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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) . I d. jX q I q. jX d I d. I q. l f. R s I a. q axis. l net. d axis. l s. leading power factor. Steady State Vector Diagram (2) . - PowerPoint PPT Presentation
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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, me
me mejj j
d d q q qI e I e jI e
I I( ) mejd q d qI jI e I I I
( ) mejd q d qV jV e V V V
( )2, me
me mejj j
d 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
f net
s
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
sλs me sjV λs V V E
( )2, me
me mejj j
d d q q qI e I e jI e
I I
E
I
VId
Iq
d axis
jXqIqjXdId
f net
s
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
DefinemII
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 qPT 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
MotorPPUavbvcv
Controllergate
con
trol s
igna
ls
aici
bi
m
DC BusElectrical Input Mechanical Output
Reference
LT
Motor Modeling (1)
abc to dq
avbvcv
ai
mLT
Dynamical
Equation
dq to abc
bici
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 ( ) ,
( ) , 0Likewise 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
34
( )
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
34
( )
e PM q
m PM d d d q
PT i
L i L i
d qL L
** eq
T
Tik
34T PMPk
*2 * 2* ( )m d q PMd
d
L ii
L
One choice would be:*m PM
Zero Direct Axis Current Control
dq CurrentCalculat
or
*eT
*di
*qi
* * * *3 34 4e PM d q d q PM qP 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 ik
34T PMPk
Steady State
Unity Power Factor Control
dq CurrentCalculat
or
*eT
*di
*qi
dI
qλnetλ
sλ
fλdλ
qII
2
me
* * *
* *
* *
34e PM d q d q
q PM d d
d q q
PT L L i i
i L ii 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 *
* *
34
tan tan2
e PM d q d q
q q q
PM d d d
PT L L i i
L i iL 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 3 cos sin4 4e PM d q d q PM d q m mP PT L L i i L L i i
*
* * **
3 1sin sin 24 2
ePM d q m
m
T P L L ii
* *
* * */ 3 cos cos2 0
4e m
PM d q m
d T i P L L idt
* 22(cos ) 1
2* * * *2 cos cos 0d q m PM d q mL L i L L i
2
* 1* *
1cos24 4
PM 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 3 cos sin4 4e PM d q d q PM d q m mP PT L L i i L L i i
* *2 * * *1 4sin(2 ) sin 02 3d q m PM m eL L i i T
P
2* * * *
**
8sin sin sin(2 )3
sin(2 )
PM PM d q e
md q
L L TPi
L L
* * *sinq mi i
* * *cosd mi i
Constant Power Loss Control
dq CurrentCalculat
or
*eT
*di
*qi
* * *34e PM d q d qPT L L i i
In the implementation, flux weakening needs to be considered.
Maximum Efficiency Control
