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Induction Motor – Vector Control or Field Oriented Control By M.Kaliamoorthy Department of Electrical Engineering. Outline. Introduction Analogy to DC Drive Principles of Field Orientation Control Rotor Flux Orientation Control Indirect Rotor Flux Orientation (IRFO) - PowerPoint PPT Presentation
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Induction Motor – Vector Control or Field Oriented ControlByM.KaliamoorthyDepartment of Electrical Engineering
1
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
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
3
Introduction
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 Drive• 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 vectors5
f
a
Te = k f Ia
Te = k f Ia
= k’ If Ia sin 90
= k’(If x Ia)
Analogy to DC Motor• In the Induction Motor:
• 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.6
a
b
b’c’
c
sr
Te = kr x s
Analogy to DC Motor• Induction 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.
7
ss iψ22
3
PTe
sr iψ22
3
r
me L
LPT
(1)
(2)
(3) afafafe kikIIkT iψ ψ90sin'
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.
8
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
9
Rotor-Flux Orientation Control
si
qs
ds
r dr
qr
rsdi
rsqi
)(22
3sdrqsqrd
r
me ii
LLPT
si
qs
ds
sds
qs
Ψssdi
Ψssqi
)(22
3sdsqsqsde iiPT
Stator-Flux Orientation Control
Principles of Field Orientation Control
• Summary of field orientation control on a selected flux vectorf
(i.e. either r , s or m):
10
Rotor Flux Orientation Control• d- axis of dq- rotating frame
is aligned with r . Hence,
• Therefore,
11
si
qs
ds
r dr
qr
rsdi
rsqi
rrdr
0rrq
(4)
(5)
r )(22
3sqrd
r
me i
LLPT (6)
= torque producing current
= field producing currentrsdi
rsqi Similar to
ia & if in DC motor
Decoupled torque and flux control
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 12
rq
rd
sq
sd
rrrrgmmrg
rrgrrmrgm
mmgsssg
mgmsgss
rq
rd
sq
sd
iiii
SLRLSLLLSLRLSL
SLLSLRLLSLLSLR
vvvv
')()()(')(
(7)
(8)
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:
13
rdqrsdqmrdq iLiL '(9)
sdqr
m
r
rdqrdq i
LL
Li ''
(10)
ψr
ψr
ψr
ψr
ψr
ψr
ψr
ψr
''''0''0''
''''
rq
rd
sq
sd
rrslrmr
slrrrmr
rmrmsssss
rmsrmssss
rq
rd
sq
sd
ii
SLRLLRSLRLLR
LSLLLLSRLLLLLSLLSR
vvvv
(11)
Rotor Flux Orientation Control• Since , hence the equations in rotor flux
orientation are:
14
Note:Total leakage factor =
sl = slip speed (elec.)
(13)
0rrq
ψrψrψrψrψrrd
r
mssqsssdssdssd dt
dLLiLi
dtdLiRv
'
ψrψrψrψrψr
' rdr
mssdsssqssqssq LLiLi
dtdLiRv
ψrψrψrψr
''0 sdr
r
mrdrd
r
rrq iR
LL
dtd
LRv
ψrψrψr
'0 sqr
r
mrdslrq iR
LLv
(12)
(14)
(15)
'
2
1rs
m
LLL
Important equations for Rotor Flux Orientation Control!
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):
15
(16)
(18)
(19)
ψrψrψrmrd
r
rmrdsd i
dtd
RLii '
ψrψrmrdmrd iL
ψrmrdi
ψrψrmrdsd ii
ψrψrmrdrsd iSi 1
(17)
r
rr RL '
Rotor Flux Orientation Control• r 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
Orientation– Direct Rotor Flux
Orientation16
si
qs
ds
r dr
qr
rsdi
rsqi
r
dt sr
(20)
dq- reference frame orientation angle
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 ( ):
17
ψr
ψr
ψr
ψrψr
ψrmrdr
sq
rdr
sqmsq
rd
r
r
msl i
iiLiR
LL
'
(21)
(22)
dt sr
dtdt rslsr
ψr
ψr
sdr
sqsl i
i
(23)
ψrψrsdmrd ii
Indirect Rotor Flux Orientation (IRFO) - implementation
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.
18
(24)
(25)
m
rdmrdsd Lii
***
ψrψrψr
r
mt
sdt
esq L
LPkikTi
2
ψr*
*ψr*
223 where
Indirect Rotor Flux Orientation (IRFO) - implementation
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).
19
(26) dt2
dtdt ψr*
ψr**
m
sdr
sqrsls
Pii
r
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*
PIvsq
r*+PI
+-
isdr
isqr
--
isqr*isd
r*
r
NO field weakening
(constant flux)
2-phase (dsqs ) to 3-phase (abc)transformation
drqr dsqs transformation
IRFO Scheme
Indirect Rotor Flux Orientation (IRFO) - implementation
drqr dsqs transformation
dsqs drqr transformation
21
ssq
ssd
sq
sd
xx
xx
rr
rr
r
r
cossinsincos
r
r
rr
rr
sq
sdssq
ssd
xx
xx
cossinsincosvsq
s*
vsds*
vsdr*
vsqr*
ejr
e-jr
isds
isqs
isdr
isqr
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
22
abcabcsdq xTx
sdqabcabc xTx 1
3
13
1
00
01
abcT
23
23
21211
01Tabc
2/3
vsqs*
vsds*
vas*
vbs*
vcs*
3/2
ias
ibs
ics
isds
isqs
Example – IRFO Control of IM
• An induction motor has the following parameters:
23
Parameter Symbol ValueRated 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.
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*
25
Example – IRFO Control of IM ctd.• Answers:
26
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)
27
ψrψrψrmrd
r
rmrdsd i
dtd
RLii '
ff
ff
f
f idtd
RL
iRv
imrd*
r
imrd (rated)
r (base)
Indirect Rotor Flux Orientation (IRFO) – field weakening implementation
28
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*
PIvsq
r*+PI
+-
isdr
isqr
--
isqr*
imrdr*
r
With field weakening
+-
imrd r
rS11
r*
Same as in slide 20
PI
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
componentsConsequences:
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)
29
Direct Rotor Flux Orientation (DRFO)
• 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:
30
(27)srd
srq
r
1tan
22 srq
srd rψ (28)
Direct Rotor Flux Orientation (DRFO) – Direct measurements md
s & mq
s
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.
31
(29)s
sdqlrs
mdqm
rsrdq iL
LL '
'
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*
PIvsq
r*+PI
+-
isdr
isqr
--md
s
mqs
rd
s
rq
s
r
r
NO field weakening
(constant flux)
DRFO Scheme
Flux sensing coils arranged in quadrature
Direct Rotor Flux Orientation (DRFO) – Estimated from vsdq
s & isdq
s
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)
33
(30) 0s
sdqs
sdqss
sdqs
sdq iRv
ssdqss
sdqm
rsrdq iL
LL
'
(31)
Direct Rotor Flux Orientation (DRFO) – Estimated from vsdq
s & isdq
s
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)
34
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*
PIvsq
r*+PI
+-
isdr
isqr
--sd
s
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
36
r*
imrd r *
isqr*
isdr* vsq
s*
vsds*
r
+
Rotating frame (drqr) Stationary frame (dsqs)
ejr
e-jr
isds
isqs
PIvsd
r*
PIvsq
r*+PI
+-
isdr
isqr
--
With field weakening
+-
imrd r
rS11
r*
Same as in
slide 26 or 29
tan-1
rds
rq
s
r
r
PI
Stator Flux Orientation Control• d- axis of dq- rotating frame
is aligned with s. Hence,
• Therefore,
37
sψsd ψψ s
0ψ sψsq
(32)
(33)
)(22
3sqsde iPT (34)
= torque producing current
= field producing currentΨssdi
Ψssqi
Similar to ia & if in DC motor
Decoupled torque and flux control
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 38
rq
rd
sq
sd
rrrrgmmrg
rrgrrmrgm
mmgsssg
mgmsgss
rq
rd
sq
sd
iiii
SLRLSLLLSLRLSL
SLLSLRLLSLLSLR
vvvv
')()()(')(
(7)
(8)
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:
39
rdqmsdqs iLiL sdqΨ (35)
sdqm
s
mrdq i
LL
Li sdqΨ
(36)
ψs
ψs
ψs
ψs
ψs
ψs
ψs
ψs
1111
00
sq
sd
sq
sd
rrslrssrsl
rslrsrslrs
ss
ss
rq
rd
sq
sd
ii
SSLLSLSL
SRSR
vvvv
(37)
Stator Flux Orientation Control• Since , hence the equations in stator flux
orientation are:
40
(39)
0ψ sψsq
ψsψsψssdsdssd dt
diRv
ψsψsψssdssqssq iRv
ψsψsψsψsψsψs 0 sqsrslsdrsdssdrsdrd iLidtdiL
dtdv
(38)
(40)
(41) ψsψsψsψsψs 0 sdssdrslsqrsqsrq iLidtdiLv
Important equations for Stator Flux Orientation Control!
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 .
41
sψsqi sψ
sdψVarying to control torque causes change in
(42) ψsψsψs 11 sqsrslsdsrsdr iLiLSS
sψsdψ sψ
sdi sψsqi
sψsdψ sψ
sqi
sψsqiTorque will not react immediately to
sψsdψ sψ
sqi
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
42
(43)
ψssdψ ψs
sqi
r
sqsls
sd
rsd
S
iL
Si
1
1 ψs**ψs*
ψs*
ψs*sdi
ψs*sqi
*sl
ψssqiψs
sdψ
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.
43
(44)ψs*
ψs*ψs*
*
1
sq
sds
sd
rsl i
iL
S
*sl
ψs*sdψ *
sψ
ψssqiψs*
sdi
Stator Flux Orientation Control – Dynamic Decoupling
• Dynamic decoupling system implementation:
44
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 isdqs
Hence, Indirect Stator Flux Orientation scheme unessential.
45
s
dq- reference frame orientation
angle
si
qs
ds
sds
qs
Ψssdi
Ψssqi
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 isq
r* Te
* based on (34):
Obtain vsdqs* from isdq
s* via inner current control loop.
46
(45)223 where*ψs
*ψs* Pk
ikTi tsdt
esq
Direct Stator Flux Orientation (DSFO) - implementation
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
47
(46)s
sd
ssq
1ψ tan
s
22
sψ ssq
ssd
(47) 0s
sdqs
sdqss
sdqs
sdq iRv (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. 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 sdq
s(0)
Solution: A low-pass filter can be used to replace the pure integrator and avoid the problems above.
48
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/2 m
PWMVSI
3/2e-js
ias
ibs
ics
isqs
isds
PIvsq
s*
PIvsd
s*
+
PI+
-
isqs
isds
-
-
sds sq
s
s
s
Eq. (47)vsdq
s
isdqs
+
-PI
Eq. (48)
sds
sqs
+
+
|s|r
S
11
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.
50