induction motor – vector control or field oriented control by dr. ungku anisa ungku amirulddin...
TRANSCRIPT
Induction Motor – Vector Control or Field Oriented ControlByDr. Ungku Anisa Ungku AmirulddinDepartment of Electrical Power EngineeringCollege of Engineering
Dr. Ungku Anisa, July 2008 1EEEB443 - Control & Drives
OutlineIntroductionAnalogy to DC DrivePrinciples of Field Orientation ControlRotor Flux Orientation Control
Indirect Rotor Flux Orientation (IRFO)Direct Rotor Flux Orientation (DRFO)
Stator Flux Orientation ControlDirect Stator Flux Orientation (DSFO)
References
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 2
IntroductionInduction Motor (IM) drives are replacing DC drives
because:Induction motor is simpler, smaller in size, less maintenanceLess costCapability of faster torque responseCapability of faster speed response (due to lower inertia)
DC motor is superior to IM with respect to ease of controlHigh performance with simple control Due to decoupling component of torque and flux
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 3
Introduction
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 4
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
Analogy to DC DriveIn 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 vectorsDr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 5
f
a
Te = k f Ia
Te = k f Ia
= k’ If Ia sin 90
= k’(If x Ia)
Analogy to DC MotorIn the Induction Motor:
s produced by stator currentsr produced by induced rotor
currentsBoth 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.
a
b
b’c’
c
sr
Dr. Ungku Anisa, July 2008 6EEEB443 - Control & Drives
Te = kr x s
Analogy to DC MotorInduction Motor torque equation :
Compared with DC Motor torque equation:
Hence, if the angle betweens orr andis is made to be 90, then the IM will behave like a DC motor.
ss iψ22
3
PTe
sr iψ22
3
r
me L
LPT
Dr. Ungku Anisa, July 2008 7EEEB443 - Control & Drives
(1)
(2)
(3) afafafe kikIIkT iψ ψ90sin'
Principles of Field Orientation ControlHence, 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 8EEEB443 - Control & Drives
Achieved through orientation (alignment) of rotating dq frame on r or s
Rotor-Flux Orientation Control
Stator-Flux Orientation Control
Principles of Field Orientation Control
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 9
Rotor-Flux Orientation Control
si
qs
ds
r dr
qr
rsdi
rsqi
)(22
3sdrqsqrd
r
me ii
L
LPT
si
qs
ds
sds
qs
Ψssdi
Ψssqi
)(22
3sdsqsqsde ii
PT
Stator-Flux Orientation Control
Principles of Field Orientation ControlSummary of field orientation control on a selected flux vectorf
(i.e. either r , s or m):
Dr. Ungku Anisa, July 2008 10EEEB443 - Control & Drives
Rotor Flux Orientation Controld- axis of dq- rotating frame is
aligned with r . Hence,
Therefore,
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives
si
qs
ds
r dr
qr
rsdi
rsqi
rrdr
0r
rq
(4)
(5)
r )(22
3sqrd
r
me i
L
LPT (6)
= torque producing current
= field producing currentrsdi
rsqi
Similar to ia & if in DC motor
Decoupled torque and flux control
11
Rotor Flux Orientation ControlFrom 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, 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 12EEEB443 - Control & Drives
rq
rd
sq
sd
rrrrgmmrg
rrgrrmrgm
mmgsssg
mgmsgss
rq
rd
sq
sd
i
i
i
i
SLRLSLL
LSLRLSL
SLLSLRL
LSLLSLR
v
v
v
v
')()(
)(')(
(7)
(8)
Rotor Flux Orientation ControlRotor 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:
Dr. Ungku Anisa, July 2008 13EEEB443 - Control & Drives
rdqrsdqmrdq iLiL ' (9)
sdqr
m
r
rdqrdq i
L
L
Li
''
(10)
ψr
ψr
ψr
ψr
ψr
ψr
ψr
ψr
''''0
''0''
''
''
rq
rd
sq
sd
rrslrmr
slrrrmr
rmrmsssss
rmsrmssss
rq
rd
sq
sd
i
i
SLRLLR
SLRLLR
LSLLLLSRL
LLLLSLLSR
v
v
v
v
(11)
Since , hence the equations in rotor flux orientation are:
Note:Total leakage factor =
sl = slip speed (elec.)
Rotor Flux Orientation Control
Dr. Ungku Anisa, July 2008 14EEEB443 - Control & Drives
(13)
0r
rq
ψrψrψrψrψrrd
r
mssqsssdssdssd dt
d
L
LiLi
dt
dLiRv
'
ψrψrψrψrψr
' rdr
mssdsssqssqssq L
LiLi
dt
dLiRv
ψrψrψrψr
''0 sdr
r
mrdrd
r
rrq iR
L
L
dt
d
L
Rv
ψrψrψr
'0 sqr
r
mrdslrq iR
L
Lv
(12)
(14)
(15)
'
2
1rs
m
LL
L
Important equations for 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):
Rotor Flux Orientation Control
Dr. Ungku Anisa, July 2008 15EEEB443 - Control & Drives
(16)
(18)
(19)
ψrψrψrmrd
r
rmrdsd i
dt
d
R
Lii
'
ψrψrmrdmrd iL
ψrmrdi
ψrψrmrdsd ii
ψrψrmrdrsd iSi 1
(17)
r
rr R
L '
Rotor Flux Orientation Controlr rotates at synchronous speed
s
drqr- 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 OrientationDirect Rotor Flux Orientation
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives
si
qs
ds
r dr
qr
rsdi
rsqi
r
dt sr (20)
16
dq- reference frame orientation angle
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 ( ):
Indirect Rotor Flux Orientation (IRFO)
Dr. Ungku Anisa, July 2008 17EEEB443 - Control & Drives
ψr
ψr
ψr
ψrψr
ψrmrdr
sq
rdr
sqmsq
rd
r
r
msl i
iiLi
R
L
L
'
(21)
(22)
dt sr
dtdt rslsr
ψr
ψr
sdr
sqsl i
i
(23)
ψrψrsdmrd ii
Closed-loop implementation under constant flux condition:1. Obtain isd
r* from r* using (16):
Obtain isqr* from outer speed control loop since isq
r* Tm
* based on (6):
Obtain vsdqr* from isdq
r* via inner current control loop.
Indirect Rotor Flux Orientation (IRFO) - implementation
Dr. Ungku Anisa, July 2008 18EEEB443 - Control & Drives
(24)
(25)
m
rdmrdsd Lii
***
ψrψrψr
r
mt
sdt
esq L
LPk
ik
Ti
2
ψr*
*ψr*
22
3 where
Closed-loop implementation under constant flux condition:2. 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 drqr dsqs conversion of stator voltage (i.e. vsdq
r* to vsdqs* concersion).
Indirect Rotor Flux Orientation (IRFO) - implementation
Dr. Ungku Anisa, July 2008 19EEEB443 - Control & Drives
(26) dt2
dtdtψr*
ψr**
m
sdr
sqrsls
P
i
ir
Indirect Rotor Flux Orientation (IRFO) - implementation
20
r*
r*
2/3
isqr*
isdr*
vsqs*
vsds*
vas*
vbs*
vcs*
slip r
+
+
Rotating frame (drqr) Staionary frame (dsqs)
Eq. (24)ejr
P/2Eq. (23) m
PWMVSI
+
3/2e-jr
ias
ibs
ics
isds
isqs
PIvsd
r*
PI
vsqr*
+PI+
-
isdr
isqr
--
isqr*isd
r*
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives
r
NO field weakening
(constant flux)
2-phase (dsqs ) to 3-phase (abc)transformation
drqr dsqs transformation
IRFO Scheme
Indirect Rotor Flux Orientation (IRFO) - implementationdrqr dsqs transformation
dsqs drqr transformation
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 21
ssq
ssd
sq
sd
x
x
x
x
rr
rr
r
r
cossin
sincos
r
r
rr
rr
sq
sdssq
ssd
x
x
x
x
cossin
sincosvsq
s*
vsds*
vsdr*
vsqr*
ejr
e-jr
isds
isqs
isdr
isqr
2-phase (dsqs ) to 3-phase (abc) transformation:
3-phase (abc) to 2-phase (dsqs ) transform is given by:
where:
and
Indirect Rotor Flux Orientation (IRFO) - implementation
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 22
abcabcsdq xTx
sdqabcabc xTx 1
3
13
1
00
0
1abcT
23
23
21
211
01
Tabc
2/3
vsqs*
vsds*
vas*
vbs*
vcs*
3/2
ias
ibs
ics
isds
isqs
Example – IRFO Control of IMAn induction motor has the following parameters:
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 23
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
Example – IRFO Control of IM ctd.
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 24
Parameter Symbol Value
Rated torque Te,rat 183 Nm
Stator resistance Rs 0.294
Stator self inductance
Ls 0.0424 H
Referred rotor resistance
Rr’ 0.156
Referred rotor self inductance
Lr’ 0.0417 H
Mutual inductance Lm 0.041 H
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:
1. the stator reference currents isd* and isq* in the dq-rotating frame2. the slip speed sl of the motor3. the orientation angle r of the dq-rotating frame4. the stator reference currents isd
s* and isqs* in the stationary dsqs
frame5. the three-phase stator reference currents ias*, ibs* and ics*
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 25
Example – IRFO Control of IM ctd.Answers:
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives 26
Closed-loop implementation under field weakening condition:Employed for operations above base speedDC 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)
Indirect Rotor Flux Orientation (IRFO) – field weakening
Dr. Ungku Anisa, July 2008 27EEEB443 - Control & Drives
ψrψrψrmrd
r
rmrdsd i
dt
d
R
Lii
'
ff
ff
f
f idt
d
R
Li
R
v
imrd*
r
imrd (rated)
r (base)
Indirect Rotor Flux Orientation (IRFO) – field weakening implementation
r*
imrd r *
isqr*
isdr* vsq
s*
vsds*
slip r
+
+
Rotating frame (drqr) Staionary frame (dsqs)
ejr
Eq. (22) +
e-jr
isds
isqs
PIvsd
r*
PI
vsqr*
+PI+
-
isdr
isqr
--
isqr*
imrdr*
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives
r
With field weakening
+
-imrd
r
28
rS1
1
r*
Same as in slide 20
PI
Indirect Rotor Flux Orientation (IRFO) – Parameter sensitivityMismatch 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
Orientation angle:
obtained from:1. Direct measurements of airgap fluxes md
s and mq
s
2. Estimated from motor’s stator voltages vsdqs
and stator currents isdqs
Note that:
Direct Rotor Flux Orientation (DRFO)
Dr. Ungku Anisa, July 2008 30EEEB443 - Control & Drives
(27)s
rd
s
rq
r
1tan
22 srq
srd rψ (28)
1. Direct measurements of airgap fluxes mds and mq
s
mds and mq
s measured using:Hall sensors – fragileflux sensing coils on the stator windings – voltages induced
in coils are integrated to obtain mds and mq
s The rotor flux r is then obtained from:
Disadvantages: sensors are inconvenient and spoil the ruggedness of IM.
Direct Rotor Flux Orientation (DRFO) – Direct measurements md
s & mq
s
Dr. Ungku Anisa, July 2008 31EEEB443 - Control & Drives
(29)s
sdqlr
s
mdqm
rs
rdq iLL
L ''
Direct Rotor Flux Orientation (DRFO) – Direct measurements md
s & mq
s
32
r*
r*
2/3
tan-1
isqr*
isdr*
vsqs*
vsds*
vas*
vbs*
vcs*
r
+
Rotating frame (drqr) Stationary frame (dsqs)
Eq. (24)ejr
P/2
Eq. (29)m
PWMVSI
3/2e-jr
ias
ibs
ics
isds
isqs
PIvsd
r*
PI
vsqr*
+PI+
-
isdr
isqr
--md
s
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives
mqs
rd
s
rq
s
r
r
NO field weakening
(constant flux)
DRFO Scheme
Flux sensing coils arranged in quadrature
2. Estimated from motor’s stator voltages and currentssd
s and sq
s 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)
Direct Rotor Flux Orientation (DRFO) – Estimated from vsdq
s & isdq
s
Dr. Ungku Anisa, July 2008 33EEEB443 - Control & Drives
(30) 0s
sdq
s
sdqs
s
sdq
s
sdq iRv
ssdqs
s
sdqm
rs
rdq iLL
L '
(31)
2. Estimated from motor’s stator voltages and currentsThis 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)
Direct Rotor Flux Orientation (DRFO) – Estimated from vsdq
s & isdq
s
Dr. Ungku Anisa, July 2008 34EEEB443 - Control & Drives
Direct Rotor Flux Orientation (DRFO) – Estimated from vsdq
s & isdq
s
35
r*
r*
2/3
tan-1
isqr*
isdr*
vsqs*
vsds*
vas*
vbs*
vcs*
r
+
Rotating frame (drqr) Stationary frame (dsqs)
Eq. (24)ejr
P/2
Eq. (31)m
PWMVSI
3/2e-jr
ias
ibs
ics
isds
isqs
PIvsd
r*
PI
vsqr*
+PI+
-
isdr
isqr
--sd
s
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives
sqs
rd
s
rq
s
r
r
Eq. (30)vsdq
s
isdqs
NO field weakening
(constant flux)
DRFO Scheme
Direct Rotor Flux Orientation (DRFO) – field weakening implementation
r*
imrd r *
isqr*
isdr* vsq
s*
vsds*
r
+
Rotating frame (drqr) Stationary frame (dsqs)
ejr
e-jr
isds
isqs
PIvsd
r*
PI
vsqr*
+PI+
-
isdr
isqr
--
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives
With field weakening
+
-imrd
r
36
rS1
1
r*
Same as in
slide 26 or 29
tan-1
rds
rq
s
r
r
PI
Stator Flux Orientation Controld- axis of dq- rotating frame is
aligned with s. Hence,
Therefore,
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives
sψsd ψψ s
0ψ sψsq
(32)
(33)
)(22
3sqsde i
PT (34)
= torque producing current
= field producing currentΨssdi
Ψssqi
Similar to ia & if in DC motor
Decoupled torque and flux control
37
si
qs
ds
sds
qs
Ψssdi
Ψssqi
Stator Flux Orientation ControlFrom 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, 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 38EEEB443 - Control & Drives
rq
rd
sq
sd
rrrrgmmrg
rrgrrmrgm
mmgsssg
mgmsgss
rq
rd
sq
sd
i
i
i
i
SLRLSLL
LSLRLSL
SLLSLRL
LSLLSLR
v
v
v
v
')()(
)(')(
(7)
(8)
Stator Flux Orientation ControlStator 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:
Dr. Ungku Anisa, July 2008 39EEEB443 - Control & Drives
rdqmsdqs iLiL sdqΨ (35)
sdqm
s
mrdq i
L
L
Li sdqΨ
(36)
ψs
ψs
ψs
ψs
ψs
ψs
ψs
ψs
11
11
0
0
sq
sd
sq
sd
rrslrssrsl
rslrsrslrs
ss
ss
rq
rd
sq
sd
i
i
SSLL
SLSL
SR
SR
v
v
v
v
(37)
Since , hence the equations in stator flux orientation are:
Stator Flux Orientation Control
Dr. Ungku Anisa, July 2008 40EEEB443 - Control & Drives
(39)
0ψ sψsq
ψsψsψssdsdssd dt
diRv
ψsψsψssdssqssq iRv
ψsψsψsψsψsψs 0 sqsrslsdrsdssdrsdrd iLidt
diL
dt
dv
(38)
(40)
(41) ψsψsψsψsψs 0 sdssdrslsqrsqsrq iLidt
diLv
Important equations for Stator Flux Orientation Control!
Equation (40) can be rearranged to give:
should be independent of torque producing currentFrom (42), is proportional to and .Coupling exists between and .
sψsqi
sψsdψVarying to control torque causes change in
Stator Flux Orientation Control
Dr. Ungku Anisa, July 2008 41EEEB443 - Control & Drives
(42) ψsψsψs 11 sqsrslsdsrsdr iLiLSS
sψsdψ sψ
sdi sψsqi
sψsdψ sψ
sqi
sψsqiTorque will not react immediately to
sψsdψ sψ
sqi
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 loopHowever, eq. (43) requires
Stator Flux Orientation Control – Dynamic Decoupling
Dr. Ungku Anisa, July 2008 42EEEB443 - Control & Drives
(43)
ψssdψ ψs
sqi
r
sqsls
sd
rsd
S
iL
S
i
1
1 ψs**ψs*
ψs*
ψs*sdi
ψs*sqi
*sl
ψssqiψs
sdψ
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.
Stator Flux Orientation Control – Dynamic Decoupling
Dr. Ungku Anisa, July 2008 43EEEB443 - Control & Drives
(44)ψs*
ψs*ψs*
*
1
sq
sds
sd
rsl i
iL
S
*sl
ψs*sdψ
*sψ
ψssqi
ψs*sdi
Dynamic decoupling system implementation:
Stator Flux Orientation Control – Dynamic Decoupling
Dr. Ungku Anisa, July 2008 44EEEB443 - Control & Drives
x
s*
isqs*
isds*+
+sL1
r
S1
r
S
1
r
S
11
x sl*
ψs**sψ
1
sds
iL
isqs*
from speed controller
Stator Flux Orientation Controldsqs- 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 OrientationDirect Stator Flux Orientation
s easily estimated from motor’s stator voltages vsdq
s and stator currents isdq
s
Hence, Indirect Stator Flux Orientation scheme unessential.
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives
s
45
dq- reference frame orientation
angle
si
qs
ds
sds
qs
Ψssdi
Ψssqi
Closed-loop implementation:1. Obtain isd
s* from s control loop and dynamic decoupling system shown in slide 38.
Obtain isqs* from outer speed control loop since isq
r* Te*
based on (34):
Obtain vsdqs* from isdq
s* via inner current control loop.
Direct Stator Flux Orientation (DSFO) - implementation
Dr. Ungku Anisa, July 2008 46EEEB443 - Control & Drives
(45)22
3 where
*ψs
*ψs* P
kik
Ti t
sdt
esq
Closed-loop implementation:2. Determine the angular position s using:
sds and sq
s obtained from stator voltage equations:
Note that:
Eq. (48) will be used as feedback for the s control loop
Direct Stator Flux Orientation (DSFO) - implementation
Dr. Ungku Anisa, July 2008 47EEEB443 - Control & Drives
(46)s
sd
ssq
1ψ tan
s
22
sψ ssq
ssd
(47) 0s
sdq
s
sdqs
s
sdq
s
sdq iRv (48)
Closed-loop implementation:3. s to be used in the dsqs dsqs conversion of
stator voltage (i.e. vsdqs* to vsdq
s* 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.
Direct Stator Flux Orientation (DSFO) - implementation
Dr. Ungku Anisa, July 2008 48EEEB443 - Control & Drives
Direct Stator Flux Orientation (DSFO) - implementation
49
r*
s*2/3
tan-1
isqs*
isds*
vsqs*
vsds*
vas*
vbs*
vcs*
r
+
Rotating frame (dsqs ) Stationary frame (dsqs )
Decoupling system
ejs
P/2m
PWMVSI
3/2e-js
ias
ibs
ics
isqs
isds
PIvsq
s*
PI
vsds*
+
PI+
-
isqs
isds
-
-
sds
Dr. Ungku Anisa, July 2008 EEEB443 - Control & Drives
sqs
s
s
Eq. (47)vsdq
s
isdqs
+
-PI
Eq. (48)
sds
sqs
+
+
|s|r
S
11
ReferencesTrzynadlowski, 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 50EEEB443 - Control & Drives