Today - Electrical, Computer & Energy Engineeringecee.colorado.edu/~ecen5017/lectures/CU/L38_out.pdf0 50 100 150 200 250 300 350 400 450 500-400-200 0 200 400 Phase Voltages [V] v

Today

1

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

• Finish inverter+PMSM simulation example• Electric drive (inverter+PMSM): losses and efficiency• Overview of induction machine, an alternative to PMSM• Summary and conclusions

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-1MP 12

32

Id

da

r

vqref

vdref

va0refvb0ref

vc0ref

Drive‐cycle example: 0‐60 mph‐0

3

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)

4

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

80

Spe

ed [m

ph]

Reference SpeedVehicle Speed

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

-100

0

100

200To

rque

[Nm

]

Motor Torque

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

-500

0

500

1000

Rot

or R

ef. F

rm. 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. F

rm. V

olta

ges

[V]

vqvdv0

5

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

-200

0

200

400

Pha

se V

olta

ges

[V]

vavbvc

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

-100

0

100

200

300R

otor

Ref

. Frm

. Vol

tage

s [V

]

vqvdv0

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

-500

0

500

1000

Rot

or R

ef. F

rm. 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

6

0 50 100 150 200 250 300 350 400 450 5000

20

40

60

80

Spe

ed [m

ph]

Reference SpeedVehicle Speed

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

-100

0

100

200

Torq

ue [N

m]

Motor Torque

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

-200

0

200

400

Pha

se V

olta

ges

[V]

vavbvc

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

dadbdc

7

249.8 250 250.2 250.4 250.6 250.8 2510

20

40

60

80

Spe

ed [m

ph]

Reference SpeedVehicle Speed

249.8 250 250.2 250.4 250.6 250.8 251-200

-150

-100

-50

0

50

Torq

ue [N

m]

Motor Torque

249.8 250 250.2 250.4 250.6 250.8 251-600

-400

-200

0

200

Rot

or R

ef. F

rm. 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. F

rm. V

olta

ges

[V]

vqvdv0

8

249.8 250 250.2 250.4 250.6 250.8 251-400

-200

0

200

400

Pha

se V

olta

ges

[V]

vavbvc

249.8 250 250.2 250.4 250.6 250.8 251-100

0

100

200

300

Rot

or R

ef. F

rm. V

olta

ges

[V]

vqvdv0

249.8 250 250.2 250.4 250.6 250.8 251-600

-400

-200

0

200

Rot

or R

ef. F

rm. 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

9

249.8 250 250.2 250.4 250.6 250.8 2510

20

40

60

80

Spe

ed [m

ph]

Reference SpeedVehicle Speed

249.8 250 250.2 250.4 250.6 250.8 251-200

-150

-100

-50

0

50

Torq

ue [N

m]

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]

vavbvc

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

dadbdc

10

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.154

56

58

60

Spe

ed [m

ph]

Reference SpeedVehicle Speed

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-20

-10

0

10

20

Torq

ue [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

Rot

or R

ef. F

rm. 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. F

rm. V

olta

ges

[V]

vqvdv0

11

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]

vavbvc

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. F

rm. V

olta

ges

[V]

vqvdv0

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. F

rm. 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

12

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.154

56

58

60

Spe

ed [m

ph]

Reference SpeedVehicle Speed

250.03 250.04 250.05 250.06 250.07 250.08 250.09 250.1-20

-10

0

10

20

Torq

ue [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

Pha

se V

olta

ges

[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

Pha

se D

uty

Cyc

les

dadbdc

13

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10

0.5

1

1.5

2

Spe

ed [m

ph]

Reference SpeedVehicle 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

Torq

ue [N

m]

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. F

rm. 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. F

rm. V

olta

ges

[V]

vqvdv0

14

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]

vavbvc

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10

1

2

3

Rot

or R

ef. F

rm. V

olta

ges

[V]

vqvdv0

269.96 269.98 270 270.02 270.04 270.06 270.08 270.1-40

-30

-20

-10

0

Rot

or R

ef. F

rm. 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

15

269.96 269.98 270 270.02 270.04 270.06 270.08 270.10

0.5

1

1.5

2

Spe

ed [m

ph]

Reference SpeedVehicle 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

-10.9To

rque

[Nm

]

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]

vavbvc

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

dadbdc

PMSM Electric Drive Modeling and Control Conclusions

16

• PMSM dynamic model in rotor reference frame 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” i.e. “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: 

PMSM drive averaged model, including losses

17

PMSM

+–

+–

+–

Vbus

ia

ib

ic

r

r

r

L

L

L

rm

rm

rm

rxa

rxb

rxc

vxa

vxb

vxc

dcVbusdbVbusdaVbusdaia dbib dcic

Isw

Ibus+

_

Inverter

0 ,

0 ,

aDaCESa

aDaCESaxa iVdVd

iVdVdv

0 ,0 ,

aDaCEa

aDaCEaxa iRdRd

iRdRdr

swcswbswasw IIII

PMSM drive efficiency map example

18

Evaluation of 2004 Toyota Prius Hybrid Electric Drive System(2005 report by Oak Ridge National Lab)

An alternative: Induction Machine

A two‐phase induction motor Tesla demonstrated in a lecture onMay 16, 1888, before the American Institute of Electrical Engineersat Columbia University. The motor developed 1/5 horsepower andshowed the commutator and brushes could be dispensed with.

Induction Machine (IM), also known as Asynchronous Machine• Short‐circuited rotor windings, “squirrel‐cage” rotor bars

• Rotor‐winding currents (rotor field) induced by stator currents

• Rotor speed not equal to synchronous speed, hence “asynchronous” machine

Induction Machine: principles of operation

20

Figure 6.12‐1 from P.Krause, O.Wasynczuk, S.Pekarek, Electromechanical Motion Devices, 2nd edition, Wiley 2012

• Stator voltages and currents are 3‐phase sinusoidal waveforms at electrical frequency

P = 2 poles

• Rotor turns at mechanical speede

rmr • Frequency of the current induced in the rotor is

reer • MMF vector generated by stator currents rotates at speed  

e• MMF vector generated by rotor currents rotates at speed  

eerr • Torque is generated by interaction between the stator and the rotor generated MMFs, both rotating at synchronous speed 

e

Induction Machine: slip s

21

P = 2 pole machine

• Electrical frequency of stator voltages and currents = Speed of rotation of magnetic fields = Synchronous speed = Speed of rotation of synchronous reference frame = 

• Mechanical speed of rotation =

• Slip frequency =

• Slip  

e

r

erre

e

res

Induction Machine Equations in Synchronous Reference Frame

22

dseqs

qssqs dtd

irv

qseds

dssds dtdirv

drreqrqrr dtd

ir

0

qrredrdrr dtdir 0

qrMqssqs iLiL

drMdssds iLiL

0 qsMqrrqr iLiL

dsMdrrdr iLiL

qsdrr

Mqrdr iL

LPiPT 22

322

3

Flux linkagesVoltage equations

Stator dq

Rotor dq

Torque

Induction Machine:Torque in terms of stator currents

23

dtdir drdrr

0

qsdrr

Mqrdr iL

LPiPT 22

322

3

dtd

rLiL dr

r

rdrdsM

dsr

Mdr is

L

1

qsdsrr

M iisL

LPT

1

122

3 2

dsMdrrdr iLiL Eliminate idr and solve for dr

Induction Machine Equations: slip and synchronous frequency calculations

24

0 qsMqrrqr iLiL

qsr

Mqr iL

Li

drreqrrir 0

dr

qrrre

ir

dsr

Mdr is

L

1

dr

qs

r

Mrre

iLLr

where

Field‐oriented (vector) control of induction machine

25

+–

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

Ids

Kr

Iqs

e

Tref Iqsref

Iqs

Idref

Current‐loopcompensators PWM db

dc

Kr-1dsrefM

r

ILL

P12

32

2

Ids

da

e

vqsref

vdsref

va0refvb0ref

vc0ref

IM

Slip and sync.frequency& angle calc.

Iqsref

Idref rmIdsref

26

• Higher efficiency at low and medium speeds

• Simpler control• Active R&D

• Higher efficiency at high speeds• No need for rare‐earth permanent magnet materials, lower cost

• More mature motor technology

PMSM IM

Comparison of PMSM and IM

Another alternative: Variable Reluctance (VR)

27

Variable Reluctance (VR) machine, also Switched Reluctance machines

• Salient poles: inductance of the stator windings depends on position

• Many configurations possible

• Good efficiency over wide range of speeds

• Relatively low cost

• Pulsating torque, higher noise levels

• In R&D for automotive applications

More Research and Development Directions“Hub” or “In‐Wheel” Motors

28

Example:http://www.proteanelectric.com