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