 2008

E1  Vs

Rr’/s

Im
–

EEEB443 - Control & Drives

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Slide 32

Constant Airgap Flux Control
 From torque equation (with ag kept constant at rated value),

since ss = sl and ignoring Rs and Lls,
2

'

2

Rr
 P  Vs
 P  E1
Te  3 
 3 
2
'
2
s



 
 2   sl
s

Rr 
2
   X ls  X lr  
  R s 
s 
 


'

Rr
2
 R '


2
r
 
 s    s L lr  
   sl



 By rearranging the equation:
2

PE
Te  3  1 2
 2   s  R '
  r
   sl

 R r'


 sl






P 2

T

3
  ag
e
2

 2

2
   L lr  




 R r'


 sl
 R '
  r
   sl








2
   L lr  



2

Te  sl  sl can be varied instantly  instantaneous (fast)
Te response 32
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives


Slide 33

Constant Airgap Flux Control
 Constant airgap flux requires control of magnetising current Im which is

not accessible
 From equivalent circuit
(on slide 31):
'
j  s L lr 
'

Im 

Rr

j  s ( L lr  L m ) 
'

Is 

s
R

'
r

Is

s

j  sl T r  1
 r
j  sl 
1  r


T r  1


Im ,

(10)

 From equation (10), plot Is against sl when Im is kept at rated value.
 Drive is operated to maintain Is against sl relationship when frequency

is changed to control speed.
 Hence, control is achieved by controlling stator current Is and stator
frequency:
 Is controlled using current-controlled VSI

 Control scheme sensitive to parameter variation (due to Tr and r)
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

Note : T r 

Lr
R

'
r

'

, r 

L lr
Lm

,  sl

elec

 s

elec

 r

33


Slide 34

Constant Airgap Flux Control Implementation
Current Controlled VSI

3-phase
supply

Rectifier

C

Current controller options:
• Hysteresis Controller
• PI controller + PWM
r* +

PI

-

IM

Current
controller
slip

|Is|

i*a
i*b

+

s

r
+

Dr. Ungku Anisa, July 2008

Voltage
Source
Inverter
(VSI)

r

EEEB443 - Control & Drives

i*c

Equation (10)
(from slide 33)
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Slide 35

Current-Controlled VSI
Implementation
 Hysteresis Controller
i*a

i*b
i*c

+
Voltage
Source
Inverter
(VSI)

+
+

Motor
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 36

Current-Controlled VSI
Implementation
 PI Controller + Sinusoidal PWM
i*a

+

i*b
i*c

PI
+

PWM

PI
+

PWM

PI

•Due to interactions between phases
(assuming balanced conditions)
 actually only require 2 controllers
Dr. Ungku Anisa, July 2008

Voltage
Source
Inverter
(VSI)

EEEB443 - Control & Drives

PWM

Motor
36


Slide 37

Current-Controlled VSI
Implementation
 PI Controller + Sinusoidal PWM (2 phase)
i*a
i d*

i*b

abcdq

PI
dq abc

i q*

PI

PWM
Voltage
Source
Inverter
(VSI)

i*c
iq
id

abcdq

Motor
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

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Slide 38

References
 Krishnan, R., Electric Motor Drives: Modeling, Analysis and Control,






Prentice-Hall, New Jersey, 2001.
Bose, B. K., Modern Power Electronics and AC drives, Prentice-Hall,
New Jersey, 2002.
Trzynadlowski, A. M., Control of Induction Motors, Academic Press,
San Diego, 2001.
Rashid, M.H, Power Electronics: Circuit, Devices and Applictions, 3rd
ed., Pearson, New-Jersey, 2004.
Nik Idris, N. R., Short Course Notes on Electrical Drives,
UNITEN/UTM, 2008.
Ahmad Azli, N., Short Course Notes on Electrical Drives,
UNITEN/UTM, 2008.

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