PMSM - IEA

Industrial Electrical Engineering and Automation

Lund University, Sweden

PMSM

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n

© Mats Alaküla L9-torque generation

Mechanical Design

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Mathematical Model

m

x

y

ai

bi

ci

si

ssmsss

sss iLdt

diR

dt

diRu

xyss

xymr

xys

sxy

ss

xyss

xymr

xyss

xym

xyss

xys

iLjdt

idLiR

iLjiLdt

diRu

• Compare to the vector control of a generic 3-phase load...

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Torque Control

sysxsysxsym

sxsysysysxsxm

sxsysysxss

iiLLi

iiLiiL

iiiT

)(

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Simplest, only y-axis current

control

sym iT

msy

sx

Ti

i

**

* 0

m x

y

s i

s

s s j e

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Drawback with y-axis control

• Does not utilize the reluctance torque

• Phase lag between voltage and current

xyss

xymr

xys

sxy

ssxys iLj

dt

idLiRu

xyss iR

xymrj

xy

ssr iLj

xysi

xym

xyss iL

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Better – max Torque/Ampére

control

• Orient the current vector for maximum

Torque.

)sin()cos()()cos(

)(

2

ssysxsm

sysxsysxsym

iLLi

iiLLiT

-20 -10 0 10 20-20

-10

0

10

20ISO-torque (blue) and max(T/I) (red)

Lsy=5mH /Lsx=2mH

-20 -10 0 10 20 -20

-10

0

10

20 ISO-torque (blue) and max(T/I) (red)

-20 -10 0 10 20-20

-10

0

10

20ISO-torque (blue) and max(T/I) (red)

Lsy=5mH /Lsx=5mH Lsy=2mH /Lsx=5mH

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Look up table for current setpoints

-30 -20 -10 0 10 20 30-20

-15

-10

-5

0

5

10

15

20

T*

isx*

(red)

& isy*

(blu

e)

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Voltage limitation

• When the machine speeds up, a voltage

limit is reached.

• The voltage can be limited with ”field

weakening”

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Voltage limitation

22sxsxmrsyssysyrsxss iLiRiLiRu

• What current combinations satisfy a limited voltage vector?

-20 -10 0 10 20 -20

-15

-10

-5

0

5

10

15

20 ISO-torque (blue), max(T/I) (red) and Constant Voltage (green)

Follow (T/I)max to

Voltage limit, then

T=const.

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


EV traction motor

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Drive Unit Specifications

Max power 50 kW (2 min)

Continuous power 32 kW

Max torque 191 Nm (2 min)

Continuous torque 130 Nm

Efficiency range ~ 85 - 95 %

Nominal DC-link voltage: 200 - 320 V (braking 240 - 350 V)

Base speed 2500 rpm

Speed range 0 - 10000 rpm

Max cooling liquid temp 70 °C

Length Motor 250 mm Converter 392 mm

Width Motor (dia) 260 mm Converter 260 mm

Height Motor (dia) 260 mm Converter 80/128 mm System 340 mm

Weight Ca 60 kg

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Torque & Power vs Speed

0

50

100

150

200

250

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Continuous and

2 min. peak

load

(50 kW motor)

Nm

rpm

kW

50

25

0

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Efficiency Curves 50 kW motor

0

5

10

15

20

25

30

35

40

45

50

55

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Speed, [rpm]

Ou

tpu

t p

ow

er, [k

W]

95% 93% 91%

87%

(at typical DC and line voltages)

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Typical DC and Line Voltages

130

140

150

160

170

180

190

200

210

220

230

240

250

260

270

280

290

300

310

320

0 5 10 15 20 25 30 35 40 45 50

Power, [kW]

Vo

ltag

e, [V

] Motor dc voltage

Generator dc voltage

Motor line voltage

Generator line voltage

(based on typical internal battery parameters)

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


A-sample Characteristics

Interior Permanent

Magnet Motor

Water Cooled

Field Weakening

Position Feedback

with resolver

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Magnetic saturation (Lq)

0

100

200

300

400

500

0100

200300

400500

0

1

2

3

4

5

6

7

x 10-4

abs(isd)

abs(isq)

Lq

Ld=0.2mH

Lq=

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Torque control

-600 -400 -200 0 200 400 600 -600

-400

-200

0

200

400

600

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n

© Mats Alaküla L5 – 3-phase modulation

3-phase load

R

R

R

L

L

L

ae

be

ce

au

bu

cu

ai

bi

ci

edt

diLiRu

edt

diLiRue

edt

diLiRue

edt

diLiRu

ca

cc

j

ba

bb

j

aa

aa

3

2

3

2

3

2

3

2

3

2

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


3-phase sampled vector control : 1

Rotating vs. stationary reference frame

ie

t

2

t

d

q Stationary errors a

problem in the (,)

frame.

Use the (d,q)-frame

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n



Assume sampled control @ [..., k, k+1, k+2, ...]Ts

Calculate voltage average over one sample period

)1,()()1(

)1,()1,(

)1()1()1()1()1(

kkeT

kikiLkkiLjRkku

T

dtedtiLjdtdt

idLdtiR

T

dtu

s

s

Tk

Tk

Tk

Tk

Tk

Tk

Tk

Tk

s

Tk

Tk

s

s

s

s

s

s

s

s

s

s

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n



Assume:

)()()(*)(

)()()1,(

)(2

)()(*)1,(

)()(*)1(

)()(*)1,(

1

0

eniniki

dkekke

ckiki

kki

bkiki

akukku

kn

n

forwardFeed

kn

ns

s

s

kn

ns

s

s

kekiLjniniT

R

L

Tkiki

R

T

L

kekiLjniniRkikiR

T

L

kekiki

LjT

kikiLkiR

kikiR

keT

kikiL

kikiLjRku

)()()()(*

2

)()(*2

)()()()(*)()(*2

)(2

)()(*)()(*)(

2

)()(*

)()()(*

2

)()(*)(*

Integral

1

0alProportion

1

0

Gives:

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n



Components:

)()()()(

2

)()(2

)(

)()()(

2

)()(2

)(

1

0

***

1

0

***

kekiLniniT

R

L

Tkiki

R

T

Lku

kiLniniT

R

L

Tkiki

R

T

Lku

qd

kn

n

qqs

sqq

sq

q

kn

n

dds

sdd

sd

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


End of PMSM story

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


-200 -150 -100 -50 0 50 100 150 200-600

-400

-200

0

200

400

600

Torque refernce [Nm]

isx*

(blu

e)

and isy*

(red)

Current references

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Minimum stator current control

m x

y

si

-500 -400 -300 -200 -100 0 100 200 300 400 500-0.1

-0.05

0

0.05

0.1

isx

Psisx = f(isx)

-500 -400 -300 -200 -100 0 100 200 300 400 500

-0.1

-0.05

0

0.05

0.1

Psisy = f(isy)

isy

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


”Iso”-torque curves

-400 -300 -200 -100 0 100 200 300 400-500

-400

-300

-200

-100

0

100

200

300

400

Increasing torqe

m x

y

si

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Look up tables for minimal

stator currents

20 40 60 80 100 120 140-300

-200

-100

0

100

200

300

400

500

T*

isx*

& isy*

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Simulation 2

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Field Weakening

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Field Weakening

22 ),(),( sxsysxsxmrsyssysysxsyrsxss iiiLiRiiiLiRu

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

T=constant

us=constant

increasing

speed

increasing

torque

optimal

stator current

maximuml

stator current

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


Priorit

y

Action

1

Stator current less than maximum stator current

(Current limitation to protect machine and power

electronics)

2

Stator voltage less than maximum stator voltage

(Voltage limitation to facilitate current control)

3

Minimal stator current for a given torque (Stator

current on the optimal line)

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


2

isdq

1

u*

u(1)

half Ts advance

i

thetaOut1

emf-estimator

v ect

angle

Out

alfa/beta Ü> d/q

ref

act

emf

di*

Umax

u*lim

u*

PIE-controller

4

-1

T

T*

u*_unlim

delta_i*

Umax

Field Weakening Controller

iue

i_hat

Current estimator

v ect

angle

Out

d/q > alfa/beta

5

T*

4

T

3

thetaR

2

i

1

idq*

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


2Umax

1

delta_i*

1/z

Unit Delay1

Switch

Sign

Relay

1

s

Integrator1

1

s

Integrator

-K-5

11.2

50

5

f(u)

Fcn2

(0 0)

100

InOutLP

OutHP

1'st order fi lter

3

u*_unlim

2

T*

1

T

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


0 1 2 3-20

0

20

40

60Torque reference and torque response [Nm]

0 1 2 3100

200

300

400

500Mechanical speed [rad/s]

0 1 2 3-20

0

20

40

60Torque reference and torque response [Nm]

0 1 2 3100

200

300

400

500Mechanical speed [rad/s]

Ind

ustr

ial E

lectr

ica

l E

ng

ine

erin

g a

nd

Au

tom

atio

n


-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

-600 -400 -200 0 200 400 600-600

-400

-200

0

200

400

600

Documents

PMSM - IEA