Experiment of Magnetic Resonant Coupling Three-Phase Wireless Power Transfer Phase Wireless Power Transfer

Experiment of Magnetic Resonant Coupling ThreeThree----phasephase Wireless Power Transfer

Yusuke Tanikawa, Masaki Kato, Takehiro Imura, Yoichi Hori

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Organized by Hosted by In collaboration with Supported by 3/26 Contents 0. What is our study? : Movie 1. Background of Wireless Power Transfer 1.1. General information of WPT 1.2. Why three phase? 2. Approach of our study 2.1. General info. & parameters 2.2. Theoretical formula 2.3. Experiment and result 3. Conclusion and future works

Organized by Hosted by In collaboration with Supported by 4/26 Contents 0. What is our study? : Movie 1. Background of Wireless Power Transfer 1.1. General information of WPT 1.2. Why three phase? 2. Approach of our study 2.1. General info. & parameters 2.2. Theoretical formula 2.3. Experiment and result 3. Conclusion and future works

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Wireless Power Transfer (WPT) Applications: EV , mobile, and battery charger Conventional WPT: Single phase AC transfer

Organized by Hosted by In collaboration with Supported by 6/26 1.1. General info. for WPT 2/3 Three methods of WPT technologies Magnetic Magnetic Resonant Methods Microwave Induction Coupling

Images

Transfer Gap Up to 0.2 m Up to 10 m A few hundred km Efficiency Up to 95% Up to 97% Up to 60 % Robustness for Poor Great Good Displacement

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6/26 7/26 1.1. General info. for WPT 3/3 Magnetic Resonant Coupling • Transmitter and receiver: LC resonators • High efficiency (around 90%) at 1 m gap • Transfer frequency: 100 kHz to 20 MHz – Power devices for kHz switching • Relay resonators (single phase) – Suitable for charging EVs while running

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a a' ~~~ Z N N' Z + ~~~ ~~~ c+ b c' Z b'

Organized by Hosted by In collaboration with Supported by 9/26 1.2. Why three phase? 2/3 Advantages for high power transfer • Larger power capacity with same devices – Capacity limit: three times of single phase (High frequency devices: Low power limit) • Relatively simple system Single phase Three phase Power limit ratio 1 3 Device quantity 2 (4 switches, 2 lines) 3 (6 switches, 3 lines)

Circuits

Organized by Hosted by In collaboration with Supported by 10/26 1.2. Why three phase? 3/3 Suitable characteristics for WPT • Smaller ripples of rectified DC

ACU相 (U) V相AC (V) 2 2 ACW相 (W) DC整流波形整流前波形 1.5 AC DC整流波形 1.5 1 1 0.5 0.5 ×Vo 0 ×Vo 0 0 60 120 180 240 300 360 -0.5 -0.5 0 60 120 180 240 300 360 -1 -1 -1.5 -1.5 位相角[°] 位相角[°] Single phase Three図三相交流の全波整流 phase 単相交流の整流電圧 • Rotation symmetry: contact-less terminal Conventional method

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Organized by Hosted by In collaboration with Supported by 11/26 Contents 0. What is our study? : Movie 1. Background of Wireless Power Transfer 1.1. General information of WPT 1.2. Why three phase? 2. Approach of our study 2.1. General information & parameters 2.2. Theoretical formula 2.3. Experiment and result 3. Conclusion and future works

Organized by Hosted by In collaboration with Supported by 12/26 2.1. General info. & parameters 1/2 Experiment & analysis of ThreeThree----phasephase WPT 1. Comparison of data and theoretical formula 2. Rotation experiment: collection of measured values • Each 15 degree from 0 to 360 degree • Mutual inductance between resonators • Ratio of voltage (V), current (I), and power (P) Mutual inductance Ratio between transmitter and receiver Formula (Measured value) (Calculated value) Transmitter V, I, and P Comparison (Measured value) Ratio between transmitter and receiver Receiver V, I, and P (Measured value) (Measured value)

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Voltage ratio I2 V Receiver2nd side side 2 V2 Av = V1

I1 Current ratio Lm V1 st ~~~ 1Transmitterside side I 2 ~~~ ~~~ Ai = I1

Coupling coefficient Efficiency (Power ratio) (nondimensionalized mutual inductance) P V ⋅ I L L L η = out = 2 2 = A ⋅ A k = m = m = m v i Pin V1 ⋅ I1 L1 L2 880 µH Power factor = 1.0 (resonant condition) Organized by Hosted by In collaboration with Supported by 14/26 2.2. Theoretical formula 1/3 Base theoretical formula of single phase

Resonance: simple formula of mutual inductance andLm load resistance RL

ω0 = L1C1 = L2C2 At experiment; RL=50 ohm Voltage ratio

V2 ω0 Lm RL Av = = j 2 = Av (Lm , RL ) V1 R1RL + R1R2 + (ω0 Lm )

Current ratio I 2 ω0 Lm Ai = = j = Ai (Lm , RL ) I1 (RL + R2 )

Efficiency (Power ratio)

(ω L )2 R η = A ⋅ A = 0 m L Masaki Kato, Takehiro Imura, Yoichi Hori, “The Characteristics when Changing Transmission Distance v i 2 and Load Value in Wireless Power Transfer via Magnetic Resonance Coupling”, (RL + R2 ){R1RL + R1R2 + (ω0 Lm ) } The 34th International Telecommunications Energy Conference (INTELEC 34th), 2012 Organized by Hosted by In collaboration with Supported by 15/26 2.2. Theoretical formula 2/3 Modification of formula to three phase • Three phase; a lot of mutual inductance values To adapt the single phase formula; how to combine the values into one value ? • Combination of trigonometric function ~ π 2π Phase difference L = L sin( ω t ) + L sin( ω t + ) + L sin( ω t + ) m m 1 m 2 3 m 3 3 2 2 2 = ( L m 1 + L m 2 + L m 3 ) − ( L m 1 L m 2 + L m 2 L m 3 + L m 3 L m 1 ) sin( ω t + φ )

I2 Combined Lm V Receiver2nd sideside 2  ( )2/3 L − ( )2/3 L sin φ = m2 m3  2 2 2 (Lm1 + Lm2 + Lm ) − (Lm1Lm2 + Lm2 Lm3 + Lm3Lm1) I1  3 Lm  V1 L − (L )2/ − (L )2/ ~~~ Transmitter1st side side cosφ = m1 m2 m3 ~~~ ~~~  2 2 2  (Lm1 + Lm2 + Lm3 ) − (Lm1Lm2 + Lm 2 Lm3 + Lm3Lm1)

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• Efficient formula: function of load resistance 2 ω0 (Lm RL ) η = Av ⋅ Ai = 2 (RL + R2 ){R1RL + R1R2 + (ω0 Lm ) } • Optimal value of load resistance

2 R2 2 RL = R2 + (ω0 Lm ) R1

Organized by Hosted by In collaboration with Supported by 17/26 2.3. Experiment 1/7 (Setting) • Resonant frequency: 120 kHz • Cable: Y connection – Rotation symmetry – 50 ohm load resistance • Resonators Phase a Phase b Phase c Self inductance ［μH ］ 8.73 ×10 2 8.68 ×10 2 8.69 ×10 2 Cable: 2 mm 2 Internal resistance ［Ω］ 1.21 1.23 1.12 Diameter: 1.7 mm Resonant capacitance ［pF ］ 2.04 ×10 3 2.09 ×10 3 2.04 ×10 3 Pitch of coil: 2.5 mm Quality factor 5.46 ×10 2 5.36 ×10 2 5.89 ×10 2

Resonant frequency ［kHz ］ 1.19 ×10 2 1.19 ×10 2 1.20 ×10 2 Capacitor: 2000 pF Self inductance ［μH ］ 8.67 ×10 2 8.69 ×10 2 8.69 ×10 2

Internal resistance ［Ω］ 1.17 1.23 1.20

Resonant capacitance ［pF ］ 2.07 ×10 3 2.03 ×10 3 2.04 ×10 3

Quality factor 5.63 ×10 2 5.36 ×10 2 5.49 ×10 2 Receiver Transmitter Resonant frequency ［kHz ］ 1.19 ×10 2 1.20 ×10 2 1.20 ×10 2

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Mutual inductance Lm (Coupling coefficient k)

120 60 A-A Combined mutual inductance; B-A calculated from measured values C-A L L L k = m = m = m 0 [deg] 180 0.00 0.10 0.20 L1 L2 880 µH Lkm

240 300 Close position: small rotation angle Strong coupling

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Optimal load resistance Z L

120 60 最適負荷Optimal value

Similar shape to mutual inductance

0 [deg] 180 60 120 180 [Ω] RL

2 R2 2 RL = R2 + (ω0 Lm ) R1 240 300

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A-A 0-45 degree; phase = -90 degree 120 60 B-A 60 degree; phase = 180 degree C-A 75-120degree; phase = 150degree A-A Cal =－120 －90 ＋360 degree B-A Cal C-A Cal Precise shape Between calculation and 0 [deg] 180 30 150 270 measured value [deg]  ( )2/3 A − ( )2/3 L sin φ = 2 3  2 2 2  (L1 + L2 + L3 ) − (L1L2 + L2 L3 + L3L1)  L − (L )2/ − (L )2/ cosφ = 1 2 3  2 2 2 240 300  (L1 + L2 + L3 ) − (L1L2 + L2 L3 + L3L1 )

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ω0 Lm RL Av = j 2 R1RL + R1R2 + (ω0 Lm )

At 60 degree, Voltage ratio is maximum .

Calculated value < Measured value

At optimal load; circular shape

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Current ratio Ai

50[Ω] 負荷計算値 50[Ω] 負荷実測値最適負荷計算値 ω0 Lm Ai = j (RL + R2 )

At 60 degree, Current ratio is minimum.

1.0 2.0 3.0 Ai Calculated value > Measured value

At optimal load; circular shape

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50[Ω] 負荷計算値 50[Ω] 負荷実測値 120 60 最適負荷計算値

0 [deg] 0-45 degree ： 80% 180 00.2 0.4 0.60.8 1.0 η 60 degree ：35% 75-120 degree ：80 %

Maximum deference of calculated and measured value; 240 300 at 60 degree

Organized by Hosted by In collaboration with Supported by 24/26 Contents 0. What is our study? : Movie 1. Background of Wireless Power Transfer 1.1. General information of WPT 1.2. Why three phase? 2. Approach of our study 2.1. General information & parameters 2.2. Theoretical formula 2.3. Experiment and result 3. Conclusion and future works

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• Experiment and analysis of Three-phase WPT – 1. Comparison of data and theoretical formula Each formula draws the similar calculated value as measured value

– 2. Rotation experiment Rotation symmetry of transmitters are shown in experimental result • Future works – High power experiment and analysis – Coupling analysis as cross coupling.

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Advanced experiments are undergoing…

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Power

Voltage Current

Receiver voltage DC-DC Efficiency

Device efficiency

WPT efficiency .0 737 η = = .0 830 = 83% Organized by Hosted by In collaboration.0 with884 Supported by 回路構成

50Hz v Load Inv. (Leaf)

負荷 DC 電源高周波インバータ共振器整流器インバータ＋または可変電圧 50Hz Leaf 定電流モード有り 20Ω 琺瑯抵抗

Organized by Hosted by In collaboration with Supported by Organized by Hosted by In collaboration with Supported by π 2π A sin(ωt) + A sin(ωt + ) + A sin(ωt + ) 1 2 3 3 3

= A1 sin(ωt) π π + A {sin( ωt) cos + cos(ωt) sin } 2 3 3 2π 2π + A {sin( ωt) cos + cos(ωt) sin } 3 3 3 A A 3 3 = ( A − 2 − 3 ) sin(ωt) + ( A − A ) cos(ωt) 1 2 2 2 2 2 3 A A 3 3 = ( A − 2 − 3 ) 2 + ( A − A ) 2 sin(ωt + φ ) 1 2 2 2 2 2 3 π 2π A1 sin(ωt) + A2 sin(ωt + ) + A3 sin(ωt + ) Organized by Hosted by In collaboration3 with Supported by 3 線間電圧と相電圧

対称Y形起電力において ° ° ea ===Em1 sin(ωωωt−−− 0 )+++Em3 sin3ωωωt+++Em5 sin(5 ωωωt−−− 0 )+++ ••• ° ° eb ===Em1 sin( ωωωt−−−120 )+++Em3 sin3ωωωt+++Em5 sin(5 ωωωt−−−240 )+++ ••• ° ° ec ===Em1 sin( ωωωt−−−240 )+++Em3 sin3ωωωt+++Em5 sin(5 ωωωt−−−120 )+++ •••

各線間電eab 圧===ea−−− はeb a + ° ===Em1{sin ωωωt−−−sin( ωωωt−−−120 )} ~~~ ea eab +++E {sin5 ωωωt−−−sin(5 ωωωt−−−240 °)} +++ ••• N m5 ec eca 線間電圧に三倍次高調波はあらわれない + ~~~ ~~~ b c eb + ebc

Organized by Hosted by In collaboration with Supported by Y形結線における高調波

第1次調波など (正相) 第3次調波など (同相) 第5次調波など (逆相) e e a ea eb ec a

ec eb

eb ec

ea+++eb+++ec ===0 ea+++eb+++ec ===3Em3 sin3 ωωωt ea+++eb+++ec ===0

ia a a' + ~~~ ea Z 平衡回路でも、同相の高 iN === ia+++ ib+++ ic NN' ec Z 調波があれば中性点間に + ~~~ ~~~ 電流が流れる ceb + b c' Z b' Organized by Hosted by ic In collaboration with Supported by ib Delta connection with harmonic waves

第1次調波など (正相 ) 第3次調波など (同相 ) 第5次調波など (逆相 )

ea +++eb +++ec === 0 ea +++eb +++ec === 3Em3 sin3 ωωω t e a +++eb +++ec === 0

a a' + Z eab Z ea +++eb +++ec cg ~~~ al ig === Zca Zab Zag +++Zbg +++Zcg eca Z ig ag + ~~~ c~~~ + bZcl c' b' Zbc Zbg ebc

Zbl 平衡回路でも同相の高調波があれば起電力回路に循環電流が流れる

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ea ===e(t)===Em1 sin ωωωt+++Em3 sin3ωωωt +++Em5 sin5ωωωt+++ •••

eb ===e(t−−−T/3) ===Em1 sin ωωω(t−−−T/3) +++Em3 sin3ωωω(t−−−T/3) +++Em5 sin5ωωω(t−−−T/3) +++ ••• ° ===Em1 sin(ωωωt−−−120 )+++Em3 sin(3 ωωωt) ° +++Em5 sin(5 ωωωt−−−240 )+++ •••

° ec ===e(t−−−2T/3) ===Em1 sin(ωωωt−−−240 )+++Em3 sin(3 ωωωt) ° +++Em5 sin(5 ωωωt−−−120 )+++ •••

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• induction

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• Induction without magnetic resonant coupling Ladder coil transmitter for rail transport – Small air gap

– Three phase receivers are original of us –

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