power systems control prof. wonhee kim resistance, l is the phase winding inductance, and p is the...

Power Systems Control

Prof. Wonhee Kim

Ch.5. Permanent Magnet Synchronous Motor Control

2

3 Phase Permanent Magnet Synchronous Motor (PMSM)

3

3 Phase PMSM Modeling

1 2 2sin sin sin

3 3

1sin

1 2sin

3

1 2sin

3

m a b c l

a a n a a e

b b n b b e

c c n c c e

K p i p i p i BJ

i v v R i K pL

i v v R i K pL

i v v R i K pL

where va, vb, vc and ia, ib, ic are the voltages and currents in

phases A, B, and C, respectively. ω is the rotor (angular)

velocity, θ is the rotor (angular) position, B is the viscous

friction coefficient, J is the inertia of the motor, Km is the motor

torque constant, Ke is the back-emf constant, R is the phase

winding resistance, L is the phase winding inductance, and p is

the number of pole pair. τl is the load torque perturbation.

4

PMSM with Clarke Transformation

5

PMSM Modeling with Clarke Transformation

1sin cos

1sin

1cos

m l

e

e

K i p i p BJ

i v R i K pL

i v R i K pL

1 2 2sin sin sin

3 3

1sin

1 2sin

3

1 2sin

3

m a b c l

a a n a a e

b b n b b e

c c n c c e

K i p i p i p BJ

i v v R i K pL

i v v R i K pL

i v v R i K pL

6

PMSM with DQ (Park) Transformation

1sin cos

1sin

1cos

m l

e

e

K i p i p BJ

i v R i K pL

i v R i K pL

cos sin

sin cos

cos sin

sin cos

d

q

d

q

i ip p

i ip p

v vp p

v vp p

1

1

1

m q l

d d d d q

q q q q d e

K i BJ

i v R i pL iL

i v R i pL i KL

7

DC Motor

1

1

1

m q l

q q q q d e

d d d d q

K i BJ

i v R i pL i KL

i v R i pL iL

1

1

m l

e

K i BJ

i v Ri KL

8

DC Motor Control

DC

motorPI

dqi

d

- -

v

i

PI

eK

1

1

m l

e

K i BJ

i v Ri KL

9

PMSM Control

cos

2cos

3

2cos

3

d

d

d

p

p

p

cos

sin

d

d

p

p

10

PMSM Control

11

PMSM Control

PMSM

DQ/Clarke

Transform-

ation

Inverse

DQ/Clarke

Transform-

ation

PI

PIddi

dqi

d

- -

-

qv

dv

av

bv

ai

bi

qi

dici

PI

eK

cv

1

1

1

m q l

q q q q d e

d d d d q

K i BJ

i v R i pL i KL

i v R i pL iL

Desired current to generate the torque

cos sin

sin cos

cos sin

sin cos

d

q

d

q

i ip p

i ip p

v vp p

v vp p

cos , sind d

d ms q msi I p p i I p p

1

[ sin cos ]m m lK i p K i p BJ

d

d d

m qK i

cos,

sin

d dmsd d

d q

m ms m

p pi i

K p p K

sin

dd

m ms

IK p p

cos , sind d

ms msi I p i I p

Desired Direct Current for PMSM Control

12

Field oriented control: zero direct current for torque maximization

cos,

sin

d dmsd d

d q

m ms m

p pi i

K p p K

0,d

d d

d q

m

i iK

0.5rms

r

N

N

sin , cosd d

d d

a r b r

m m

i N i NK K


13

Field weakening control: negative direct current to avoid the input saturation

1

1

1

m q

d d d q

q q q d e

K i BJ

i v Ri pL iL

i v Ri pL i KL

Back-emf cancellation using negative id

ed

Ki

pL


14

Field weakening control: negative direct current to avoid the input saturation

cos,

sin

d dmsd d

d q

m ms m

p pi i

K p p K

tan ,d d

d d

d l q

m m

i iK K

0.5 lms

p

p

sin , cos

cos cos

d dd d

l r l

m l m l

i p i pK K

2 2

2 22 2, atand e

d ld

pLK pLKei

R p L R p L


15

Comparison of open-loop, FOC, and FWC

(a) Open-loop (b) FOC (c) FWC


16

PMSM Control

17

Inverter

18

Carrier-based PWM

19

Carrier-based PWM

20

Carrier-based PWM

21

power systems control prof. wonhee kim resistance, l is the phase winding inductance, and p is the...

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