1Today:Inverter+PMSMControl

3phaseinverter(DCtoAC)

+

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

3phaseelectricmachine

Vectorcontrolledelectricdrive(fieldoriented,rotorreferenceframecontrol)

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

Currentloopcompensators PWM db

dc

Kr-1MP 12

32

Id

da

r

vqref

vdref

va0refvb0ref

vc0ref

Ppole,3phasePMSMequationsinrotorreferenceframe

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

132sin

32cos

132sin

32cos

1sincos1

rr

rr

rr

rK

rmrP2

Electricalandmechanicalangleandspeed

rmrP2

abctoqd0 qd0toabc

Dynamicequations

PMSMsmallsignalmodelinrotorreferenceframe

4

rMdrq

qq Lidtdi

Lriv

qrd

dd LidtdiLriv

Currentcontrolloops

5

PMSMInverterFeedforward

Gciq(s)

Gcid(s)

vdref

vqref

vd

vq

v*dref

v*qref

id

iq

Idref

Iqref

rMdrqrefqref Livv *

qrdrefdref Livv * qrddd LidtdiLriv

rMdrq

qq Lidtdi

Lriv

Designofcurrentcontrolloopsinrotorreferenceframe

6

dtdi

Lriv qqq *

dtdiLriv ddd *

CurrentloopPIcompensators

7

Gci(s)

v*qrefiq

Iqref

Giv(s)

CurrentloopPIcompensators

8

Simulinkimplementation

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 *

Testofcurrentcontrolsinrotorreferenceframe

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

Numericalexample

11

#ofpoles:P =8

Peaktorque:Tmmax =240Nm

FluxlinkageM =0.125VsPhaseresistance:r =0.08Phaseinductance:L =0.5mH

DCbusvoltage:Vbus =500V

ModernPMSMSpecificpower:1.52kW/kgPowerdensity:46kW/liter

Dynamicresponses:steptorquecommand

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

0240NmstepTorquecommandnrm =1000rpm

TmTmref

iqid

vqvd

Dynamicresponses:steptorquecommand

13

0240NmstepTorquecommandnrm =2740rpm

-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

Drivecycleexample:060mph0

14

Electricdriveparameters:#ofpoles:P =4Maximumtorque:Tmmax =200NmMaximumcurrentamplitude:533AFluxlinkageM =0.125VsPhaseresistance:r =0.04Phaseinductance:L =0.5mHCurrentloopBW:10HzDCbusvoltage:Vbus =600V

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)

VehicleSystems

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

ElectricDrive

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

S

p

e

e

d

[

m

p

h

]

Reference Speed

Vehicle Speed

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

-100

0

100

200T

o

r

q

u

e

[

N

m

]

Motor Torque

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

-500

0

500

1000

R

o

t

o

r

R

e

f

.

F

r

m

.

C

u

r

r

e

n

t

s

[

A

]

iqidi0

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

-100

0

100

200

300

R

o

t

o

r

R

e

f

.

F

r

m

.

V

o

l

t

a

g

e

s

[

V

]

vqvdv0

18

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

-200

0

200

400

P

h

a

s

e

V

o

l

t

a

g

e

s

[

V

]

vavbvc

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

-100

0

100

200

300R

o

t

o

r

R

e

f

.

F

r

m

.

V

o

l

t

a

g

e

s

[

V

]

vqvdv0

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

-500

0

500

1000

R

o

t

o

r

R

e

f

.

F

r

m

.

C

u

r

r

e

n

t

s

[

A

]

iqidi0

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

-500

0

500

1000

P

h

a

s

e

C

u

r

r

e

n

t

s

[

A

]

iaibic

19

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

80

S

p

e

e

d

[

m

p

h

]

Reference Speed

Vehicle Speed

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

-100

0

100

200

T

o

r

q

u

e

[

N

m

]

Motor Torque

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

-200

0

200

400

P

h

a

s

e

V

o

l

t

a

g

e

s

[

V

]

vavbvc

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

0

0.5

1

1.5

P

h

a

s

e

D

u

t

y

C

y

c

l

e

s

dadbdc

20

249.8 250 250.2 250.4 250.6 250.8 2510

20

40

60

80

S

p

e

e

d

[

m

p

h

]

Reference Speed

Vehicle Speed

249.8 250 250.2 250.4 250.6 250.8 251-200

-150

-100

-50

0

50

T

o

r

q

u

e

[

N

m

]

Motor Torque

249.8 250 250.2 250.4 250.6 250.8 251-600

-400

-200

0

200

R

o

t

o

r

R

e

f

.

F

r

m

.

C

u

r

r

e

n

t

s

[

A

]

iqidi0

249.8 250 250.2 250.4 250.6 250.8 251-100

0

100

200

300

R

o

t

o

r

R

e

f

.

F

r

m

.

V

o

l

t

a

g

e

s

[

V

]

vqvdv0

21

249.8 250 250.2 250.4 250.6 250.8 251-400

-200

0

200

400

P

h

a

s

e

V

o

l

t

a

g

e

s

[

V

]

vavbvc

249.8 250 250.2 250.4 250.6 250.8 251-100

0

100

200

300

R

o

t

o

r

R

e

f

.

F

r

m

.

V

o

l

t

a

g

e

s

[

V

]

vqvdv0

249.8 250 250.2 250.4 250.6 250.8 251-600

-400

-200

0

200

R

o

t

o

r

R

e

f

.

F

r

m

.

C

u

r

r

e

n

t

s

[

A

]

iqidi0

249.8 250 250.2 250.4 250.6 250.8 251-1000

-500

0

500

1000

P

h

a

s

e

C

u

r

r

e

n

t

s

[

A

]

iaibic

22

249.8 250 250.2 250.4 250.6 250.8 2510

20

40

60

80

S

p

e

e

d

[

m

p

h

]

Reference Speed

Vehicle Speed

249.8 250 250.2 250.4 250.6 250.8 251-200

-150

-100

-50

0

50

T

o

r

q

u

e

[

N

m

]

Motor Torque

249.8 250 250.2 250.4 250.6 250.8 251-400

-200

0

200

400

P

h

a

s

e

V

o

l

t

a

g

e

s

[

V

]

vavbvc

249.8 250 250.2 250.4 250.6 250.8 251-0.5

0

0.5

1

1.5

P

h

a

s

e

D

u

t

y

C

y

c

l

e

s

dadbdc

23

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.154

56

58

60

S

p

e

e

d

[

m

p

h

]

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

T

o

r

q

u

e

[

N

m

]

Motor Torque

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-40

-20

0

20

40

R

o

t

o

r

R

e

f

.

F

r

m

.

C

u

r

r

e

n

t

s

[

A

]

iqidi0

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-50

0

50

100

150

R

o

t

o

r

R

e

f

.

F

r

m

.

V

o

l

t

a

g

e

s

[

V

]

vqvdv0

24

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-200

-100

0

100

200

P

h

a

s

e

V

o

l

t

a

g

e

s

[

V

]

vavbvc

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-50

0

50

100

150

R

o

t

o

r

R

e

f

.

F

r

m

.

V

o

l

t

a

g

e

s

[

V

]

vqvdv0

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-40

-20

0

20

40

R

o

t

o

r

R

e

f

.

F

r

m

.

C

u

r

r

e

n

t

s

[

A

]

iqidi0

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-40

-20

0

20

40

P

h

a

s

e

C

u

r

r

e

n

t

s

[

A

]

iaibic

25

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.154

56

58

60

S

p

e

e

d

[

m

p

h

]

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

T

o

r

q

u

e

[

N

m

]

Motor Torque

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-200

-100

0

100

200

P

h

a

s

e

V

o

l

t

a

g

e

s

[

V

]

vavbvc

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.10.2

0.4

0.6

0.8

1

P

h

a

s

e

D

u

t

y

C

y

c

l

e

s

dadbdc

26

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10

0.5

1

1.5

2

S

p

e

e

d

[

m

p

h

]

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

T

o

r

q

u

e

[

N

m

]

Motor Torque

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-40

-30

-20

-10

0

R

o

t

o

r

R

e

f

.

F

r

m

.

C

u

r

r

e

n

t

s

[

A

]

iqidi0

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10

1

2

3

R

o

t

o

r

R

e

f

.

F

r

m

.

V

o

l

t

a

g

e

s

[

V

]

vqvdv0

27

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-4

-2

0

2

4

P

h

a

s

e

V

o

l

t

a

g

e

s

[

V

]

vavbvc

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10

1

2

3

R

o

t

o

r

R

e

f

.

F

r

m

.

V

o

l

t

a

g

e

s

[

V

]

vqvdv0

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-40

-30

-20

-10

0

R

o

t

o

r

R

e

f

.

F

r

m

.

C

u

r

r

e

n

t

s

[

A

]

iqidi0

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-40

-20

0

20

40

P

h

a

s

e

C

u

r

r

e

n

t

s

[

A

]

iaibic

28

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10

0.5

1

1.5

2

S

p

e

e

d

[

m

p

h

]

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

o

r

q

u

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

P

h

a

s

e

V

o

l

t

a

g

e

s

[

V

]

vavbvc

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10.495

0.5

0.505

0.51

P

h

a

s

e

D

u

t

y

C

y

c

l

e

s

dadbdc

ElectricDriveModelingandControlConclusions

29

PMSMdynamicmodelinrotorreferenceframeremovesretainsalldynamicsbutremovestheneedtolookatangledependences

Insteadystate,rotorreferenceframevoltagesandcurrentsareallDC Techniquesusedtoextentspeedrange:

DCbusvoltagecontrolusingtheBoostDCDCconverter Fieldweakeningusingthedirectcomponentofthecurrent

Modernelectricdrivesemployvectororfieldorientedcontroltechniquesbasedonthedynamicmodelinrotorreferenceframe

Typicalcontrolsystemsincludesinnercurrentcontrolloopsthattakeadvantageofthefactthattorqueproducedisdirectlyproportionaltothequadrature componentofthecurrent

3phaseinverters=3Buckconverterlegs,modulatedtoproducestatorvoltagesnecessarytogeneraterequestedstatorcurrents.VoltageamplitudelimitedbytheDCbusvoltage.Typicalswitchingfrequency:kHz 10skHz.

Hierarchicalmodelingandcontroltechniques SwitchingtransitionsintheinverterorBoostDCDCconverter: