1. EEEB443 Control & Drives
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
Dr. Ungku Anisa, July 2008

2. Outline Stator Flux Orientation Control 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
Dr. Ungku Anisa, July 2008

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
Dr. Ungku Anisa, July 2008

4. Vector Control or Field Orientation Control
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
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
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Dr. Ungku Anisa, July 2008

5. Analogy to DC Drive f a Te = k f Ia Te = k f Ia = k’ If Ia sin 90
In the DC motor:
f controlled by controlling If
If same direction as field f
Ia same direction as field a
Ia and f always perpendicular and decoupled
Hence,
Keeping f constant, Te controlled by controlling Ia
Ia, If , a and f are space vectors f
Te = k f Ia
= k’ If Ia sin 90
= k’(If x Ia) a
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Dr. Ungku Anisa, July 2008

6. Analogy to DC Motor Te = kr x s In the Induction Motor: s
s produced by stator currents
r produced by induced rotor 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.
s
Te = kr x s a b b’ c’ c
r
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

7. Analogy to DC Motor Induction Motor torque equation :
Compared with DC Motor torque equation:
Hence, if the angle betweens orr andis is made to be 90, then the IM will behave like a DC motor.
(1)
(2)
(3)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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
Stator-Flux Orientation Control
Rotor-Flux Orientation Control
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

9. Principles of Field Orientation Control
Rotor-Flux Orientation Control
Stator-Flux Orientation Control qs ds qs ds
qr
qs
ds
dr
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

10. Principles of Field Orientation Control
Summary of field orientation control on a selected flux vectorf (i.e. either r , s or  m): 1
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* 2
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*. 3
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

11. Rotor Flux Orientation Controlqs ds
d- axis of dq- rotating frame is aligned with r . Hence,
Therefore,
qr
(4)
dr
(5)
r
(6)
= torque producing current
= field producing current
Similar to ia & if in DC motor
Decoupled torque and flux control
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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) :
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
(7)
(8)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

13. Rotor Flux Orientation Control
Rotor flux linkage is given by:
From (9):
Substituting (8) and (10) into (7) gives the IM voltage equations rotating at s in terms of vsd, vsq, isd, isq, rd, rq:
(9)
(10)
(11)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

14. Rotor Flux Orientation Control
Since , hence the equations in rotor flux orientation are:
(12)
(13)
(14)
Note:
Total leakage factor =
sl = slip speed (elec.)
(15)
Important equations for
Rotor Flux Orientation Control!
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

15. Rotor Flux Orientation Control
Let
Using (16), equation (14) can be rearranged to give:
is called the “equivalent magnetising current” or “field current”
Hence, from (17): where
Under steady-state conditions (i.e. constant flux):
(16)
(17)
(18)
(19)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

16. Rotor Flux Orientation Controlqs ds
r rotates at synchronous speed s
drqr- frame also rotates at s
Hence,
For precise control, r must be obtained at every instant in time
Leads to two types of control:
Indirect Rotor Flux Orientation
Direct Rotor Flux Orientation
qr
dr
(20)
r
dq- reference frame orientation angle
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

17. Indirect Rotor Flux Orientation (IRFO)
Orientation angle:
Synchronous speed obtained by adding slip speed and electrical rotor speed
Slip speed can be obtained from equation (15):
Under steady-state conditions ( ):
(21)
(22)
(23)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

18. Indirect Rotor Flux Orientation (IRFO) - implementation
Closed-loop implementation under constant flux condition:
Obtain isdr* from r* using (16):
Obtain isqr* from outer speed control loop since isqr*  Tm* based on (6):
Obtain vsdqr* from isdqr* via inner current control loop.
(24)
(25)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

19. Indirect Rotor Flux Orientation (IRFO) - implementation
Closed-loop implementation under constant flux condition:
Determine the angular position r using (21) and (23):
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).
(26)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

20. Indirect Rotor Flux Orientation (IRFO) - implementation
drqr  dsqs transformation
Rotating frame (drqr)
Staionary frame (dsqs)
2-phase (dsqs )
to 3-phase (abc)
transformation
isdr*
vsdr*
r*
vas*
vsqs* +
Eq. (24) PI
PWM
VSI -
vbs*
isqr*
vsqr*
ejr
2/3 +
vsds*
r* +
vcs* PI PI - -
 r
IRFO
Scheme
isdr*
isqr* 
slip r m
Eq. (23)
P/2 + +
isds
ias
NO field weakening (constant flux)
isdr
ibs
e-jr
3/2
isqr
isqs
ics
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

21. Indirect Rotor Flux Orientation (IRFO) - implementation
drqr  dsqs transformation
dsqs  drqr transformation
vsqs*
vsds*
vsdr*
vsqr*
ejr
e-jr
isds
isqs
isdr
isqr
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

22. Indirect Rotor Flux Orientation (IRFO) - implementation
2-phase (dsqs ) to 3-phase (abc) transformation:
3-phase (abc) to 2-phase (dsqs ) transform is given by:
where:
and
2/3
vsqs*
vsds*
vas*
vbs*
vcs*
isds
ias
ibs
3/2
isqs
ics
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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

24. Example – IRFO Control of IM ctd.
Parameter
Symbol
Value
Rated torque
Te,rat
183 Nm
Stator resistance Rs
0.294 
Stator self inductance Ls H
Referred rotor resistance
Rr’
0.156 
Referred rotor self inductance
Lr’ H
Mutual inductance Lm
0.041 H
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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* = 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
the three-phase stator reference currents ias*, ibs* and ics*
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

26. Example – IRFO Control of IM ctd.
Answers:
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Dr. Ungku Anisa, July 2008

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
Compared with eq. (17) for IM:
IM: flux weakened by reducing imrd
(i.e. “equivalent magnetising current”
or “field current)
imrd*
imrd (rated)
r (base) r
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

28. Indirect Rotor Flux Orientation (IRFO) – field weakening implementation
With field weakening
Rotating frame (drqr)
Staionary frame (dsqs)
Same as in slide 20
imrd r *
vsdr* +
isdr*
vsqs*
r* + PI PI - -
isqr*
vsqr*
ejr
imrd r
r* +
vsds* + PI PI - -
imrdr*
 r
isqr* 
slip r
Eq. (22) + +
isdr
isds
e-jr
isqr
isqs
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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

30. Direct Rotor Flux Orientation (DRFO)
Orientation angle:
obtained from:
Direct measurements of airgap fluxes mds and mqs
Estimated from motor’s stator voltages vsdqs
and stator currents isdqs
Note that:
(27)
(28)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

31. Direct Rotor Flux Orientation (DRFO) – Direct measurements mds & mqs
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:
Disadvantages: sensors are inconvenient and spoil the ruggedness of IM.
(29)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

32. Direct Rotor Flux Orientation (DRFO) – Direct measurements mds & mqs
Rotating frame (drqr)
Stationary frame (dsqs)
Flux sensing coils arranged in quadrature
isdr*
vsdr*
r*
vas*
vsqs* +
Eq. (24) PI
PWM
VSI -
vbs*
isqr*
vsqr*
2/3
ejr +
vsds*
r* +
vcs* PI PI - -
DRFO
Scheme
 r
 rds
mds
tan-1
 rqs
Eq. (29)
mqs r m
P/2
 r
isdr
isds
ias
NO field weakening (constant flux)
ibs
e-jr
3/2
isqr
isqs
ics
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

33. Direct Rotor Flux Orientation (DRFO) – Estimated from vsdqs & isdqs
Estimated from motor’s stator voltages and currents
sds and  sqs obtained from stator voltage equations:
The rotor flux r is then obtained from:
Disadvantages: dc-drift due to noise in electronic circuits employed, incorrect initial values of flux vector components sdq(0)
(30)
(31)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

34. Direct Rotor Flux Orientation (DRFO) – Estimated from vsdqs & isdqs
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

35. Direct Rotor Flux Orientation (DRFO) – Estimated from vsdqs & isdqs
Rotating frame (drqr)
Stationary frame (dsqs)
isdr*
vsdr*
r*
vas*
vsqs* +
Eq. (24) PI
PWM
VSI -
vbs*
isqr*
vsqr*
2/3
ejr +
vsds*
r* +
vcs* PI PI - -
DRFO
Scheme
 r
 rds
sds
vsdqs
tan-1
 rqs
Eq. (31)
Eq. (30)
sqs
isdqs r m
P/2
 r
ias
NO field weakening (constant flux)
isdr
isds
ibs
e-jr
3/2
isqr
isqs
ics
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

36. Direct Rotor Flux Orientation (DRFO) – field weakening implementation
With field weakening
Rotating frame (drqr)
Stationary frame (dsqs)
Same as in
slide
26 or 29
imrd r *
vsdr* +
isdr*
vsqs*
r* + PI PI - -
isqr*
vsqr*
ejr
imrd r
r* +
vsds* + PI PI - -
 r
 rds
tan-1
 rqs r
 r
isdr
isds
e-jr
isqr
isqs
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

37. Stator Flux Orientation Controlqs
d- axis of dq- rotating frame is aligned with s. Hence,
Therefore,
qs
(32)
ds
(33)
(34) ds
= torque producing current
= field producing current
Similar to ia & if in DC motor
Decoupled torque and flux control
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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):
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
(7)
(8)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

39. Stator Flux Orientation Control
Stator flux linkage is given by:
From (9):
Substituting (8) and (36) into (7) gives the IM voltage equations rotating at s in terms of vsd, vsq, isd, isq, sd, sq:
(35)
(36)
(37)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

40. Stator Flux Orientation Control
Since , hence the equations in stator flux orientation are:
(38)
(39)
(40)
(41)
Important equations for
Stator Flux Orientation Control!
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

41. Stator Flux Orientation Control
Equation (40) can be rearranged to give:
should be independent of torque producing current
From (42), is proportional to and
Coupling exists between and
(42)
Varying to control torque causes change in
Torque will not react immediately to
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

42. Stator Flux Orientation Control – Dynamic Decoupling
De-coupler is required to
overcome the coupling between and (so that has no effect on )
Provide the reference value for
Rearranging eq. (42) gives:
can be obtained from outer speed control loop
However, eq. (43) requires
(43)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

43. Stator Flux Orientation Control – Dynamic Decoupling
can be obtained from (41):
in (43) and (44) is the reference stator flux vector
Hence, equations (43) and (44) provide dynamic decoupling of the flux-producing and torque-producing currents.
(44)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

44. Stator Flux Orientation Control – Dynamic Decoupling
Dynamic decoupling system implementation: x
s*
isqs*
isds* +
sl*
isqs*
from speed controller
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

45. Stator Flux Orientation Controlqs
dsqs- frame also rotates at s
For precise control, s must be 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 stator voltages vsdqs and stator currents isdqs
Hence, Indirect Stator Flux Orientation scheme unessential.
qs
ds
s ds
dq- reference frame orientation angle
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

46. Direct Stator Flux Orientation (DSFO) - implementation
Closed-loop implementation:
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):
Obtain vsdqs* from isdqs* via inner current control loop.
(45)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

47. Direct Stator Flux Orientation (DSFO) - implementation
Closed-loop implementation:
Determine the angular position s using:
sds and sqs obtained from stator voltage equations:
Note that:
Eq. (48) will be used as feedback for the s control loop
(46)
(47)
(48)
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

48. Direct Stator Flux Orientation (DSFO) - implementation
Closed-loop implementation:
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

49. Direct Stator Flux Orientation (DSFO) - implementation
isqs*
vsqs*
vas* +
vsqs*
r* + PI PI
PWM
VSI -
vbs*
vsds*
2/3
ejs
s*
vsds*
Decoupling
system
vcs* PI +
isds*
 s
sds
vsdqs + +
tan-1
sqs
Eq. (47)
isdqs - +
 s PI
ias
isqs
isqs -
|s|
ibs
e-js
3/2
Eq. (48)
isds
isds
ics
sds
sqs
Rotating frame (dsqs )
Stationary frame (dsqs )
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives

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, Prentice-Hall, 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