The Control of a Continuously Operated Pole-Changing ...strangas/emd_lab/kelly_first.pdfThe Control...

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The Control of a Continuously Operated Pole-Changing InductionMachine

J.W. KellyElectrical and Computer Engineering

Michigan State University

East Lansing, MI 48824

28 February 2002

M-D Lab 1/0202 1

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Outline

Pole Changing Techniques for Induction Machines

• Reconfigurable Stator Winding

• Multiple Stator Windings

Experimental Induction Machine with a 3:1 Pole Ratio

• 3phase-12pole Configuration



• Pole-Phase Variation

M-D Lab 1/0202 2

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Nine Phase Operation

• Coordinate Transformation of Machine Variables

• 9 Phase PWM Techniques

Continuous Operation of a Pole Changing Induction Machine

• Issues During the Pole-Changing Transition

• Proposed Technique for Torque Regulation During Pole-Changing Transient

Experimental Setup

Conclusions

M-D Lab 1/0202 3

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Background

2:1 Pole-changing using Reconfigurable Stator Winding

• Series connected phase coils resulting in 8 poles

• Mechanical Contactors

- + - - - + + +

C 1 C 2 C 3 C 4

C 1

C 3

C 4

C 2

phase-belt

3phase Power supply

M-D Lab 1/0202 4

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• Series-parallel connected phase coils resulting in 4 poles

• Mechanical Contactors

- + + - + - + -

C 1 C 2 C 3 C 4

C 1

C 3

C 2

C 4

phase-belt

3phase Power supply

M-D Lab 1/0202 5

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3:1 Pole-changing using Reconfigurable Stator Winding

• Delta connected phase coils resulting in 2 poles

• 60o Phase Belt ��

��

a a a -c -c -c b b b -a -b c -a -a -b c c -b L +1

L -1

L -2

L +2 L +3

L -3

L +1 L -2 L +3 L +8 L -7 L +6 L -5 L +4 L -3 L +2 L -1 L +9 L -8 L +7 L -6 L +5 L -4 L -9 L +7

L -7 L -8

L +8 L +9

L -9

phase-belt (Mechanical degrees)

60 o

pole-pitch (Electrical degrees)

180 o

M-D Lab 1/0202 6

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• Wye connected phase coils resulting in 6 poles

• 60o Phase Belt

� �� L +1 L -2

a a a -c -c -c b b b -a

L +3 L +8 L -7 L +6 L -5 L +4 L -3 L +2 L -1 L +9 L -8 L +7 L -6 L +5 L -4 L -9

-b c -a -a -b c c -b

L -4

L +1

L -1 L +7

L -7 L +4

L -2

L -8

L +8 L -5 L +5

L +3

L -3

L +9

L -9

L +6

L -6

-b -c

-a

phase-belt (Mechanical degrees) 20 o

180 o

pole-pitch (Electrical degrees)

M-D Lab 1/0202 7

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Induction Machine with Dual Stator Windings: Lippo and Osama

• 4 pole configuration

• two 3phase inverters, 6 winding currents:[ia1,ib1,ic1,ia2,ib2,ic2]

a a a a a a a a a a a a a a a a

-a -a -a -a -a -a -a -a -a -a -a -a -a -a -a -a -c -c -c -c -c -c -c -c -c -c -c -c -c -c -c -c

b b b b b b b b b b b b b b b b

-b -b -b -b -b -b -b -b -b -b -b -b -b -b -b -b

c c c c c c c c c c c c c c c c

• 2 pole configuration

• two 3phase inverters, 6 winding currents:[ia1,ib1,ic1,−ia2,−ic2,−ib2]

a a a a a a a a

-a -a -a -a -a -a -a -a a a a a

-a -a

a a a a -c -c -c -c -c -c -c -c

-c -c -c -c -c -c -c -c b b b b b b b b

b b b b b b b b -b -b -b -b -b -b -b -b

-b -b -b -b -b -b -b -b

c c c c c c c c

c c c c c c c c -a -a -a -a -a -a

M-D Lab 1/0202 8

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Machine Variables Described in Six Dimensional Space

• Analysis in six-dimensional space too complex2666666666664

V1

V2

V3

V4

V5

V6

3777777777775

= [R][I] +d

dt[λ] (1)

• Transformation to Simplify Analysis: One 6-D Machine mapped into Two independent machines in

3-D 2666666666664

V2q

V2d

V4q

V4d

V02

V04

3777777777775

= [T]

2666666666664

V1

V2

V3

V4

V5

V6

3777777777775

(2)

M-D Lab 1/0202 9

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• Use Stator Winding MMF as basis for Transformation

=1(φ) =X

h=1,2,3...

Nsh cos (h(φ)ia(t)) (3)

=2(φ) =X

h=1,2,3...

Nsh cos (h(φ− π)ia(t)) (4)

=3(φ) =X

h=1,2,3...

Nsh cos�h(φ− π

3)ia(t)

�(5)

=4(φ) =X

h=1,2,3...

Nsh cos

�h(φ +

2π

3)ia(t)

�(6)

=5(φ) =X

h=1,2,3...

Nsh cos

�h(φ− 2π

3)ia(t)

�(7)

=6(φ) =X

h=1,2,3...

Nsh cos�h(φ +

π

3)ia(t)

�(8)

(9)

• Total MMF of Dual Stator Machine

=Total = =1 + =2 + =3 + =4 + =4 + =5 + =6 (10)

M-D Lab 1/0202 10

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• Total MMF Harmonic Composition (Fourier Series Expansion)

=Total = =fundalmental + =2nd + =3rd + =4th + =5th + =6th (11)

• The 6-D machine variables are transformed into two sets of 2-D variables.

• One set is based the MMF fundamental component. These machines describe a 2 pole machine.

• The other set is based on MMF 2nd harmonic component. These variables describe a 4 pole machine.

• The 3rd harmonic component of the Total MMF defines the 1-D zero-sequence subspace for the 2

pole machine

• The 6rd harmonic component of the Total MMF defines the 1-D zero-sequence subspace for the 4

pole machine

M-D Lab 1/0202 11

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Transformation Matrix from original six dimensional space to 2

3-dimensional subspaces

T =

266666666664

q4d4q2d20402̃̃

377777777775

=1√

3

26666666666664

1 1 −12

−12

−12

−12

0 0 −√32

−√32

√3

2

√3

21 −1 1

2−12

−12

12

0 0 −√32

√3

2−√3

2

√3

21√2

1√2

1√2

1√2

1√2

1√2

1√2

−1√2

−1√2

1√2

1√2

−1√2

37777777777775

(12)

Transformation Matrix for arbitrary reference frame rotating at θm

T (θm) =1√

3

2666666666664

cos(2θm) cos(2θm) cos(2θm − 2π3 ) cos(2θm − 2π

3 ) cos(2θm + 2π3 ) cos(2θm + 2π

3 )

sin(2θm) sin(2θm) sin(2θm − 2π3 ) sin(2θm − 2π

3 ) sin(2θm + 2π3 ) sin(2θm + 2π

3 )

cos(θm) − cos(θm) − cos(θm + 2π3 ) cos(θm + 2π

3 ) cos(θm − 2π3 ) − cos(θm − 2π

3 )

sin(θm) − sin(θm) − sin(θm + 2π3 ) sin(θm + 2π

3 ) sin(θm − 2π3 ) − sin(θm − 2π

3 )1√2

1√2

1√2

1√2

1√2

1√2

1√2

−1√2

−1√2

1√2

1√2

−1√2

3777777777775

(13)

M-D Lab 1/0202 12

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Transformed Voltage and Flux Linkage Equations

vq4s = rsiq4s + λ′q4s + ω4λd4s (14)

vd4s = rsid4s + λ′d4s − ω4λd4s (15)

vq2s = rsiq2s + λ′q2s + ω2λd2s (16)

vd2s = rsid2s + λ′d2s − ω2λd2s (17)

v04s = rsi04s + λ′04s (18)

v02s = rsi02s + λ′02s (19)

λq4s = (Lm4 + Lls)iq4s + Lm4iq4r (20)

λd4s = (Lm4 + Lls)id4s + Lm4id4r (21)

λq2s = (Lm2 + Lls)iq2s + Lm2iq2r (22)

λd2s = (Lm2 + Lls)iq2s + Lm2id2r (23)

Transformed Torque Equation

Te = 2(λd4siq4s − λq4sid4s) + (λd2siq2s − λq2sid2s) (24)

M-D Lab 1/0202 13

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Experimental 3:1 Pole Induction Machine

Winding Diagram

+

- + - -

-

-

+

+ +

+ -

+

-

+ -

+

- + - -

-

-

+

+ +

+ -

+

-

+ -

+

- + - -

-

-

+

+ +

+ -

+

-

+ -

+

- + - -

-

-

+

+ +

+ -

+

-

+ -

+

- + - -

-

-

+

+ +

+ -

+

-

+ -

+

- + - -

-

-

+

+ +

+ -

+

-

+ -

+ - + - -

-

-

+

+ +

+ -

+

-

+ -

+

- + - -

-

-

+

+ +

+ -

+

-

+ -

+

- + - -

-

-

+

+ +

+ -

+

-

+ -

i A1 i B2 i C3 i A4 i B5 i C6 i A7 i B8 i C9

i A1 i B2 i C3 i D4 i E5 i F6 i G7 i H8 i I9

9 Leg Inverter

i A1 -i A2 i A3 i B4 -i B5 i B6 i C7 -i C8 i C9

4p 3phase

4p 9phase

12p 3phase

M-D Lab 1/0202 14

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Ni

a b c c' a' b'

0 o 60 o 120 o 180 o 240 o 300 o

a b c c' a' b'

0 o 60 o 120 o 180 o 240 o 300 o

a b c c' a' b'

0 o 60 o 120 o 180 o 240 o 300 o

a b c c' a' b'

0 o 60 o 120 o 180 o 240 o 300 o

a b c c' a' b'

0 o 60 o 120 o 180 o 240 o 300 o

a b c c' a' b'

0 o 60 o 120 o 180 o 240 o 300 o

phase-belt 10 o


a a c b a' c' b a c c b c' b' a'

0 o 180 o 0 o 60 o 240 o 60 o 120 o 300 o 120 o 180 o 0 o 180 o 240 o 60 o 240 o 300 o

a' c' b' b'

120 o 120 o

Ni

phase-belt 30 o

a a c b a' c' b a c c b c' b' a'


a' c' b' b'

120 o 120 o


a b c d f' g' e f g h i h' i' a'


b' c' d' e'

320 o 340 o

a b c d f' g' e f g h i h' i' a'


b' c' d' e'

320 o 340 o

Ni

phase-belt 10 o

M-D Lab 1/0202 15

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3phase-4pole vs 9phase-4pole MMF

0 10 20 30 40 50 60 70 -150

-100

-50

0

50

100

150

slots

0

20

40

60

80

0 50

100 150

200 250

300 350

400 -200

0

200

slots

MMF 3 phase for one complete electrical cycle

degrees

0 10 20 30 40 50 60 70 -150

-100

-50

0

50

100

150

slots

0

20

40

60

80

0

100

200

300

400

-200

0

200

slots

MMF 9 phase for one complete electrical cycle

degrees

M-D Lab 1/0202 16

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9 Phase Operation

Coordinate Transformation

• 9 dimensional machine variables too complex, transform to 2-D space (for conventional Field

Orientation Control)

• Transformation from 9 to 2 dimensions is over defined

• Transformation from 2 to 9 dimensions is under defined

• Add Constraints in order to make transformation unique

M-D Lab 1/0202 17

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• Define a new 9-D coordinate system consisting of three 3phase coordinate systems, rotated 40o wrt

to each other

• Map 13

of the 2-D space vector into each 3phase system

• 2 to 9 transformation

26666666666666666664

fas

fbs

fcs

fds

fes

ffs

fgs

fhs

fis

37777777777777777775

=3

2∗

266666666666666666664

1 0 1 0 0 0 0 0 0

0 0 0 cos(α + 2π9 ) sin(α + 2π

9 ) 1 0 0 0

0 0 0 0 0 0 cos(α + 4π9 ) sin(α + 4π

9 ) 1

cos(α + 6π9 ) sin(α + 6π

9 ) 1 0 0 0 0 0 0

0 0 0 cos(α + 8π9 ) sin(α + 8π

9 ) 1 0 0 0

0 0 0 0 0 0 cos(α + 10π9 ) sin(α + 10π

9 ) 1

cos(α + 12π9 ) sin(α + 12π

9 ) 1 0 0 0 0 0 0

0 0 0 cos(α + 14π9 ) sin(α + 14π

9 ) 1 0 0 0

0 0 0 0 0 0 cos(α + 16π9 ) sin(α + 16π

9 ) 1

377777777777777777775

∗

26666666666666666666664

fq3

fd3

fo3

fq3

fd3

fo3

fq3

fd3

fo3

37777777777777777777775

(25)

M-D Lab 1/0202 18

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• 9 to 2 transformation26666666666666666664

fq1fd1fo1fq2fd2fo2fq3fd3fo3

37777777777777777775

=2

9∗

266666666666666666664

cos(α) 0 0 cos(α − 2π3 ) 0 0 cos(α + 2π

3 ) 0 0

sin(α) 0 0 sin(α − 2π3 ) 0 0 sin(α + 2π

3 ) 0 012 0 0 1

2 0 0 12 0 0

0 cos(α + 2π9 ) 0 0 cos(α − 8π

9 ) 0 0 cos(α + 8π9 ) 0

0 sin(α + 2π9 ) 0 0 sin(α − 8π

9 ) 0 0 sin(α + 8π9 ) 0

0 12 0 0 1

2 0 0 12 0

0 0 cos(α + 4π9 ) 0 0 cos(α − 10π

9 ) 0 0 cos(α + 10π9 )

0 0 sin(α + 4π9 ) 0 0 sin(α − 10π

9 ) 0 0 sin(α + 10π9 )

0 0 12 0 0 1

2 0 0 12

377777777777777777775

∗

26666666666666666664

fas

fbs

fcs

fds

fes

ffs

fgs

fhs

fis

37777777777777777775

(26)

M-D Lab 1/0202 19

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Realization of a 9-D Space Vector Voltage Command Via Pulse Width

Modulation (PWM)

• 512 possible space vectors from a 9-leg inverter

Nine-phaseVoltage Space Vectors

0 0.4 V dc 0.2 V dc -0.2 V dc -0.4 V dc -0.6 V dc 0.6 V dc

0

j0.6 V dc

-j0.6 V dc

-j0.4 V dc

-j0.2 V dc

j0.4 V dc

j0.2 V dc

M-D Lab 1/0202 20

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• Extending 3phase Space Vector PWM algorithm for 9phase Space Vector PWM

Vn, offset = max

�V1

Vdc...

Vn

Vdc

�−min

�V1

Vdc...

Vn

Vdc

�(27)

• Only 72 space vectors are used

{V 4 -5 max } {V 3-6 max }

{V 2-7 max }

{V 1-8 max }

M-D Lab 1/0202 21

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A new SVPWM for n > 3 n-phase Systems

• The Minimum Voltage Difference SVPWM Technique

� � ��

100000111

110001111

00000011

00000111

110000111 100000011 111001111 000000001

111011111 000000010 1101

1111

1

0000

0110

10

0011

111

100001111

0000

0111

1 110011111

000000111 000001111 100001111

100001111

100011111 100011111

000000111 000001111

000000111 100000111 100001111

100001111

110001111 110001111

000000111 100000111

000000011 000000111 110001111

110001111

110011111 110011111

000000011 000000111

100000011 100000111 110000111

110000111

110001111 110001111

100000011 100000111

000000011 100000011 110001111

110001111

111001111 111001111

000000011 100000011

000000001 000000011 111001111

111001111

111011111 111011111

000000001 000000011

000000010 000000011 110011111

110011111

111011111 111011111

000000010 000000011

000000010 000000110 110011111

110011111

110111111 110111111

000000010 000000110

000000110 000000111 100011111

100011111

110011111 110011111

000000110 000000111

M-D Lab 1/0202 22

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Proposal: The Control of a Continuously Operated

Pole-Changing Induction Machine

Goals:

• Decrease the Torque reduction during the pole-changing transition

• Preserve Control during the pole-changing transition

M-D Lab 1/0202 23

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Comparison of 4 pole and 12 pole Stator Current Densities

0 1 2 3 4 5 6 7

0

radians: Stators Circumference

12 pole Stator Current

Density

4 pole Stator Current

Density

M-D Lab 1/0202 24

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• Interaction between the Stator Current Density and air-gap flux results in a tangential force on the

rotordF

dθ= BgKs(t, θ) (28)

• 4 pole steady state operation

0 1 2 3 4 5 6 7

0

Tangential Force K s B g-rotor

B g air-gap flux from

rotor currents

K s stator current

radians

• Transition from 12 poles to 4 poles

radians 0 1 2 3 4 5 6 7

0

Tangential Force K s B g-rotor K s stator current

B g air-gap flux from

rotor currents

M-D Lab 1/0202 25

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Approach:

• Via a coordinate transformation, decouple the machine into two (possibly three) independent

machines

• Regulate the two independent torques in order to pole change

• Control each machine separately

M-D Lab 1/0202 26

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Experimental Setup:

PIII 600MHz RTLinux 3.0

Control Program

FPGA

SVPWM &

Communication

9-Leg Inverter

Dynamometer

position sensor

torque sensor

A/D quadature

Inputs

i a

i i

9 Winding IM

I/O board

M-D Lab 1/0202 27

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Speed-torque curves for the 12 pole and 4 pole configurations

0 100 200 300 400 500 600 700 800 0

5

10

15

20

25

30

35

40

45

rpm

Nm

9phase - 4pole Motor

3phase - 12pole Motor

Figure 1: Speed-torque curves for 12 pole and 4 pole configurations

M-D Lab 1/0202 28

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Speed control: 3phase-12pole Induction motor

• Space Vector Field Orientation Control

• 3phase SVPWM

0 50 100 150 0

100

200

300

400

500

600

700

rpm

s

seconds

Figure 2: Speed-torque curves for 12 pole and 4 pole configurations

M-D Lab 1/0202 29

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Conclusions:

• A variety of pole changing technique exists

• There are no techniques for regulating torque during the pole-changing transition

• Issues during the pole-changing transition:

– reduction in torque

– flux and torque tracking)

• Requirements for a method to decrease torque reduction during the pole-changing transition and

preserve control:

– New PWM scheme

– Modelling the machine as two independent machines

– Develop method to analyze a pole-changing machine in terms of Field Orientation Transformation

M-D Lab 1/0202 30

The Control of a Continuously Operated Pole-Changing ...strangas/emd_lab/kelly_first.pdfThe Control...

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