Transcript 11 Induction Motor - Field Oriented Control
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
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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
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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
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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
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Slide 6
Analogy to DC Motor
In the Induction Motor:
s
c’
r
a
b’
Te = kr x s
s produced by stator currents
r produced by induced rotor
b
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c
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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 betweens orr andis is made to be
90, then the IM will behave like a DC motor.
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Slide 8
Principles of Field Orientation
Control
Hence, if the angle betweens orr andis 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
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Stator-Flux
Orientation Control
8
Slide 9
Principles of Field Orientation
Control
Rotor-Flux
Orientation Control
Stator-Flux
Orientation Control
qs
qs
qr
qs
is
r
r
isq
i
Ψs
i sq
ds
3 P Lm
Te
( rd isq rq isd )
2 2 Lr
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s
dr
r
sd
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is
ds
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) dfqf - reference frame, obtain
• isqf* from given rotor speed reference r* (via speed controller)
• isdf* from given flux reference f*
• Determine the angular position f of f (i.e. reference frame
orientation angle)
• used in the dfqf dsqs conversion from vsdqf* (output of
isdqf* 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.
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Slide 11
Rotor Flux Orientation Control
qs
d- axis of dq- rotating frame is
qr
aligned with r . Hence,
is
rd r
(4)
rqr 0
(5)
r
r
r
isq
r
dr
Therefore,
r
i sd
ds
r
i
sq = torque producing current
r
i sd
= field producing current
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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, drqr- 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
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(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 SLs
sLs
ψr
Rs SLs
vsq sLs
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)
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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 sLs isq s
rd (12)
dt
Lr ' dt
Lm ψr
d ψr
ψr
ψr
ψr
(13)
vsq Rs isq Ls isq sLs 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
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(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
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Slide 16
Rotor Flux Orientation Control
qs
r rotates at synchronous speed
qr
is
r
s
drqr- frame also rotates at s
dr 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
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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
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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 isdr* from r* using (16):
ψr*
isdψr* imrd
rdψr*
(24)
Lm
Obtain isqr* from outer speed control loop since isqr*
Tm* based on (6):
*
i
ψr*
sq
Te
3 P Lm
ψr* where kt
kt isd
2 2 Lr
2
(25)
Obtain vsdqr* from isdqr* via inner current control loop.
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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 drqr dsqs conversion of stator
voltage (i.e. vsdqr* to vsdqs* concersion).
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Slide 20
Indirect Rotor Flux Orientation
(IRFO) - implementation
drqr dsqs transformation
Rotating frame (drqr)
isdr*
r*
Eq. (24) +
isqr* r* +
PI +
Staionary frame (dsqs)
vsdr*
vsq
ejr
PI
-
-
isdr* isqr*
Eq. (23)
NO field
weakening
(constant flux)
Dr. Ungku Anisa, July 2008
slip
+
vsd
s*
r
r
+
isdr
isqr
vas*
vsqs*
PI
r*
2-phase (dsqs )
to 3-phase (abc)
transformation
2/3
vcs*
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isqs
PWM
VSI
IRFO
Scheme
P/2
m
ias
isds
e-jr
vbs*
3/2
ibs
ics
20
Slide 21
Indirect Rotor Flux Orientation
(IRFO) - implementation
drqr dsqs transformation
vsqs*
vsdr*
vsqr*
ejr
vsds*
xsds cos r
s
xsq sin r
sin r xsdr
cos r xsqr
dsqs drqr transformation
isdr
isqr
isds
e-jr
Dr. Ungku Anisa, July 2008
isqs
xsdr cos r
r
xsq sin r
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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
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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
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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
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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.
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Slide 26
Example – IRFO Control of IM ctd.
Answers:
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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)
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27
Slide 28
Indirect Rotor Flux Orientation
(IRFO) – field weakening implementation
With field
weakening
r*
Rotating frame (drqr) Staionary frame (dsqs)
imrd r *
+
imrd
r
1
1 S r
isd
PI
r* +
r*
PI
-
+
isqr* +
imrdr*r
vsdr*
PI
vsqr*
ejr
PI
-
isq *
Eq. (22)
vsqs*
slip
+
r
r
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Same as
in slide 20
+
isdr
isqr
vsds*
isds
e-jr
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)
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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
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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.
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EEEB443 - Control & Drives
31
Slide 32
Direct Rotor Flux Orientation
(DRFO) – Direct measurements mds & mqs
Rotating frame
isdr*
r*
Eq. (24) +
isqr* r* +
PI +
-
-
r
NO field
weakening
(constant flux)
Dr. Ungku Anisa, July 2008
(drqr)
Stationary frame
vsdr*
vsq
r*
ejr
vsd
PI
DRFO r
Scheme tan-1
isdr
isqr
s*
2/3
vbs*
vcs*
mds
rds
rqs Eq. (29) mqs
r
e-jr
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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)
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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)
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34
Slide 35
Direct Rotor Flux Orientation
(DRFO) – Estimated from vsdqs & isdqs
Rotating frame (drqr) Stationary frame (dsqs)
isdr*
r*
Eq. (24) +
isqr* r* +
PI +
-
-
r
NO field
weakening
(constant flux)
Dr. Ungku Anisa, July 2008
vsdr*
PI
vsq
r*
ejr
vsd
PI
DRFO r
Scheme tan-1
isdr
isqr
vas*
vsqs*
r
s*
2/3
vbs*
vcs*
PWM
VSI
sds
rds
vsdqs
rqs Eq. (31) sqs Eq. (30) isdqs
m
e-jr
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 (drqr) Stationary frame (dsqs)
imrd r *
+
imrd
r
1
1 S r
isd
PI
r* +
r*
PI
+
isqr* +
-
vsdr*
PI
vsqr*
ejr
PI
-
r
tan-1
isdr
isqr
Dr. Ungku Anisa, July 2008
vsqs*
EEEB443 - Control & Drives
r
e-jr
vsds*
rds
rqs
r
Same as
in
slide
26 or 29
isds
isqs
36
Slide 37
Stator Flux Orientation Control
qs
qs
d- axis of dq- rotating frame is
aligned with s. Hence,
is
s
Ψs
i sq
i
ψs
ψsd
ψs
ds
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, dsqs- 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
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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 rLs
ψs
Ls 1 S r
vrq sl rLs
S
s
1 S r
sl r
s isdψs
S isqψs
ψs
sl r sd
ψs
1 S r sq
(37)
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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
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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
+
isds*
r
isqs*
from speed
controller
isqs*
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
dsqs- frame also rotates at s
qs
qs
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
ds
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 isds* from s control loop and dynamic
decoupling system shown in slide 38.
Obtain isqs* from outer speed control loop since isqr*
Te* based on (34):
*
i
ψs*
sq
Te
3P
ψs* where kt
kt isd
22
(45)
Obtain vsdqs* from isdqs* 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 dsqs dsqs conversion of stator
voltage (i.e. vsdqs* 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*
isqs*
+
-
PI
-
Decoupling
system
+ i s*
sd
1
+
PI
- | |
S
vsqs*
vsds*
1
r
PI
s
tan-1
isqs
s
Eq. (48)
sds sqs
ejs
isds
s
e-js
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 (dsqs ) 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
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 = kr 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 betweens orr andis 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 betweens orr andis 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
qr
qs
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
dr
r
sd
EEEB443 - Control & Drives
is
ds
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) dfqf - reference frame, obtain
• isqf* from given rotor speed reference r* (via speed controller)
• isdf* from given flux reference f*
• Determine the angular position f of f (i.e. reference frame
orientation angle)
• used in the dfqf dsqs conversion from vsdqf* (output of
isdqf* 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
qr
aligned with r . Hence,
is
rd r
(4)
rqr 0
(5)
r
r
r
isq
r
dr
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, drqr- 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 SLs
sLs
ψr
Rs SLs
vsq sLs
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 sLs isq s
rd (12)
dt
Lr ' dt
Lm ψr
d ψr
ψr
ψr
ψr
(13)
vsq Rs isq Ls isq sLs 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
qr
is
r
s
drqr- frame also rotates at s
dr 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 isdr* from r* using (16):
ψr*
isdψr* imrd
rdψr*
(24)
Lm
Obtain isqr* from outer speed control loop since isqr*
Tm* based on (6):
*
i
ψr*
sq
Te
3 P Lm
ψr* where kt
kt isd
2 2 Lr
2
(25)
Obtain vsdqr* from isdqr* 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 drqr dsqs conversion of stator
voltage (i.e. vsdqr* to vsdqs* concersion).
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
19
Slide 20
Indirect Rotor Flux Orientation
(IRFO) - implementation
drqr dsqs transformation
Rotating frame (drqr)
isdr*
r*
Eq. (24) +
isqr* r* +
PI +
Staionary frame (dsqs)
vsdr*
vsq
ejr
PI
-
-
isdr* isqr*
Eq. (23)
NO field
weakening
(constant flux)
Dr. Ungku Anisa, July 2008
slip
+
vsd
s*
r
r
+
isdr
isqr
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-jr
vbs*
3/2
ibs
ics
20
Slide 21
Indirect Rotor Flux Orientation
(IRFO) - implementation
drqr dsqs transformation
vsqs*
vsdr*
vsqr*
ejr
vsds*
xsds cos r
s
xsq sin r
sin r xsdr
cos r xsqr
dsqs drqr transformation
isdr
isqr
isds
e-jr
Dr. Ungku Anisa, July 2008
isqs
xsdr 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 (drqr) Staionary frame (dsqs)
imrd r *
+
imrd
r
1
1 S r
isd
PI
r* +
r*
PI
-
+
isqr* +
imrdr*r
vsdr*
PI
vsqr*
ejr
PI
-
isq *
Eq. (22)
vsqs*
slip
+
r
r
Dr. Ungku Anisa, July 2008
EEEB443 - Control & Drives
Same as
in slide 20
+
isdr
isqr
vsds*
isds
e-jr
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
isdr*
r*
Eq. (24) +
isqr* r* +
PI +
-
-
r
NO field
weakening
(constant flux)
Dr. Ungku Anisa, July 2008
(drqr)
Stationary frame
vsdr*
vsq
r*
ejr
vsd
PI
DRFO r
Scheme tan-1
isdr
isqr
s*
2/3
vbs*
vcs*
mds
rds
rqs Eq. (29) mqs
r
e-jr
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 (drqr) Stationary frame (dsqs)
isdr*
r*
Eq. (24) +
isqr* r* +
PI +
-
-
r
NO field
weakening
(constant flux)
Dr. Ungku Anisa, July 2008
vsdr*
PI
vsq
r*
ejr
vsd
PI
DRFO r
Scheme tan-1
isdr
isqr
vas*
vsqs*
r
s*
2/3
vbs*
vcs*
PWM
VSI
sds
rds
vsdqs
rqs Eq. (31) sqs Eq. (30) isdqs
m
e-jr
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 (drqr) Stationary frame (dsqs)
imrd r *
+
imrd
r
1
1 S r
isd
PI
r* +
r*
PI
+
isqr* +
-
vsdr*
PI
vsqr*
ejr
PI
-
r
tan-1
isdr
isqr
Dr. Ungku Anisa, July 2008
vsqs*
EEEB443 - Control & Drives
r
e-jr
vsds*
rds
rqs
r
Same as
in
slide
26 or 29
isds
isqs
36
Slide 37
Stator Flux Orientation Control
qs
qs
d- axis of dq- rotating frame is
aligned with s. Hence,
is
s
Ψs
i sq
i
ψs
ψsd
ψs
ds
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, dsqs- 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 rLs
ψs
Ls 1 S r
vrq sl rLs
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
+
isds*
r
isqs*
from speed
controller
isqs*
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
dsqs- frame also rotates at s
qs
qs
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
ds
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 isds* from s control loop and dynamic
decoupling system shown in slide 38.
Obtain isqs* from outer speed control loop since isqr*
Te* based on (34):
*
i
ψs*
sq
Te
3P
ψs* where kt
kt isd
22
(45)
Obtain vsdqs* from isdqs* 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 dsqs dsqs conversion of stator
voltage (i.e. vsdqs* 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*
isqs*
+
-
PI
-
Decoupling
system
+ i s*
sd
1
+
PI
- | |
S
vsqs*
vsds*
1
r
PI
s
tan-1
isqs
s
Eq. (48)
sds sqs
ejs
isds
s
e-js
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 (dsqs ) 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