1

Today: Inverter + PMSM Control

3‐phase inverter (DC‐to‐AC )

+–

abc

0

Vbus va0 vb0 vc0

Q1

D1

D2

Q2

Q3

D3

D4

Q4 D6Q6

D5Q5

Vbusibus

n

Tmrmrm

ia

ib

ic

PMSM+ va

+ vb

+ vc

3‐phase electric machine

Vector controlled electric drive(“field‐oriented”, “rotor reference frame” control)

2

+–

abc

0

Vbus va0 vb0 vc0

Q1

D1

D2

Q2

Q3

D3

D4

Q4 D6Q6

D5Q5

Vbusibus

n

Tmrmrm

ia

ib

ic

PMSM+ va

+ vb

+ vc

Id

Kr

Iq

r

Tref Iqref

Iq

Idref

Current‐loopcompensators PWM db

dc

Kr-1

MP 12

32

Id

da

r

vqref

vdref

va0ref

vb0ref

vc0ref

P‐pole, 3‐phase PMSM equations in rotor reference frame

3

rMdrq

qq Lidtdi

Lriv

qrd

dd LidtdiLriv

qMm iPT 22

3Torque

Park Transformations

21

21

21

32sin

32sinsin

32cos

32coscos

32

rrr

rrr

rK

13

2sin3

2cos

13

2sin3

2cos

1sincos1

rr

rr

rr

rK

rmrP2

Electrical and mechanical  angle and speed

rmrP2

abc‐to‐qd0 qd0‐to‐abc

Dynamicequations

PMSM small‐signal model in rotor reference frame

4

rMdrq

qq Lidtdi

Lriv

qrd

dd LidtdiLriv

Current control loops

5

PMSMInverterFeedforward

Gciq(s)

Gcid(s)

vdref

vqref

vd

vq

v*dref

v*qref

id

iq

Idref

Iqref

rMdrqrefqref Livv *

qrdrefdref Livv *qr

ddd Li

dtdiLriv

rMdrq

qq Lidtdi

Lriv

Design of current control loops in rotor reference frame

6

dtdi

Lriv qqq *

dtdiLriv d

dd *

Current‐loop PI compensators

7

Gci(s)

v*qrefiq

Iqref

Giv(s)

Current‐loop PI compensators

8

Simulink implementation

9

5

vd

4

vq

3

id

2

iq

1

Tmlambda_m

lambda_m

0

idref

Vq voltage limit

Vd voltage limit

4/3/P/lambda_m

Torque reference to current reference

Product1

Product

L

L1

L

L

PI(s)

Iq compensator

PI(s)

Id compensator

3*P*lambda_m/4

GeneratedTorque

P/2

Gain2

v q

v d

wr

iq

id

Dynamic DQ Equations

Add

2

wrm

1

Tmref

Iqrefv qrev *

v dref *

v q

v d

rMdrqrefqref Livv *

qrdrefdref Livv *

Test of current controls in rotor reference frame

10

ECEB5017DQ current control

of PMSM

2*pi*1000/60

mechanicalspeed wrm

Torque referencecommand Tmref

Scope

Tmref

wrm

Tm

iq

id

v q

v d

DQ current controlled PMSM

Tmref

wrm

iq

id

iq_id

v q_v d

Tm

v q

v d

Torque

Numerical example

11

# of poles: P = 8

Peak torque: Tmmax = 240 Nm

Flux linkage M = 0.125 Vs

Phase resistance: r = 0.08 

Phase inductance:  L = 0.5 mH

DC bus voltage: Vbus = 500 V

Modern PMSMSpecific power: 1.5‐2 kW/kgPower density: 4‐6 kW/liter

Dynamic responses: step torque command

12

-200

-100

0

100

200

-300

-200

-100

0

100

200

300

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-200

-100

0

100

200

0‐240 Nm step Torque commandnrm = 1000 rpm

TmTmref

iqid

vqvd

Dynamic responses: step torque command

13

0‐240 Nm step Torque commandnrm = 2740 rpm

-200

-100

0

100

200

-300

-200

-100

0

100

200

300

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

-200

-100

0

100

200

TmTmref

iqid

vqvd

Drive‐cycle example: 0‐60 mph‐0

14

Electric drive parameters:# of poles: P = 4Maximum torque: Tmmax = 200 NmMaximum current amplitude: 533 AFlux linkage M = 0.125 VsPhase resistance: r = 0.04 Phase inductance:  L = 0.5 mHCurrent‐loop BW: 10 HzDC bus voltage: Vbus = 600 V

Top-level model of EV for use in ECEN 5017 course. Driving cycle is a speed-vs-time profile for the vehicle, operating on flat road. Driver uses torque command (gas & brake

pedals) to follow the reference speed.

Top-Level EV Model

m

Vref

speedsForces

Pdist

SOCIinvIbat

VbatvabciabcTm

iqd0vqd0dabc

Unit Conversion

Scope1

Scope

Electric VehicleDriver model

Driving cycleReference Speed

Vehicle Speed

Torque command(gas & brake pedals)

Vehicle Systems

15

Vehicle Systems ModelModel for a sample vehicle system during driving cycle.

4Electrical Signals

3Tm

2theta_rm

1Fdrive

Tire

OLD

SOC-only EV Battery Memory

[EDsigs]

Goto4

[Iinv]

Goto3

[Ibat]

Goto2

[Vbat]

Goto1

[SOC]

Goto

Gearing

2

Gain

[EDsigs]

From4

[Iinv]

From3

[Ibat]

From2

[SOC]

From1

[Vbat]

From

Electric Drive

DC-DC Converter

50

Constant

2Tcommand

1Vev

Battery Voltage

Battery Current

BatterySOC

DC Bus Voltage

Motor Torque

Wheel Torque

Wheel Angular Speed

Rotor Angular Speed

Inverter Input Current / DC-DC Output Current

rotor position

DC Bus Voltage

Electric Drive

16

5Vs

4I_DC

2theta_rm

1Tm

va

vb

vc

wrm

theta_rm

Tm

iabc

vqd0

PMSM

[Vbus]

Goto5

[iqd0]

Goto4

[vqd0]

Goto3

[iabc]

Goto2

[vabc]

Goto1

[dabc]

Goto

Tmref

theta_rm

iabc

wrm

Vabc*

iqd0

Vs

DQ Controller

Vg

Vref

Iout

Vout

Iin

dabc

3-Phase BuckAveraged Model

3V_DC2

Tcommand1

1wrm

wrm

rotor position

rotor position

Motor Torquevabc

iabc

iabc

Tmref

17

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

80

Spe

ed [

mph

]

Reference Speed

Vehicle Speed

0 50 100 150 200 250 300 350 400 450 500-200

-100

0

100

200T

orqu

e [N

m]

Motor Torque

0 50 100 150 200 250 300 350 400 450 500-1000

-500

0

500

1000

Rot

or R

ef.

Frm

. C

urre

nts

[A]

iqidi0

0 50 100 150 200 250 300 350 400 450 500-200

-100

0

100

200

300

Rot

or R

ef.

Frm

. V

olta

ges

[V]

vq

vd

v0

18

0 50 100 150 200 250 300 350 400 450 500-400

-200

0

200

400

Pha

se V

olta

ges

[V]

va

vb

vc

0 50 100 150 200 250 300 350 400 450 500-200

-100

0

100

200

300R

otor

Ref

. F

rm.

Vol

tage

s [V

]

vq

vd

v0

0 50 100 150 200 250 300 350 400 450 500-1000

-500

0

500

1000

Rot

or R

ef.

Frm

. C

urre

nts

[A]

iqidi0

0 50 100 150 200 250 300 350 400 450 500-1000

-500

0

500

1000

Pha

se C

urre

nts

[A]

iaibic

19

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

80

Spe

ed [

mph

]

Reference Speed

Vehicle Speed

0 50 100 150 200 250 300 350 400 450 500-200

-100

0

100

200

Tor

que

[Nm

]

Motor Torque

0 50 100 150 200 250 300 350 400 450 500-400

-200

0

200

400

Pha

se V

olta

ges

[V]

va

vb

vc

0 50 100 150 200 250 300 350 400 450 500-0.5

0

0.5

1

1.5

Pha

se D

uty

Cyc

les

da

db

dc

20

249.8 250 250.2 250.4 250.6 250.8 2510

20

40

60

80

Spe

ed [

mph

]

Reference Speed

Vehicle Speed

249.8 250 250.2 250.4 250.6 250.8 251-200

-150

-100

-50

0

50

Tor

que

[Nm

]

Motor Torque

249.8 250 250.2 250.4 250.6 250.8 251-600

-400

-200

0

200

Rot

or R

ef.

Frm

. C

urre

nts

[A]

iqidi0

249.8 250 250.2 250.4 250.6 250.8 251-100

0

100

200

300

Rot

or R

ef.

Frm

. V

olta

ges

[V]

vq

vd

v0

21

249.8 250 250.2 250.4 250.6 250.8 251-400

-200

0

200

400

Pha

se V

olta

ges

[V]

va

vb

vc

249.8 250 250.2 250.4 250.6 250.8 251-100

0

100

200

300

Rot

or R

ef.

Frm

. V

olta

ges

[V]

vq

vd

v0

249.8 250 250.2 250.4 250.6 250.8 251-600

-400

-200

0

200

Rot

or R

ef.

Frm

. C

urre

nts

[A]

iqidi0

249.8 250 250.2 250.4 250.6 250.8 251-1000

-500

0

500

1000

Pha

se C

urre

nts

[A]

iaibic

22

249.8 250 250.2 250.4 250.6 250.8 2510

20

40

60

80

Spe

ed [

mph

]

Reference Speed

Vehicle Speed

249.8 250 250.2 250.4 250.6 250.8 251-200

-150

-100

-50

0

50

Tor

que

[Nm

]

Motor Torque

249.8 250 250.2 250.4 250.6 250.8 251-400

-200

0

200

400

Pha

se V

olta

ges

[V]

va

vb

vc

249.8 250 250.2 250.4 250.6 250.8 251-0.5

0

0.5

1

1.5

Pha

se D

uty

Cyc

les

da

db

dc

23

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.154

56

58

60

Spe

ed [

mph

]

Reference Speed

Vehicle Speed

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-20

-10

0

10

20

Tor

que

[Nm

]

Motor Torque

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-40

-20

0

20

40

Rot

or R

ef.

Frm

. C

urre

nts

[A]

iqidi0

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-50

0

50

100

150

Rot

or R

ef.

Frm

. V

olta

ges

[V]

vq

vd

v0

24

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-200

-100

0

100

200

Pha

se V

olta

ges

[V]

va

vb

vc

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-50

0

50

100

150

Rot

or R

ef.

Frm

. V

olta

ges

[V]

vq

vd

v0

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-40

-20

0

20

40

Rot

or R

ef.

Frm

. C

urre

nts

[A]

iqidi0

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-40

-20

0

20

40

Pha

se C

urre

nts

[A]

iaibic

25

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.154

56

58

60

Spe

ed [

mph

]

Reference Speed

Vehicle Speed

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-20

-10

0

10

20

Tor

que

[Nm

]

Motor Torque

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-200

-100

0

100

200

Pha

se V

olta

ges

[V]

va

vb

vc

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.10.2

0.4

0.6

0.8

1

Pha

se D

uty

Cyc

les

da

db

dc

26

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10

0.5

1

1.5

2

Spe

ed [

mph

]

Reference Speed

Vehicle Speed

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-11.4

-11.3

-11.2

-11.1

-11

-10.9

Tor

que

[Nm

]

Motor Torque

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-40

-30

-20

-10

0

Rot

or R

ef.

Frm

. C

urre

nts

[A]

iqidi0

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10

1

2

3

Rot

or R

ef.

Frm

. V

olta

ges

[V]

vq

vd

v0

27

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-4

-2

0

2

4

Pha

se V

olta

ges

[V]

va

vb

vc

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10

1

2

3

Rot

or R

ef.

Frm

. V

olta

ges

[V]

vq

vd

v0

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-40

-30

-20

-10

0

Rot

or R

ef.

Frm

. C

urre

nts

[A]

iqidi0

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-40

-20

0

20

40

Pha

se C

urre

nts

[A]

iaibic

28

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10

0.5

1

1.5

2

Spe

ed [

mph

]

Reference Speed

Vehicle Speed

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-11.4

-11.3

-11.2

-11.1

-11

-10.9T

orqu

e [N

m]

Motor Torque

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-4

-2

0

2

4

Pha

se V

olta

ges

[V]

va

vb

vc

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10.495

0.5

0.505

0.51

Pha

se D

uty

Cyc

les

da

db

dc

Electric Drive Modeling and Control Conclusions

29

• PMSM dynamic model in rotor reference frame removes retains all dynamics but removes the need to look at angle dependences

• In steady state, rotor reference frame voltages and currents are all DC• Techniques used to extent speed range:

• DC bus voltage control using the Boost DC‐DC converter • Field‐weakening using the direct component of the current 

• Modern electric drives employ “vector” or “field‐oriented” control techniques based on the dynamic model in rotor reference frame

• Typical control systems includes inner current control loops that take advantage of the fact that torque produced is directly proportional to the quadrature component of the current

• 3‐phase inverters = 3 Buck converter legs, modulated to produce stator voltages necessary to generate requested stator currents. Voltage amplitude limited by the DC bus voltage. Typical switching frequency: kHz – 10’s kHz. 

• Hierarchical modeling and control techniques• Switching transitions in the inverter or Boost DC‐DC converter: < s

• Switching period: 10’s of s

• Converter dynamics and current control loops: 10’s of ms

• Vehicle dynamics and drive cycles: seconds to minutes