Induction Motor – Scalar Control
By
Mr.M.Kaliamoorthy
Department of Electrical & Electroncis Engineering
PSNA College of Engineering and Technology
1
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
2
INDUCTION MOTOR DRIVES
Three-phase induction motor are commonly used in adjustable-speed
drives (ASD).
Basic part of three-phase induction motor :
Three-phase
windings
Rotor windings
• Stator
Threephase
supply
• Rotor

• Air gap
Stator
Air gap
s
Rotor
m
T
Three-phase
windings
Rotor windings
Threephase
supply

Stator
Air gap
s
Rotor
m
T
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 :
ωs is syncronous speed [rad/sec]
2
Ns is syncronous speed [rpm]
s 
or
p is numbers of poles
p
ω is the supply frequency [rad/sec]
f is the supply frequency [Hz]
120 f
Ns 
Nm is motor speed
p
The motor speed
m s (1 S )
The rotor speed or motor speed is :
Where S is slip, as defined as :
Three-phase
windings
  m
S S
S
Rotor windings
Threephase
supply

Stator
Air gap
s
Rotor
m
T
Or
S
NS  Nm
NS
The motor speed
m s (1 S )
The rotor speed or motor speed is :
Where S is slip, as defined as :
Three-phase
windings
  m
S S
S
Rotor windings
Threephase
supply

Stator
Air gap
s
Rotor
m
T
Or
S
NS  Nm
NS
Equivalent Circuit Of Induction Motor
Three-phase
windings
Where :
Rotor windings
Rs is resistance per-phase of stator winding
Threephase
supply
Rr is resistance per-phase of rotor winding

Air gap
Stator
Rotor
m
s
Is
Xs
Xs is leakage reactance per-phase of the
winding stator
Xs is leakage reactance per-phase of the
winding rotor
T
Xr’
Rs
Im
Xm is magnetizing reactance
Ir’
Rr’/s
Vs
Xm
Stator
Rm
Air gap
motor
Rm is Core losses as a reactance
Performance Characteristic of Induction Motor
Is
Xs
Xr’
Rs
Im
Ir’
Rr’/s
Vs
Xm
Stator
Rm
Air gap
motor
Stator copper loss :
Ps cu  3 I s Rs
Rotor copper loss :
Pr cu  3 ( I r ) 2 Rr
2
'
2
Core losses :
2
V
V
Pc  3 m  3 s
Rm
Rm
'
Performance Characteristic of
Induction Motor
- Power developed on air gap (Power fropm stator to
'
rotor through air gap) :
' 2 Rr
Pg  3 ( I r )
S
'
2
- Power developed by motor : Pd  Pg  Pr cu  3 ( I r )
'
Pd  Pg (1 S )
or
- Torque of motor :
or
Td 

Pd
m
Pd 60
Td 
2 N m
or
Pg (1  S )
S (1  S )

Pg
s
Rr
(1  S )
S
Performance Characteristic of
Induction Motor
Input power of motor :
Pi  3Vs I s cosm
 Pc  Ps cu  Pg
Output power of motor :
Po  Pd  Pno load
Pd  Pno load
Po
Efficiency :   
Pi Pc  Ps cu  Pg
Performance Characteristic of
Induction Motor
If
Pg  (Pc  Ps cu )
and
Pd  Pno load
so, the efficiency can calculated as :
Pd Pg (1  S )
 
1  S
Pg
Pg
Performance Characteristic of
Induction Motor
Generally, value of reactance magnetization Xm >> value Rm (core
losses) and also X m 2  ( Rs 2  X s 2 )
So, the magnetizing voltage same with the input voltage :
Vm  Vs
Therefore, the equivalent circuit is ;
Is
Xs
Ii
Im
Xm
Xr’
Rs
Rr’/s
Xm
Vs
Rm
Po
Pi
Stator
Air gap
motor
Is=Ir’
Ir’
Im
Ir’
Rr’/s
Vs
Xs
Xr’
Rs
Stator
Air gap
rotor
Performance Characteristic of
Induction Motor
Ii
Xs
Xr’
Rs
Is=Ir’
Ir’
Im
Rr’/s
Vs
Ir 
Po
Pi
Stator
Air gap
Vs
'

Rr'
 Rs 
S




' 
  j X s  X r 


rotor
Xm
Ir 
Vs
'
The rotor current is :

Rr' 
'
 Rs    X s  X r
S 

2


2



1
2
Ii
Xs
Xr’
Rs
Is=Ir’
Ir’
Im
Td 
Rr’/s
Vs
Po
Pi
Stator
Air gap
3 Rr' Vs2

Rr'
S s  Rs 
S

2

  X s  X r'


rotor
Tmax
Td
Tst
TL
Tm=TL
Operating point
S=1
Nm =0
Torque – speed Characteristic
Smax S=Sm S=0
m s
Nm Ns

2



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
1
sm
rated
rotors
rotor’
0
r
Requires speed
control of motor
15
Speed Control of IM
• Given a load T– characteristic, the steady-state speed can be
changed by altering the T– curve of the motor
'
r
2
2
3R
Vs
Te 
' 2
ss 

Rr 
2
 Rs     X ls  X lr  
s 


3
2
4
s    f
P
P
1
Varying voltage
(amplitude)
Varying line
frequency
Pole Changing
16
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
17
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) :
'
r
3R
Te 
ss 
Rr'
 Rs 
s

bV 
2
s


2
   X ls  X lr  


2
Note: b  1
18
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
Practical
speed range
19
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
20
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
21
Constant Volts/Hz (V/f) Control
 Airgap flux in the motor is related to the induced stator
voltage E1 :
E1 Vs
ag 

f
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)
22
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
E1 Vs
ag 

f
f
Tmax 
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)
23
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
Non-linear offset
curve –
• for low-starting
torque loads
Non-linear offset – varies with Is
frated
f
24
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)
KVs ,rated , when f s  f s ,rated
– Stator voltage:Vs  
(2)
 Vs ,rated , when f s  f s ,rated
–Voltage-to-frequency ratio = d = constant:
d
Vs,rated
s,rated
(3)
25
Constant Volts/Hz (V/f) Control
 For operation at frequency K times rated frequency:
Hence, the torque produced by the motor:
Te 
'
r
3R
ss 
Rr'
 Rs 
s

Vs
2


2
2
  K  X ls  X lr  


2
(4)
where s and Vs are calculated from (1) and (2)
respectively.
26
Constant Volts/Hz (V/f) Control
 For operation at frequency K times rated frequency:
The slip for maximum torque is:
smax  
Rr'
(5)
Rs  K 2  X ls  X lr 
2
2
 The maximum torque is then given by:
Tmax 
Vs
3
2
2 s  R  R  K 2  X  X  
s
ls
lr
 s

2
2
(6)
where s and Vs are calculated from (1) and (2)
respectively.
27
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.
28
Constant Volts/Hz (V/f) Control
Constant Torque Area
Constant Power Area
29
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
30
Constant Volts/Hz (V/f) Control –
Open-loop Implementation
PWM
Voltage-Source
Inverter
(VSI)
Note: e= s = synchronous speed
31
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
32
Constant Volts/Hz (V/f)
Control – Open-loop Implementation
 Problems in open-loop drive operation:
 Motor speed not controlled precisely
P
m 
2
P
  s   sl 
2
r 
 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
 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
33
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
34
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  inverterlosses
s
Pin  Vdc I dc
 Te
 sl  
 Te ,rated
(8)

 sl ,rated


(7)
Note: In the figure,
slip= sl = slip speed
syn= s = synchronous speed
(9)
35
Constant Volts/Hz (V/f) Control –
Closed-loop Implementation
Open-loop system
(as in slide 23)
Slip Controller
Note: e= s = synchronous speed
36
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
37
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
38
Constant Airgap Flux Control
• Constant airgap flux in the motor means:
E1
ag 
 Lm I m  constant
2f
Assuming small voltage drop
across Rs and Lls
• 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
E1  Vs
Rr’/s
Im
–
39
Constant Airgap Flux Control
• From torque equation (with ag kept constant at rated value),
since ss = sl and ignoring Rs and Lls,
2
 P  Vs
Te  3 
 2  ss 
Rr'
 Rs 
s

2
Rr
 P  E1

3


2
2
'
2






sl



R
2
2
r
   X ls  X lr  

s   s Llr  

 sl 


'
r
R
'
• By rearranging the equation:
2
P E
Te  3  12
 2  s  R '
 r
 sl
 Rr'

 sl



P 2

T

3
 ag
e
2

2

2
  Llr  


 Rr'

 sl
 R '
 r
 sl





2
  Llr  


2
Te  sl  sl can be varied instantly  instantaneous (fast)
40
Te response
Constant Airgap Flux Control
 Constant airgap flux requires control of magnetising current Im which is
not accessible
 From equivalent circuit' (on slide 31):
R
jsl Tr  1
js L'lr  r
Is 
Im ,
s
 r 
Im 
Is
(10)
'

Tr  1
j

sl
R
js ( L'lr  Lm )  r
1  r 
s
 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)
L'lr elec
Lr
Note: Tr  ' ,  r 
, sl  selec  41
r
Rr
Lm
Constant Airgap Flux Control Implementation
Current Controlled VSI
3-phase
supply
Rectifier
C
Current controller options:
• Hysteresis Controller
• PI controller + PWM
r* +
PI
-
Voltage
Source
Inverter
(VSI)
IM
Current
controller
slip
|Is|
i*a
i*b
+
s
r
+
r
i*c
Equation (10)
(from slide 33)
42
Current-Controlled VSI
Implementation
• Hysteresis Controller
i*a
i*b
i*c
+
Voltage
Source
Inverter
(VSI)
+
+
Motor
43
Current-Controlled VSI
Implementation
• PI Controller + Sinusoidal PWM
i*a
i*b
i*c
+
PI
+
PWM
PI
+
•Due to interactions between phases
(assuming balanced conditions)
 actually only require 2 controllers
Voltage
Source
Inverter
(VSI)
PWM
PI
PWM
Motor
44
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
45
References
 Krishnan, R., Electric Motor Drives: Modeling, Analysis and
Control, Prentice-Hall, New Jersey, 2001.
 Bose, B. K., Modern Power Electronics and AC drives, PrenticeHall, 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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