a new high frequency signal injection method without ......(v) original injected total duty cycle v...

1

A New High Frequency Signal Injection Method Without Maximum

Fundamental Voltage Magnitude Loss and its Application

Dong Wang, Kaiyuan Lu, Peter O. Rasmussen Aalborg University, Denmark

6 April 2017

2

Content

• Background – why new High Frequency Signal Injection (HFSI) method

• Proposed HFSI method – duty cycle shifting

• Application example – sensorless FOC

• Summary

3

Background

Why new HFSI method? • Most HFSI based position estimation algorithms are

machine parameter independent – Do not require machine inductance profile

05

1015 0

510

15

40455055

40

45

50

Id (A) Iq (A)

05

1015 0

510

15

10

20

30

10152025

Id (A) Iq (A)

Machine inductance variation caused by self- and cross-saturation

Indu

ctan

ce (m

H)

4

Background

Why new HFSI method? • Existing HFSI methods have the drawback of

– Maximum fundamental voltage magnitude (MFVM) loss – Limited the machine speed and load operation range

𝑈𝑈�4 100

𝑈𝑈�6(110) 𝑈𝑈�2(010)

𝑈𝑈�3(011)

𝑈𝑈�1(001) 𝑈𝑈�5(101)

𝑈𝑈�0(000) 𝑈𝑈�7(111)

Sector I

Sector II

Sector III

Sector IV

Sector V

Sector VI

MFVM Boundary

𝑉𝑉0

𝑑𝑑1 𝑑𝑑2 𝛿𝛿

Time (s)

Dut

y C

ycle

Without injection With injection

0 0.02 0.04 0.06 0.08 0.10

0.5

1

5

Proposed HFSI method

General idea of proposed method – duty cycle shifting: • Shifting between two neighboring switching periods • The average voltage vector is kept to the commanded vector • The total duty cycle within each switching period should be

limited to one, i.e

𝑈𝑈�4

𝑈𝑈�6

𝑉𝑉0 𝑉𝑉2 𝑉𝑉1

𝑉𝑉0

𝑑𝑑1 + ∆𝑑𝑑1 𝑑𝑑2 − ∆𝑑𝑑2

𝑑𝑑1 − ∆𝑑𝑑1

𝑑𝑑2 + ∆𝑑𝑑2

𝛿𝛿 𝑉𝑉1,𝑝𝑝1

𝑉𝑉2,𝑝𝑝1

𝑉𝑉1,𝑝𝑝2 𝑉𝑉1,𝑝𝑝3

𝑉𝑉2,𝑝𝑝3 𝑉𝑉2,𝑝𝑝2

∆𝑉𝑉𝑐𝑐

𝑉𝑉0

1 1 2 2 1 1 2 21, 1d d d d d d d d+ ∆ + − ∆ ≤ − ∆ + + ∆ ≤

𝑈𝑈�4 =23𝑈𝑈𝑑𝑑𝑐𝑐

𝑈𝑈�6

𝑉𝑉0

𝑑𝑑1

𝑑𝑑2 𝛿𝛿

𝑉𝑉max =𝑈𝑈𝑑𝑑𝑐𝑐

3

6

Proposed HFSI method

The injected voltage vector: • Per-unit value of 𝑈𝑈�4 and 𝑈𝑈�6

• The injected voltage vector (carrier signal)

00 64 3

4, 6,max max

(2 / 3)/ 3

2 ,3 3

2 j jjdc

dcpu pu

e UUU e UV VU

eUπ

= = = = =

( )( )

, 1, 2,

1 1 4, 2 2 6,

1 1 4, 2 2 6,

0 31 2

( ) ( )

( ) ( )

43 3

4

c pu pu pu

pu pu

pu pu

jj

V V V

d d U d d U

d d U d d U

d e d eπ

∆ = −

= + ∆ + − ∆

− − ∆ + + ∆

= ∆ ⋅ − ∆ ⋅

𝑈𝑈�4

𝑈𝑈�6

𝑉𝑉0 𝑉𝑉2 𝑉𝑉1

𝑉𝑉0

𝑑𝑑1 + ∆𝑑𝑑1 𝑑𝑑2 − ∆𝑑𝑑2

𝑑𝑑1 − ∆𝑑𝑑1

𝑑𝑑2 + ∆𝑑𝑑2

𝛿𝛿

7

Duty cycle shifting – Type 1

Duty cycle shifting with fixed Δd1 and Δd2 = 0: • Injected voltage vector:

• Fixed injection in each switching vector range, ( fs=3kHz)

Can be used for existing position estimation algorithm [1]

𝑈𝑈�4

𝑈𝑈�6 𝑈𝑈�2

𝑈𝑈�3


[1] D. Paulus, P. Landsmann, and R. Kennel, “Sensorless field- oriented control for permanent magnet synchronous machines with an arbitrary injection scheme and direct angle calculation,” in Proc. SLED, pp. 41–46, Sep. 2011

0 60 120 180 240 300 360 420 480 540 600 660 720-180-120

-600

60120180

Position of commanded voltage vector (deg)

Dire

ctio

n (d

eg)

Injected Pulsating Voltage Envelope

0, 13

4 jc puV d e∆ = ∆ ⋅

8


Maximum Δd1=1−d1 , i.e. 𝑈𝑈�4 occupies a full period s1 for 0 ≤ δ < 30˚

• Before shifting

• After shifting

𝐷𝐷1

𝐷𝐷2

𝐷𝐷3

𝐷𝐷1

𝐷𝐷2

𝐷𝐷3

𝑑𝑑22

𝑑𝑑22

𝑑𝑑12

𝒔𝒔𝟏𝟏 𝒔𝒔𝟐𝟐

𝒔𝒔𝟏𝟏 𝒔𝒔𝟐𝟐

𝑑𝑑22

𝑈𝑈�4 𝑈𝑈�4 𝑈𝑈�6 𝑈𝑈�6

𝑈𝑈�4 𝑈𝑈�4 𝑈𝑈�4 𝑈𝑈�6 𝑈𝑈�6

𝑈𝑈�4 𝑈𝑈�4 𝑈𝑈�6 𝑈𝑈�6

9


Maximum Δd1=1−d1 : • Maximum d1 of traditional SVM is • Maximum Δd1 always available • For Udc = 575V and Δd2 = 0 :

When d1 + d2 + Δd1 > 1, • Δd2 ≠ 0, • e.g. Δd2 = d1 + d2 + Δd1 − 1

1 3 2d =

1 1 3 2 0.134d∆ = − =

0 0, 1

43 3 3

102.73j jdc dcc c puU UV V d e e∆ = ∆ = ∆ ⋅ =

𝑈𝑈�4

𝑈𝑈�6

𝑉𝑉0

𝑑𝑑1

𝑑𝑑1 + 𝑑𝑑2 = 1

10


Duty cycle shifting with Δd1 = Δd2: • Injected voltage vector:


𝑈𝑈�4


𝑈𝑈�3


0 3 3, 1 2 1

4 4 43 3 3

j jjc puV d e d e d e

π π−∆ = ∆ ⋅ − ∆ ⋅ = ∆ ⋅

0 60 120 180 240 300 360 420 480 540 600 660 720-180-120

-600

60120180


Dire

ctio

n (d

eg)

Injected Pulsating Voltage Envelope

[1] D. Paulus, P. Landsmann, and R. Kennel, “Sensorless field- oriented control for permanent magnet synchronous machines with an arbitrary injection scheme and direct angle calculation,” in Proc. SLED, pp. 41–46, Sep. 2011

11

Duty cycle shifting – Type 3 Rotary Pulsating Carrier Signal: • With

• The injected voltage is which is perpendicular to • fs = 9kHz


1

2

cos( 3 )cos

d dd d

π δδ

∆ = ∆ ⋅ −∆ = ∆ ⋅

, 2j

c puV j d eδ∆ = − ∆ ⋅

0 20 40 60 80 100 120 140 160 180

-90

0

90


Dire

ctio

n (d

eg)

[2] Y. D. Yoon, S. K. Sul, S. Morimoto, and K. Ide, “High-bandwidth sensorless algorithm for AC machines based on square-wave-type voltage injection,” IEEE Trans. Ind. Appl., vol. 47, no. 3, pp. 1361–1370, May/Jun. 2011

0 0jV V e δ= 𝑈𝑈

�4

𝑈𝑈�6

𝑉𝑉0

𝑑𝑑1

𝑑𝑑2 𝛿𝛿

∆𝑉𝑉𝑐𝑐,𝑝𝑝𝑝𝑝

12

Proposed position estimation method

Existing HFSI based position estimation methods: • Requires BPF and/or LPF for:

– carrier response demodulation – machine saliency information extraction

• with the cost of: – error caused by phase shift of filters – degraded dynamic performance

13

Proposed position estimation method Proposed algorithm: • Based on the changing of flux-linkage and current during

two neighboring switching periods • SynRM flux-linkage in the stator frame: where

• Define

• Then • The inductance L2 will only influence the magnitude of �̅�𝐴,

not the argument (angle). The proposed algorithm is machine inductance independent.

1 2( ) 2 and ( ) 2d q d qL L L L L L= + = −

2*1 2

rjL i L i e θαβ αβ αβλ = +

2 1 1 2A i iαβ αβ αβ αβλ λ= −

ˆ2*2 2 1

ˆIm( ) 2 2 2rj rA L i i je Aθ

αβ αβ θ π= ⋅ ⇒ = ∠ +

14

Proposed position estimation method

Proposed algorithm: • Pros

– No special requirement to current sampling – No BPF and/or LPF needed – Suitable for proposed HFSI method, till rated speed

• Cons – Flux-linkage needed, not suitable for very low speed to

standstill

15

Proposed position estimation method Cross-saturation effect: • ldq term is introduced and distort the magnetic saliency axes • SynRM flux-linkage in the rotor frame:

• Then

• The estimated position by using the indication vector �̅�𝐴

• Instead of the rotor mechanical saliency ( ), the distorted magnetic saliency ( ) is obtained.

ˆ2*2 2 1

ˆ(2 )*2 2 1

( ) Im( ) 2

Im( ) 2

r

r

jdq

j

A L l i i je

L i i je

θαβ αβ

θ εαβ αβ

+

= + ⋅

′= ⋅

*1 2( ) ( )dq d d dq q q q dq d dq dq dqL i l i j L i l i L i L l iλ = + + + = + +

ˆ2 4 2est rAθ π θ ε= ∠ + = +

2where arctan dq

d q

lL L

ε =−

r̂θ

estθ

16

Application example – sensorless FOC Sensorless FOC with high torque per ampere operation:

• Torque

and maximum torque is obtained when • Current vector location in the stationary frame

• The current vector should locate at 45° with respect to θest i.e. 45° in the estimated rotor frame (magnetic saliency) • There is no need to compensate the error (ε) caused by

cross-saturation effect • Sensorless FOC do not require any inductance information

223 3( ) sin(2 )

2 2 cosrm

q d d q ipL IT p i iλ λ θ ε

ε= − = −

2 2riθ ε π− =

ˆ4 2 4si r estθ π ε θ π θ= + + = +

17

Verification of proposed HFSI method: • Open-circuit no-load tests • Type 1 with 220V grid input and Δd1 = 0.065

Experiment results

-200

0

200

0 0.005 0.01 0.015 0.020.3

0.4

0.5

Time (s)

Volta

ge (V

)

Original Injected

Tota

l dut

y cy

cle

vβ

vα

100 V 50 Hz output

-200

0

200

0 0.005 0.01 0.015 0.020.850.9

0.951

Time (s)

Volta

ge (V

)

Original Injected

Tota

l dut

y cy

cle

vβ vα

220 V 50 Hz output

18

Verification of proposed HFSI method: • Type 2 with full voltage output and Δd1 = Δd2 = 0.05 • Type 3 with full voltage output and Δd = 0.05

Experiment results

-200

0

200

0 0.005 0.01 0.015 0.020.850.9

0.951

Time (s)

Volta

ge (V

)

Original Injected

Tota

l dut

y cy

cle

vβ

vα


-200

0

200

0 0.005 0.01 0.015 0.020.850.9

0.951

Time (s)

Volta

ge (V

)

Original Injected

Tota

l dut

y cy

cle

vβ

vα


19

Proposed HFSI based position estimation method: • With position encoder • 300rpm, no load • Duty cycle shifting

with Δd1 = 0.065 • Injected current is 0.6A

0 0.05 0.1 0.15 0.2 0.25 0.3-5

0

5

-10

0

10

200

300

400

0

6.4

Time (s)

Spee

d (r

pm)

Posi

tion

erro

r (d

eg)

Real Estimated

Cur

rent

(A

)

iβ iα

Posi

tion

(rad

) Real Estimated

-50

0

50

0.08 0.1 0.12 0.14 0.16-50

0

50

Time (s)

v α (V

) v β

(V)

Original Injected

Original Injected

Experiment results

20

Experiment results

-20

0

201400

1500

1600

0 0.01 0.02 0.03 0.04 0.05-20

0

20

-200

0

200

Time (s)

Spee

d (r

pm)

Posi

tion

erro

r (d

eg e

lec)

Real Estimated

Volta

ge (V

) C

urre

nt (A

)

vβ

vα

iβ

iα

Sensorless FOC at 1500 rpm 13.9 Arms

2000

2100

2200

-20

0

20

0 0.01 0.02 0.03 0.04 0.05-20

0

20

-300

0

300

Time (s)

Spee

d (r

pm)

Posi

tion

erro

r (d

eg e

lec)

Real Estimated

Volta

ge (V

) C

urre

nt (A

)

vβ

vα

iβ

iα

Sensorless FOC at 2100 rpm 20 A id

21

Experiment results

• Maximum voltage output achieved (vβ 320 Vpk at 0.02 s)

• Signal injection without influence the fundamental output

2000

2100

2200

-20

0

20

0 0.01 0.02 0.03 0.04 0.05-20

0

20

-300

0

300

Time (s)

Spee

d (r

pm)

Posi

tion

erro

r (d

eg e

lec)

Real Estimated

Volta

ge (V

) C

urre

nt (A

)

vβ

vα

iβ

iα

Sensorless FOC at 2100 rpm 20 A id

0.015 0.016 0.017 0.018 0.019 0.02 0.021 0.022240260280300320340

Time (s)

Volta

ge (V

)

vβ vα

22

High torque per ampere operation: Current vector position 45° • Top: constant load of

7 Arms motor current (amplitude 9.90 A) 48.9° – 46.5° = 2.4°

• bottom: constant load of 13.9 Arms motor current (amplitude 19.65 A) 53.3° – 51.0° = 2.3°

• The position error is consistent at different load

Experiment results

30 35 40 45 50 55 60 65 7018

20

22

24

26

9

10

11

12

13

Current vector position (deg elec)

Cur

rent

vec

tor

mag

nitu

de (A

) C

urre

nt v

ecto

r m

agni

tude

(A)

46.5˚ (9.89 A)

51.0˚ (19.31 A)

48.9˚ (9.91 A)

53.3˚ (19.34 A)

9.90 A

19.65 A

23

Summary

• A new HFSI method is proposed and verified – with the advantage of no output voltage amplitude sacrifice – different types of injection can be achieved by controlling the

values of Δd1 and Δd2 – open the possibilities to apply HFSI based inductance independent

position estimation method at full speed and load • New position estimation algorithm is proposed and verified

– machine inductance independent – with arbitrary voltage injection, including the proposed HFSI – no BPF and/or LPF needed for position information extraction – for middle to high-speed operation range of SynRM drive

24 24

• Any comment?

A New High Frequency Signal Injection Method Without Maximum Fundamental Voltage Magnitude Loss and its ApplicationContentBackgroundBackgroundProposed HFSI methodProposed HFSI methodDuty cycle shifting – Type 1Duty cycle shifting – Type 1Duty cycle shifting – Type 1Duty cycle shifting – Type 2Duty cycle shifting – Type 3Proposed position estimation methodProposed position estimation methodProposed position estimation methodProposed position estimation methodApplication example – sensorless FOCExperiment resultsExperiment resultsExperiment resultsExperiment resultsExperiment resultsExperiment resultsSummarySlide Number 24

a new high frequency signal injection method without ......(v) original injected total duty cycle v...

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