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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
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2
Content
• Background – why new High Frequency Signal Injection (HFSI) method
• Proposed HFSI method – duty cycle shifting
• Application example – sensorless FOC
• Summary
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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)
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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
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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
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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
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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
𝑈𝑈�1 𝑈𝑈�5
[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∆ = ∆ ⋅
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8
Duty cycle shifting – Type 1
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
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9
Duty cycle shifting – Type 1
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
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10
Duty cycle shifting – Type 2
Duty cycle shifting with Δd1 = Δd2: • Injected voltage vector:
Can be used for existing position estimation algorithm [1]
𝑈𝑈�4
𝑈𝑈�6 𝑈𝑈�2
𝑈𝑈�3
𝑈𝑈�1 𝑈𝑈�5
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
Position of commanded voltage vector (deg)
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
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11
Duty cycle shifting – Type 3 Rotary Pulsating Carrier Signal: • With
• The injected voltage is which is perpendicular to • fs = 9kHz
Can be used for existing position estimation algorithm [2]
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
Position of commanded voltage vector (deg)
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
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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
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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= ⋅ ⇒ = ∠ +
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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
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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
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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= + + = +
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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
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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
Duty cycle shifting – Type 2
-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
Duty cycle shifting – Type 3
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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
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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
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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
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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
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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
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