PMSM Control Strategy Reference: R. Krishnan, Permanent Magnet Synchronous and Brushless DC Motor Drives, CRC, 2010.
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PMSM Control Strategy
Reference:R. Krishnan, Permanent Magnet Synchronous and Brushless DC Motor Drives, CRC, 2010.
Steady State Vector Diagram (1)
s d d q qR jX jX V I I I E , d me d q me qX L X L
( )2me
mej j
me PM me PM me fe j e j
E λ
( )2,
meme me
jj jd d q q qI e I e jI e
I I( ) mej
d q d qI jI e I I I
( ) mejd q d qV jV e V V V
( )2,
meme me
jj jd d q q qV e V e jV e
V V
d s d q qR jX V I I
q s q d dR jX V I I E
E
I
VId
Iq
d axis
jXqIqjXdId
lf lnet
ls
RsIaq axis
leading power factor
Steady State Vector Diagram (2)
( )
d d q q
e d d q q f me net
jX jX
j L L j
V I I E
I I λ λ
, d me d q me qX L X L me fjE λ
d s d me q s d me q q me q qR j R j L j L V I λ I I I
Neglect Rs
sλ
s me sjV λs V V E
( )2,
meme me
jj jd d q q qI e I e jI e
I I
E
I
VId
Iq
d axis
jXqIqjXdId
lf lnet
ls
q axis
leading power factor
( ) ( )q s q me d s q me d d f me d d fR j R j L j L V I λ I I λ I λ
( )e d d f q q me netj L L j V I λ I λ
Or
dλ qλ
net s f d q λ λ λ λ λ
Steady State Vector Diagram (3)
dI
qλnetλ
sλ
fλdλ
qII
2
me
Close to Unity Power Factor
Define
mII
net mλ
mii
f PMλ
2
22 2 2( )m d q PM d d q qL i L i
cosd mi i sinq mi i
General Considerations
2a f
e a
C B lrT i 3
4e PM d q d q
PT L L i i
DC Motor PMSM
dI
qλnetλ
sλ
fλdλ
qII
2
me
Can use id for flux weakening control for IPM
General Control Block Diagram
MotorPPU
av
bv
cv
Controllergate
contr
ol si
gnals
aici
bi
m
DC BusElectrical Input Mechanical Output
Reference
LT
Motor Modeling (1)
abc to dq
av
bv
cv
ai
mLT
Dynamical
Equation
dq to abc
bi
ci
dv
qv
di
qi
Motor Modeling (2)
Inside the Controller
CurrentController
* For reference
gate control signals
m
, , a b ci i iactually need two of them
Speed Controller
PositionController
d/dt
m
*m*
m
m
* ,di*qi
abc to dq
, d qi i
m
Example: Hysteresis Current Controller
dq CurrentCalculat
or
*eT
gate control signals
m
, , a b ci i i
*di
* For reference
*qi
dq toabc
Hysteresis
Controller
*ai
*bi
*ci
Algorithm:
*
*
Set up a hysteresis current window
If ( ) ,
( ) , 0
Likewise for phases b and c.
a a aN dc
a a aN
i
i i i v V
i i i v
Current Controller
Example: PI Current Controller
*dv
*qv
m
di
qi
avbv
cv
gate control signals
*av
*bv
*cv
Current Controller
PMSM Control Strategies
Constant Torque and Flux Control Zero Direct Axis Current Control Unity Power Factor Control Given Power Factor Control Optimum Torque per Unit Current Control Constant Power Loss Control Maximum Efficiency Control
Constant Torque and Flux Control
dq CurrentCalculat
or
*eT
*di
*qi
dI
qλnetλ
sλ
fλdλ
qII
2
me
*m
* * *
2* * * 2
3
4
( )
e PM d q d q
m PM d d q q
PT L L i i
L i L i
Solve (transcendental) equations
* ,di*qi
SPM
* *
2* * * 2
3
4
( )
e PM q
m PM d d d q
PT i
L i L i
d qL L
** eq
T
Ti
k 3
4T PM
Pk
*2 * 2
*( )m d q PM
dd
L ii
L
One choice would be:
*m PM
Zero Direct Axis Current Control
dq CurrentCalculat
or
*eT
*di
*qi
* * * *3 3
4 4e PM d q d q PM q
P PT L L i i i
* 0di
dI
qλnetλ
sλ
fλdλ
qII
2
me
d me q mV L I
22( )q s m me PMV R I
d s d me q qR j L V I I
( )q s q me d d fR j L V I I λ
** * eq m
T
Ti i
k
3
4T PM
Pk
Steady State
Unity Power Factor Control
dq CurrentCalculat
or
*eT
*di
*qi
dI
qλnetλ
sλ
fλdλ
qII
2
me
* * *
* *
* *
3
4e PM d q d q
q PM d d
d q q
PT L L i i
i L i
i L i
Solve (transcendental) equations
* ,di*qi
* 0
* * * *
2 2
* *tan cot
* *tan cot
Given Power Factor Control
dq CurrentCalculat
or
*eT
*di
*qi
dI
qλnetλ
sλ
fλdλ
qII
2
me
* * *
* *1 1 *
* *
3
4
tan tan2
e PM d q d q
q q q
PM d d d
PT L L i i
L i i
L i i
Solve transcendental equations
* ,di*qi
* is given
* * *
2
* * *
2
Optimum Torque per Unit Current Control (1)
dq CurrentCalculat
or
*eT
*di
*qi
* * * * * * *3 3cos sin
4 4e PM d q d q PM d q m m
P PT L L i i L L i i
*
* * **
3 1sin sin 2
4 2e
PM d q mm
T PL L i
i
* *
* * */ 3
cos cos2 04
e m
PM d q m
d T i PL L i
dt
* 22(cos ) 1
2* * * *2 cos cos 0d q m PM d q mL L i L L i
2
* 1
* *
1cos
24 4PM PM
d q m d q mL L i L L i
Optimum Torque per Unit Current Control (2)
dq CurrentCalculat
or
*eT
*di
*qi
* * * * * * *3 3cos sin
4 4e PM d q d q PM d q m m
P PT L L i i L L i i
* *2 * * *1 4sin(2 ) sin 0
2 3d q m PM m eL L i i TP
2* * * *
*
*
8sin sin sin(2 )
3sin(2 )
PM PM d q e
m
d q
L L TPi
L L
* * *sinq mi i
* * *cosd mi i
Constant Power Loss Control
dq CurrentCalculat
or
*eT
*di
*qi
* * *3
4e PM d q d q
PT L L i i
In the implementation, flux weakening needs to be considered.
Maximum Efficiency Control
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