Slide 1

Induction Motor – Vector Control or Field
Oriented Control
By
Dr. Ungku Anisa Ungku Amirulddin
Department of Electrical Power Engineering
College of Engineering

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

1


Slide 2

Outline
 Introduction
 Analogy to DC Drive
 Principles of Field Orientation Control
 Rotor Flux Orientation Control
 Indirect Rotor Flux Orientation (IRFO)
 Direct Rotor Flux Orientation (DRFO)

 Stator Flux Orientation Control
 Direct Stator Flux Orientation (DSFO)
 References
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

2


Slide 3

Introduction
 Induction Motor (IM) drives are replacing DC drives

because:
 Induction motor is simpler, smaller in size, less maintenance
 Less cost
 Capability of faster torque response
 Capability of faster speed response (due to lower inertia)

 DC motor is superior to IM with respect to ease of control
 High performance with simple control
 Due to decoupling component of torque and flux
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

3


Slide 4

Introduction
Induction Motor Drive
Scalar Control

• Control of current/voltage/frequency
magnitude based on steady-state
equivalent circuit model
• ignores transient conditions
•
•
•
•

• for low performance drives
Simple implementation
Inherent coupling of torque and flux
• Both are functions of voltage and
frequency
Leads to sluggish response
Easily prone to instability
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

Vector Control or Field Orientation
Control
• control of magnitude and phase of
currents and voltages based on
dynamic model
• Capable of observing steady state
& transient motor behaviour
• for high performance drives
• Complex implementation
• Decoupling of torque and flux
• similar to the DC drive
• Suitable for all applications previously
covered by DC drives
4


Slide 5

Analogy to DC Drive

 In the DC motor: Te = k f Ia
 f controlled by controlling If

f

 If same direction as field f

 Ia same direction as field a
 Ia and f always perpendicular

and decoupled
 Hence, Te = k f Ia

= k’ If Ia sin 90
= k’(If x Ia)

a

 Keeping f constant, Te

controlled by controlling Ia
 Ia, If , a and f are space vectors
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

5


Slide 6

Analogy to DC Motor
 In the Induction Motor:

s
c’

r

a

b’

Te = kr x s

 s produced by stator currents

 r produced by induced rotor

b

Dr. Ungku Anisa, July 2008

c

EEEB443 - Control & Drives

currents
 Both s and r rotates at
synchronous speed s
 Angle between s and r
varies with load, and motor
speed r
 Torque and flux are coupled.
6


Slide 7

Analogy to DC Motor
 Induction Motor torque equation :

3P
Te 
ψ s  is
22
3 P Lm
Te 
ψr  is
2 2 Lr

(1)

(2)

 Compared with DC Motor torque equation:



Te  k I f I a  k ψ f ia sin 90  k ψ f  i a
'



(3)

 Hence, if the angle betweens orr andis is made to be

90, then the IM will behave like a DC motor.
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

7


Slide 8

Principles of Field Orientation
Control
 Hence, if the angle betweens orr andis is made to be

90, then the IM will behave like a DC motor.

Achieved through orientation (alignment) of rotating dq frame
on r or s

Rotor-Flux
Orientation Control
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

Stator-Flux
Orientation Control
8


Slide 9

Principles of Field Orientation
Control
Rotor-Flux
Orientation Control

Stator-Flux
Orientation Control

qs

qs

qr
qs

is
r
r
isq

i

Ψs
i sq

ds

3 P Lm
Te 
( rd isq  rq isd )
2 2 Lr
Dr. Ungku Anisa, July 2008

s

dr

r
sd

EEEB443 - Control & Drives

is
ds

Ψs
i sd

ds

3P
Te 
( sd isq  sq isd )
22
9


Slide 10

Principles of Field Orientation
Control
 Summary of field orientation control on a selected flux vector
(i.e. either r , s or  m):

1

2

3

f

• In revolving (rotating) dfqf - reference frame, obtain
• isqf* from given rotor speed reference r* (via speed controller)
• isdf* from given flux reference f*
• Determine the angular position f of f (i.e. reference frame
orientation angle)
• used in the dfqf  dsqs conversion from vsdqf* (output of
isdqf* current controller) to vsdqs*.
• In the stationary dsqs - frame, obtain the reference stator voltages
vabcs*
• fed to the PWM inverter feeding the IM from vsdqs* using the
dsqs  abc transformation.

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

10


Slide 11

Rotor Flux Orientation Control
qs

 d- axis of dq- rotating frame is

qr

aligned with r . Hence,

is

 rd   r

(4)

 rqr  0

(5)

r

r
r
isq

r

dr

 Therefore,

r
i sd

ds
r
i
 sq = torque producing current
r
 i sd
= field producing current
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

3 P Lm
Te 
( rd isq ) (6)
2 2 Lr
Similar to
ia & if in
DC motor

Decoupled
torque and
flux control
11


Slide 12

Rotor Flux Orientation Control
 From the dynamic model of IM, if dq- frame rotates at general

speed g (in terms of vsd, vsq, isd, isq, ird, irq) :

vsd   Rs  SLs
  
vsq     g Ls
vrd  
SLm
  
 vrq  ( g  r ) Lm

  g Ls

SLm

Rs  SLs

 g Lm

 ( g  r ) Lm

Rr ' SLr

SLm

( g  r ) Lr

  g Lm

 isd 
  
SLm
  isq  (7)
 ( g  r ) Lr  ird 
  
Rr ' SLr  irq 

 r rotates at synchronous speed s
 Hence, drqr- frame rotates at s

Therefore, g = s
 These voltage equations are in terms of isd, isq, ird, irq
 Better to have equations in terms of isd, isq, rd,  rq
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

(8)

12


Slide 13

Rotor Flux Orientation Control
'


L
i

L
 Rotor flux linkage is given by:
rdq
m sdq
r irdq
rdq Lm
 From (9):
irdq  '  ' isdq
Lr
Lr

(9)
(10)

 Substituting (8) and (10) into (7) gives the IM voltage

equations rotating at s in terms of vsd, vsq, isd, isq, rd, rq:

vsdψr   Rs  SLs
  sLs
 ψr  
Rs  SLs
vsq     sLs
vrdψr   Rr ' Lm Lr '
0
 ψr  
0
 Rr ' Lm Lr '
vrq  

S Lm Lr '

s Lm Lr '

Rr '

Lr '  S

 sl

  s Lm Lr '   isdψr 
 ψr 

SLm Lr '   isq 
 ψr
  rd 
  sl
  ψr 
Rr ' Lr '  S   rq 
(11)

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

13


Slide 14

Rotor Flux Orientation Control


 Since  rqr  0 , hence the equations in rotor flux

orientation are:

Lm d ψr
d ψr
ψr
v  R i  Ls isd   sLs isq  s
 rd (12)
dt
Lr ' dt
Lm ψr
d ψr
ψr
ψr
ψr
(13)
vsq  Rs isq  Ls isq  sLs isd  s
 rd
dt
Lr '
Rr ψr d ψr Lm
ψr
vrq  0   rd   rd 
Rr isdψr (14)
Lr '
dt
Lr '
ψr
sd

ψr
s sd

v  0   sl
ψr
rq

ψr
rd

Lm

Rr isqψr
Lr '

Important equations for
Rotor Flux Orientation Control!

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

(15)

Note:
Total leakage factor =
2

L
  1 m '
Ls Lr
sl = slip speed (elec.)
14


Slide 15

Rotor Flux Orientation Control
 Let

ψr
 rdψr  Lmimrd

 Using (16), equation (14) can be rearranged to give:
Lr ' d ψr
ψr
ψr
isd  imrd 
imrd
Rr dt

(16)

(17)

ψr
i
 mrd is called the “equivalent magnetising current” or “field
current”
Lr '
ψr
ψr
(18)
isd  1  S r imrd where  r 
 Hence, from (17):
Rr
 Under steady-state conditions (i.e. constant flux):
ψr
(19)
isdψr  imrd

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

15


Slide 16

Rotor Flux Orientation Control
qs

 r rotates at synchronous speed

qr

is
r

s
 drqr- frame also rotates at s
dr  Hence,

   s dt
r

r
isq

r

r
i sd

dq- reference frame
orientation angle
Dr. Ungku Anisa, July 2008

(20)

 For precise control, r must be

obtained at every instant in time
ds
 Leads to two types of control:
 Indirect Rotor Flux Orientation
 Direct Rotor Flux Orientation

EEEB443 - Control & Drives

16


Slide 17

Indirect Rotor Flux Orientation
(IRFO)


 Orientation angle:  r  s dt
 Synchronous speed obtained by adding slip speed and

electrical rotor speed
 r   s dt   sl  r  dt

(21)

 Slip speed can be obtained from equation (15):

Lmisqψr

isqψr

Lm Rr ψr
 sl 
i 
 ψr
ψr sq
ψr
Lr '  rd
 r rd  r imrd
ψr
mrd

 Under steady-state conditions (i

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

i

ψr
sd

):  sl 

(22)

isqψr

 r isdψr

(23)

17


Slide 18

Indirect Rotor Flux Orientation
(IRFO) - implementation
 Closed-loop implementation under constant flux condition:
1.

Obtain isdr* from r* using (16):
ψr*
isdψr*  imrd


 rdψr*

(24)

Lm
Obtain isqr* from outer speed control loop since isqr* 
Tm* based on (6):
*

i

ψr*
sq

Te
3 P Lm
 ψr* where kt 
kt isd
2 2 Lr

2

(25)

Obtain vsdqr* from isdqr* via inner current control loop.
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

18


Slide 19

Indirect Rotor Flux Orientation
(IRFO) - implementation
 Closed-loop implementation under constant flux condition:
2.

Determine the angular position r using (21) and (23):
ψr*


i
P
sq
*
 r   s dt   sl  r dt    ψr*  m  dt
(26)
2
  r isd

where m is the measured mechanical speed of the motor
obtained from a tachogenerator or digital encoder.





r to be used in the drqr  dsqs conversion of stator
voltage (i.e. vsdqr* to vsdqs* concersion).
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

19


Slide 20

Indirect Rotor Flux Orientation
(IRFO) - implementation

drqr  dsqs transformation

Rotating frame (drqr)
isdr*
r*
Eq. (24) +
isqr* r* +
PI +

Staionary frame (dsqs)

vsdr*

vsq

ejr

PI

-

-

isdr* isqr*

Eq. (23)
NO field
weakening
(constant flux)
Dr. Ungku Anisa, July 2008

slip
+



vsd

s*

 r
r

+

isdr
isqr

vas*

vsqs*

PI
r*

2-phase (dsqs )
to 3-phase (abc)
transformation

2/3

vcs*

EEEB443 - Control & Drives

isqs

PWM
VSI

IRFO
Scheme
P/2

m
ias

isds

e-jr

vbs*

3/2

ibs
ics
20


Slide 21

Indirect Rotor Flux Orientation
(IRFO) - implementation
 drqr  dsqs transformation
vsqs*

vsdr*
vsqr*

ejr

vsds*

 xsds  cos  r
 s 
 xsq   sin  r

 sin  r   xsdr 
 
cos  r   xsqr 

 dsqs  drqr transformation
isdr
isqr

isds

e-jr

Dr. Ungku Anisa, July 2008

isqs

 xsdr   cos  r
 r   
 xsq   sin  r

EEEB443 - Control & Drives

sin  r   xsds 
 
cos  r   xsqs 

21


Slide 22

Indirect Rotor Flux Orientation
(IRFO) - implementation
 2-phase (dsqs ) to 3-phase (abc) transformation:
vas*

vsqs*
vsd

s*

2/3

1 s
xabc  Tabc
xdq

vbs*
vcs*

 3-phase (abc) to 2-phase (dsqs ) transform is given by:
ias

isds
isqs

3/2

x  Tabcxabc
s
dq

ibs
ics

where:

Tabc
Dr. Ungku Anisa, July 2008

1 0 0 
 1 1 
0 3  3 
EEEB443 - Control & Drives

and

1
Tabc

1 0 
  12 23 
 12  23 

22


Slide 23

Example – IRFO Control of IM
 An induction motor has the following parameters:
Parameter

Symbol

Value

Rated power

Prat

30 hp (22.4 kW)

Stator connection

Delta ()

No. of poles

P

6

Rated stator phase
voltage (rms)

Vs,rat

230 V

Rated stator phase
current (rms)

Is,rat

39.5 A

Rated frequency

frat

60 Hz

Rated speed

nrat

1168 rpm

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

23


Slide 24

Example – IRFO Control of IM ctd.
Parameter

Symbol

Value

Rated torque

Te,rat

183 Nm

Stator resistance

Rs

0.294 

Stator self
inductance
Referred rotor
resistance

Ls

0.0424 H

Rr’

0.156 

Referred rotor self
inductance

Lr ’

0.0417 H

Mutual inductance

Lm

0.041 H

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

24


Slide 25

Example – IRFO Control of IM ctd.
The motor above operates in the indirect rotor field orientation (IRFO)
scheme, with the flux and torque commands equal to the respective
rated values, that is r* = 0.7865 Wb and Te* = 183 Nm. At the
instant t = 1 s since starting the motor, the rotor has made 8
revolutions. Determine at time t = 1s:
the stator reference currents isd* and isq* in the dq-rotating frame
the slip speed sl of the motor
the orientation angle r of the dq-rotating frame
the stator reference currents isds* and isqs* in the stationary dsqs
frame
5. the three-phase stator reference currents ias*, ibs* and ics*
1.
2.
3.
4.

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

25


Slide 26

Example – IRFO Control of IM ctd.
 Answers:

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

26


Slide 27

Indirect Rotor Flux Orientation
(IRFO) – field weakening
 Closed-loop implementation under field weakening condition:
 Employed for operations above base speed
 DC motor: flux weakened by reducing field current if
vf
Lf d
 if 
if
imrd*
Rf
R f dt
 Compared with eq. (17) for IM:
imrd (rated)
Lr ' d ψr
ψr
ψr
isd  imrd 
imrd
Rr dt
 IM: flux weakened by reducing imrd
r

r
(base)
(i.e. “equivalent magnetising current”
or “field current)
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

27


Slide 28

Indirect Rotor Flux Orientation
(IRFO) – field weakening implementation
With field
weakening

r*

Rotating frame (drqr) Staionary frame (dsqs)

imrd r *
+
imrd

r

1
1  S r 

isd

PI
r* +

r*

PI
-

+
isqr* +

imrdr*r

vsdr*

PI
vsqr*

ejr

PI

-

isq *

Eq. (22)

vsqs*

slip
+



 r
r

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

Same as
in slide 20

+

isdr
isqr

vsds*

isds
e-jr

isqs
28


Slide 29

Indirect Rotor Flux Orientation
(IRFO) – Parameter sensitivity
 Mismatch between IRFO Controller and IM may occur
 due to parameter changes with operating conditions (eg.
increase in temperature, saturation)
 Mismatch causes coupling between T and  producing

components
 Consequences:
 r deviates from reference value (i.e. r*)
 Te deviates in a non-linear relationship from command

value (i.e. Te*)
 Oscillations occurs in r and Te response during torque
transients (settling time of oscillations = r)
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

29


Slide 30

Direct Rotor Flux Orientation
(DRFO)
 Orientation angle:

  tan

1

r

 rq

s

 rd

s

(27)

obtained from:
1. Direct measurements of airgap fluxes mds and mqs
2. Estimated from motor’s stator voltages vsdqs

and stator currents isdqs
s2

Note that: ψ r   rd  rq
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

s2

(28)
30


Slide 31

Direct Rotor Flux Orientation
(DRFO) – Direct measurements mds & mqs
1. Direct measurements of airgap fluxes mds and mqs
 mds and mqs measured using:

Hall sensors – fragile
 flux sensing coils on the stator windings – voltages induced
in coils are integrated to obtain mds and mqs
 The rotor flux r is then obtained from:


rdq

s

s
s
L'r
'

mdq  Llr isdq
Lm

(29)

 Disadvantages: sensors are inconvenient and spoil the

ruggedness of IM.
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

31


Slide 32

Direct Rotor Flux Orientation
(DRFO) – Direct measurements mds & mqs
Rotating frame
isdr*
r*
Eq. (24) +
isqr* r* +
PI +
-

-

r
NO field
weakening
(constant flux)
Dr. Ungku Anisa, July 2008

(drqr)

Stationary frame

vsdr*

vsq

r*

ejr

vsd

PI

DRFO  r
Scheme tan-1
isdr
isqr

s*

2/3

vbs*
vcs*

mds
 rds
 rqs Eq. (29) mqs

 r
e-jr

EEEB443 - Control & Drives

P/2

PWM
VSI

m

ias

isds
isqs

Flux sensing coils
arranged in quadrature

vas*

vsqs*

PI

(dsqs)

3/2

ibs
ics
32


Slide 33

Direct Rotor Flux Orientation
(DRFO) – Estimated from vsdqs & isdqs
2. Estimated from motor’s stator voltages and currents
 sds and  sqs obtained from stator voltage equations:





sdq   vsdq  Rs isdq  sdq 0
s

s

s

 The rotor flux r is then obtained from:

rdq

s



s
s
L'r

sdq  Ls isdq
Lm

s



(30)

(31)

 Disadvantages: dc-drift due to noise in electronic circuits

employed, incorrect initial values of flux vector components
sdq(0)
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

33


Slide 34

Direct Rotor Flux Orientation
(DRFO) – Estimated from vsdqs & isdqs
2. Estimated from motor’s stator voltages and currents
 This scheme is part of sensorless drive scheme


using machine parameters, voltages and currents to estimate flux and
speed

 sdqs calculations (eq. 30) depends on Rs
 Poor field orientation at low speeds ( < 2 Hz), above 2 Hz, DRFO scheme
as good as IRFO


Solution: add boost voltage to vsdqs at low speeds

 Disadvantages: Parameter sensitive, dc-drift due to noise in

electronic circuits employed, incorrect initial values of flux vector
components sdq(0)
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

34


Slide 35

Direct Rotor Flux Orientation
(DRFO) – Estimated from vsdqs & isdqs
Rotating frame (drqr) Stationary frame (dsqs)
isdr*
r*
Eq. (24) +
isqr* r* +
PI +
-

-

r
NO field
weakening
(constant flux)
Dr. Ungku Anisa, July 2008

vsdr*

PI
vsq

r*

ejr

vsd

PI

DRFO  r
Scheme tan-1
isdr
isqr

vas*

vsqs*

 r

s*

2/3

vbs*
vcs*

PWM
VSI

sds
 rds
vsdqs
 rqs Eq. (31) sqs Eq. (30) isdqs
m

e-jr

EEEB443 - Control & Drives

P/2

ias

isds
isqs

3/2

ibs
ics
35


Slide 36

Direct Rotor Flux Orientation
(DRFO) – field weakening implementation
With field
weakening

r*

Rotating frame (drqr) Stationary frame (dsqs)

imrd r *
+
imrd

r

1
1  S r 

isd

PI
r* +

r*

PI

+
isqr* +

-

vsdr*

PI
vsqr*

ejr

PI

-

 r

tan-1
isdr
isqr

Dr. Ungku Anisa, July 2008

vsqs*

EEEB443 - Control & Drives

 r
e-jr

vsds*
 rds
 rqs
r

Same as
in
slide
26 or 29

isds
isqs
36


Slide 37

Stator Flux Orientation Control
qs
qs

 d- axis of dq- rotating frame is

aligned with s. Hence,

is
s

Ψs
i sq

i

ψs
ψsd
 ψs

ds

ψ 0
ψs
sq

(33)

 Therefore,

Ψs
sd

ds

Ψs
i
 sq = torque producing current

 i sdΨs = field producing current
Dr. Ungku Anisa, July 2008

(32)

EEEB443 - Control & Drives

3P
Te 
( sd isq )
22
Similar to
ia & if in
DC motor

(34)

Decoupled
torque and
flux control
37


Slide 38

Stator Flux Orientation Control
 From the dynamic model of IM, if dq- frame rotates at general

speed g (in terms of vsd, vsq, isd, isq, ird, irq):

vsd   Rs  SLs
  
vsq     g Ls
vrd  
SLm
  
 vrq  ( g  r ) Lm

  g Ls

SLm

Rs  SLs

 g Lm

 ( g  r ) Lm

Rr ' SLr

SLm

( g  r ) Lr

  g Lm

 isd 
  
SLm
  isq  (7)
 ( g  r ) Lr  ird 
  
Rr ' SLr  irq 

 s rotates at synchronous speed s
 Hence, dsqs- frame rotates at s

Therefore, g = s
 These voltage equations are in terms of isd, isq, ird, irq
 Better to have equations in terms of isd, isq, sd,  sq
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

(8)

38


Slide 39

Stator Flux Orientation Control
Ψsdq  Lsisdq  Lmirdq
Ls

isdq
Lm

 Stator flux linkage is given by:
 From (9):

irdq 

Ψ sdq
Lm

(35)
(36)

 Substituting (8) and (36) into (7) gives the IM voltage

equations rotating at s in terms of vsd, vsq, isd, isq, sd, sq:

vsdψs  
Rs
0
 ψs  
0
Rs
vsq   
vrdψs   Ls 1  S r 
sl rLs
 ψs  
 Ls 1  S r 
vrq     sl rLs

S

s

1  S r 
sl r

  s   isdψs 


S   isqψs 
 ψs
  sl r   sd 
  ψs 
1  S r   sq 
(37)

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

39


Slide 40

Stator Flux Orientation Control
 Since

ψ  0 , hence the equations in stator flux
ψs
sq

orientation are:

d ψs
 R i   sd
dt

(38)

ψs
vsq
 Rsisqψs  s sdψs

(39)

v

vrdψs  0   sdψs   r

ψs
sd

ψs
s sd

d ψs
d


 sd  Ls  isdψs   r isdψs   sl r Ls isqψs (40)
dt
dt 




d ψs 
 ψs
v  0   Ls  isq   r isq   sl r  sdψs  Ls isdψs
dt 

ψs
rq

Important equations for
Stator Flux Orientation Control!

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives



(41)

40


Slide 41

Stator Flux Orientation Control
 Equation (40) can be rearranged to give:

1  S r  sdψs  1  S r Lsisdψs  sl r Lsisqψs

(42)

ψs
ψs
ψ
i
 sd should be independent of torque producing current s q
ψs
ψs
ψ
ψ
i
 From (42), sd is proportional to sd and is qs .
ψs
ψs
ψ
 Coupling exists between sd and is q .

ψ

ψs
s
i
Varying s q to control torque causes change in ψ sd

Torque will not react immediately to isψqs
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

41


Slide 42

Stator Flux Orientation Control
– Dynamic Decoupling
 De-coupler is required to
ψs
ψ
 overcome the coupling between sd and
ψs
ψ
no effect on sd )
ψs*
 Provide the reference value for is d
 Rearranging eq. (42) gives:



ψs*
sq

ψs
sq

i

ψs
sq

(so that i


1   sdψs*
*
 S  
 sl isqψs*
 r  Ls

ψs*
isd 

1 
 S 

 r 


has

(43)

i

can be obtained from outer speed control loop
*
 However, eq. (43) requires  sl
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

42


Slide 43

Stator Flux Orientation Control
– Dynamic Decoupling
*

 sl can be obtained from (41):

sl



ψ

ψs*
sd

*


1
 S 
 r





 i ψs*

 sdψs* ψs*
 isd
Ls

(44)

sq

*
ψ
in (43) and (44) is the reference stator flux vector s

 Hence, equations (43) and (44) provide dynamic decoupling
ψs*
s d and

of the flux-producing i

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

ψs
i
torque-producing sq currents.

43


Slide 44

Stator Flux Orientation Control
– Dynamic Decoupling
 Dynamic decoupling system implementation:
1
1
1
+
s*
S
1
S

r
 Ls

+

isds*

r

isqs*

from speed
controller

isqs*

S

1

 r
x

x

sl*

1
ψ
ψs*
 isd
Ls
*
s

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

44


Slide 45

Stator Flux Orientation Control
 dsqs- frame also rotates at s

qs
qs

 For precise control, s must be

is
s

Ψs
i sq

s

Ψs
i sd

dq- reference frame
orientation angle
Dr. Ungku Anisa, July 2008

ds

obtained at every instant in time
 Leads to two types of control:
 Indirect Stator Flux Orientation
 Direct Stator Flux Orientation
 s easily estimated from motor’s
s
d
stator voltages vsdqs and stator
currents isdqs
 Hence, Indirect Stator Flux
Orientation scheme unessential.

EEEB443 - Control & Drives

45


Slide 46

Direct Stator Flux Orientation
(DSFO) - implementation
 Closed-loop implementation:
1.

Obtain isds* from s control loop and dynamic
decoupling system shown in slide 38.
Obtain isqs* from outer speed control loop since isqr* 
Te* based on (34):
*

i

ψs*
sq

Te
3P
 ψs* where kt 
kt isd
22

(45)

Obtain vsdqs* from isdqs* via inner current control loop.
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

46


Slide 47

Direct Stator Flux Orientation
(DSFO) - implementation
 Closed-loop implementation:
2.

Determine the angular position s using:

 ψ  tan
s

s

sq
1

 sd

(46)

s

sds and sqs obtained from stator voltage equations:





sdq   vsdq  Rs isdq  sdq 0
s

s

s

s2

Note that: ψ s   sd  sq

s2

s

(47)

(48)

Eq. (48) will be used as feedback for the s control loop
Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

47


Slide 48

Direct Stator Flux Orientation
(DSFO) - implementation
 Closed-loop implementation:
3.

s to be used in the dsqs  dsqs conversion of stator
voltage (i.e. vsdqs* to vsdqs* concersion).

 s estimated from pure integration of motor’s stator voltages

equations eq. (47) which has disadvantages of:

dc-drift due to noise in electronic circuits employed

incorrect initial values of flux vector components
sdqs(0)
 Solution: A low-pass filter can be used to replace the pure
integrator and avoid the problems above.

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

48


Slide 49

Direct Stator Flux Orientation
(DSFO) - implementation
r

r* +
s*

isqs*
+

-

PI

-

Decoupling
system
+ i s*
sd
1

+

PI

- | |

S

vsqs*

vsds*

1

 r

PI
 s

tan-1

isqs

s

Eq. (48)
sds sqs

ejs

isds

 s

e-js

vsds*
sds

2/3

PWM
VSI

vbs*
vcs*

vsdqs
Eq. (47) isdqs

sqs
ias

isqs
isds

m
vas*

vsqs*

PI

+
-

+

P/2

3/2

ibs
ics

Rotating frame (dsqs ) Stationary frame (dsqs )

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

49


Slide 50

References
 Trzynadlowski, A. M., Control of Induction Motors, Academic

Press, San Diego, 2001.
 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.
 Asher, G.M, Vector Control of Induction Motor Course Notes,
University of Nottingham, UK, 2002.

Dr. Ungku Anisa, July 2008

EEEB443 - Control & Drives

50