pmsm control strategy

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