Field-Oriented Control of Induction Machine
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Field-Oriented Control of Induction Machine
• IM is superior to DC machine with respect to size, weight, inertia, cost, speed
Why FOC ?
• DC motor is superior to IM with respect to ease of control– High performance with simple control due de-coupling
component of torque and flux
• FOC transforms the dynamics of IM to become similar to the DC motor’s – decoupling the torque and flux components
Basic Principles DC machine
Current in
Current out
a
f
By keeping flux constant, torque can be controlled by controlling armature current
Te = k If Ia
Basic Principles of IM
a
b
b’c’
c
Stator current produce stator flux
s r
Interaction between stator and rotor fluxes produces torque
Space angle between stator and rotor fluxes varies with load, and speed
Stator flux induces rotor current produces rotor flux
FOC of IM drive
Torque equation :
sse i2
p
2
3T
srr
me i
L
L
2
p
2
3T
In d-q axis :
)ii(LL
2p
23
T sdrqsqrdr
me
FOC of IM drive
In d-q axis :
)ii(LL
2p
23
T sdrqsqrdr
me
Choose a frame such that:
rrdr
0r
rq
FOC of IM drive
Choose a frame such that:
rrdr
0r
rq
FOC of IM drive
)ii(LL
2p
23
T sdrqsqrdr
me
Choose a frame such that:
rrdr
0r
rq
qs
ds
si
r
sqi
rq
sdi rd
As seen by stator reference frame:
FOC of IM drive
rsqr
r
me i
LL
2p
23
T
si
Choose a frame such that:
rrdr
0r
rq
qs
ds
r dr
qr
rsdi
rsqi
)ii(LL
2p
23
T sdrqsqrdr
me
Rotating reference frame:
FOC of IM driveTo implement rotor flux FOC need to know rotor flux position:
(i) Indirect FOC
grrg
grg
sr
rmgr
r
r )(jdtd
iLRL
LR
0
rsliprr
sqr
sdr
rmr
r
r )(jdtd
jiiLRL
LR
0
Synchronous speed obtain by adding slip speed and rotor speed
Rotor voltage equation:
grrg
grg
rr )(jdt
diR0
gsm
grr
gr iLiL
Rotor flux equation:
FOC of IM drive - indirect
dtd
iLRL
LR
0 rrsd
r
rmr
r
r
d component
rslipr
sqr
rm )(iLRL
0
q component
rsliprr
sqr
sdr
rmr
r
r )(jdtd
jiiLRL
LR
0
FOC of IM drive - indirect
dtd
iLRL
LR
0 rrsd
r
rmr
r
r
d component
rslipr
sqr
rm )(iLRL
0
q component
rsliprr
sqr
sdr
rmr
r
r )(jdtd
jiiLRL
LR
0
m
*r
sd L*i r
r
sqr
*r
rmslip i
LRL
)(
m
r
r
*e
sq LL
p3T4
*i r
FOC of IM drive - indirect
T*
*
2/3
1/s
irsq*
irsd*
isq*
isd*
ia*
ib*
ic*
CCVSI
slip r
+ +
Rotating frame Stationary frame
m
*r
sd L*i r
m
r
r
*e
sq LL
p3T4
*i r
rsq
r*r
rmslip i
LRL
)(
ej
FOC of IM drive
grr
rs
r
rmr
r
r jdt
di
L
RL
L
R0
(ii) Direct FOC
Rotor flux can be estimated by:
Rotor flux estimated from motor’s terminal variables
srr
me i
LL
2p
23
T
Express in stationary frame
FOC of IM drive
grr
rs
r
rmr
r
r jdtd
iLRL
LR
0
(ii) Direct FOC
)j(jdt
)j(di)jii(
LRL
)j(LR
0 rqrdrrqrd
sqsdr
rmrqrd
r
r
dti
LRL
LR
rqrsdr
rmrd
r
rrd
dti
LRL
LR
rdrsqr
rmrq
r
rrq
d q
rd
rq
2rq
2rdr
FOC of IM drive - direct
T*
r*2/3
isq*
isd*
ia*
ib*
ic*
CCVSI
TC
FC
irsq*
irsd*
ej
Te
r
srr
me i
LL
2p
23
T
grr
rs
r
rmr
r
r jdt
di
L
RL
L
R0
Rotating frame Stationary frame