Three-phase Wireless Power Transfer for Dynamic...

IEEJ International Workshop on Sensing, Actuation, and Motion Control

Three-phase Wireless Power Transfer for Dynamic Charging of ElectricVehicle for High Efficiency and Reducing Voltage Unbalancing

Considering Magnetic Flux Canceling

Daiki Kimura∗ Student Member, Takehiro Imura∗ Member

Hiroshi Fujimoto∗ Senior Member, Yoichi Hori∗ Fellow

Most of the available Electric Vehicles (EVs) can hardly be driven for long distances due to battery limitations.Therefore, as one of the most promising solutions, dynamic-hcarging based wireless power transfer (WPT) from coilsunder the ground to EVs has been widely studied recently. For dynamic charging of EVs, high power transmission isneeded, moreover, the charging system should be robust to large gap and large misalignment. Therefore, in this paper,three-phase alternating current WPT system is for dynamic charging of EVs. In this paper, specifically, V-minus type isproposed to increase efficiency and decrease the the rate of voltage unbalancing. The rectangular coil, which is suitablefor dynamic charging, is applied to transmit three-phase power. The performance of proposed methods is verified bysimulations and experiments.

Keywords: Wirelss Power Transfer, Magnetic Resonance Coupling, Three-phase Alternating Current, Electromagnetic Field, CrossCoupling

1. Introduction

Electric Vehicls(EVs) are considered to be better in com-parison with internalcombustion engine-based vehicles interms of controllability and enviromental-friendly(1). Nev-ertheless, Nevertheless, most of the off-the-shelf EVs haveshort crusing range due to small capacity of batteries. In or-der to solve this problem, the concept of wireless power trans-fer (WPT) from coils under the grouond to EVs while drivingis proposed(2) (3). Dynamic charging can reduce the burden ofbattery charging, prevents electric shock, and enable EVs todrive longer.

As one of the WPT methods , magnetic resonance cou-pling, which was found in MIT (Massachusetts Institute ofTechnology) is gathering attentions(4). This is the method oftuning resonance frequencies of the transmitter and the re-ceiver. It can work over misalignment and long gap. It is con-sidered to be applicable to dynamic charging. Besides, three-phase alternating current is suitable for high power transmis-sion because it can reduce the number of semiconductor de-vices and the ohmic loss. Three-phase WPT, which integratesWPT via magnetic resonance coupling and three-phase alter-nating current, is a suitable method for the dynamic chargingfor EV (5).

However, the transmission of phase-different electricpower from multiple coils has many difficulties. Cross cou-pling occours between another phases, and the fluxies gener-ated by other phases disturbs each others(7). This may lowerthe efficiency(8).

In this paper, firstly, a detailed account in three-phase WPT

∗ The University of Tokyo5-1-5, Kashiwanoha, Kashiwa, Chiba, 227-8561 Japan

is explained. Secondly, new three-phase WPT method, V-minus type, is proposed for the dynamic charging. Thirdly,analysis method of three-phase WPT is shown. Finally, sim-ulation and experiment results are provided to demonstratethe advantages of the proposed method.

2. Outline of the three-phase wireless powertransfer

2.1 Three-Phase WPT for dynamic charging Therewere researches about three-phase WPT. However, these pa-pers focused on only WPT of three-phase to single-phase(9)

(10), studied limited coil shape such as circular coil(5) (6) or sec-tor (11) (12), or ignoring the mutual inductances between coilswhich is not the same phases.

Assuming that dynamic charging for EVs, WPT from rect-angular three-phase coils buried in the road to rectangularcoils loaded on the bottom of EV as shown in Fig.1. Inthis paper, to simplifications, WPT to EV while stopping isconsidered. Fig.2 shows the equivalent circuit of three-phaseWPT. In order to consider the premise of the accounting un-balanced three-phase, three-phase four-wire system is used.

3. Equation of three-phase wireless power trans-fer

Considering cross-coupling between several coils, three-phase WPT can be caluculated by Eq.(1). The parameteresand variables are defined as table.1.

V1a

V1b

V1c

V2a

V2b

V2c

=

R1a jωM1a1b jωM1a1c

jωM1b1a R1b jωM1b1c

jωM1c1a jωM1c1b R1c

jωM2a1a jωM2a1b jωM2a1c

jωM2b1a jωM2b1b jωM2b1c

jωM2c1a jωM2c1b jωM2c1c

c⃝ 2015 The Institute of Electrical Engineers of Japan. 1

Three-Phase WPT for EV considering Magnetic Flux Canceling (Daiki Kimuraet al.)

Fig. 1. Appearance of dynamic charging

V1a

R1aC1aR2aC2a

R1bC1bR1cC1c R2bC2b R2cC2c

I1b

I1a

I1c

V1b

V1c

V2a

I2a

I2b I2c

V2b

V2c

Transmitter Receiver

PowerZLa

ZLcZLb

Fig. 2. Equivalent circuit of three-phase wireless power transfer

　Table 1. Definition of the symbols

Symbols MeaningV1a,V1b,V1c Transmitter side voltageV2a,V2b,V2c Receiver side voltageI1a,I1b,I1c Transmitter side currentI2a,I2b,I2c Receiver side current

R1a,R1b,R1c Transmitter side resistanceR2a,R2b,R2c Receiver side resistanceRLa,RLb,RLc Load resistanceC1a,C1b,C1c Transmitter side capacitanceC2a,C2b,C2c Receiver side capacitance

ω Resonance angular frequency






lωM2c2a jωM2c2b R2c

I1a

I1b

I1c

I2a

I2b

I2c

(1)

Diagonal elements of impedance matrix in Eq.(1) to be exact,has reactance component due toL andC. In this case, usingresonance coupling method, the equation satisfies Eq.(2).

ω =1√

LC· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (2)

When deviding Impedance matrix in Eq.(1) into 3× 3 matrix,and voltage and current vector into 1× 3 matrix, the equationcan be simplified to Eq.(3). Each bold-faced type means asshown in Eq.(4)∼ Eq.(9). Symbols asM1a2b means mutualinductances between transmitter phase-A and receiver phase-B.

Unipolar

U

V

W

V-minus

U

V-

W

Fig. 3. Phaser of Unipolar-Type and V-minus Type

[V1

V2

]=

[Z1 MMT Z2

] [I1

I2

]· · · · · · · · · · · · · · · · · · · (3)

V1 =

V1a

V1b

V1c

,V2 =

V2a

V2b

V2c

· · · · · · · · · · · · · · · · · · · · · (4)

I1 =

I1a

I1b

I1c

, I2 =

I2a

I2b

I2c

· · · · · · · · · · · · · · · · · · · · · · · · (5)

Z1 =




· · · · · · · · · (6)

Z2 =




· · · · · · · · · (7)

2


Fig. 4. The image of magnetic flux cancelation

ZL =

RLa 0 00 RLb 00 0 RLc

· · · · · · · · · · · · · · · · · · · · · · · (8)

M =




· · · · · · · · · (9)

V2 = ZL I2 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (10)

Defining input voltage asV1, and rearranging these equationsorder,I1,I2,V2 can be calculated by Eq.(11)∼ Eq.(13).

I1 = (Z1 + M(−ZL − Z2)MT)−1V1 · · · · · · · · · · · · · (11)

I2 = (−ZL − Z2)−1MT I1 · · · · · · · · · · · · · · · · · · · · · · · (12)

V2 = ZL(−ZL − Z2)−1MT I1 · · · · · · · · · · · · · · · · · · · (13)

4. Magnetic flux canceling by shifting phaser(proposed method)

In the previous research of three-phase WPT, three coilsare adjacently aligned. Each coil has phase difference of 120degrees namely the Phase U, Phase V, and Phase W. Becausein this conventional method, the three phases has 120 degreedifference, when a receiver coil receives the magnetic fluxgenerated by adjacent transmitter coils, as shown in Fig.4,the magnetic flux canceling occurs and efficiency becomeslower. When using threefold asymmetry coils, mutual in-ductances differs. As a result, the three-phase will be un-balanced. The rectified voltage through three-phase rectifierwill become low. And it causes a bad influence on electricpower system.

In order to solve these problems, a new method is pro-posed. As seen in Fig.5 , the center phase is reversed andadjusted coils is only 60 degrees. This may decrease the mag-netic flux canceling. In this method, even if horizontal mis-aligned , one receiver coil covers over two transmitter coils,efficiency is not as lower as the unipolar type as shown inFig.6. The V-minus type can be realized by reversing thewiring of the central phase or turning the central coil in theother way. Wiring diagram of the each methods are shownin Fig.7. The conventional method is defined as the Unipo-lar type and the new center-reversed method is defined as the

V-minus type. Fig.3 shows the phaser of the Unipolar typeand the V-minus type. Fig.5 shows the outline of the coils ofUnipolar-type and V-minus type.

Charastristics of the Unipolar type and V-minus type, arecompared. Efficiency and rate of voltage unbalancing areconsidered to evaluate these methods.

5. Outcome measures

5.1 Transmission efficiency EfficiencyAp is the ra-tio of the sum of the input power to the sum of the outputpower，and it is shown as Eq.(14).

Ap =Re(I2aV2a + I2bV2b + I2cV2c)

Re(I1aV1a + I1bV1b + I1cV1c)· · · · · · · · · · · · · · (14)

5.2 Rate of voltage unbalancing By substitutingEq.(11) for Eq.(13), transformation equation from input volt-age to output voltage is shown as Eq.(15).

V2 = ΩV1 · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (15)

where

Ω = Z1(MT)−1 − (Z1(MT)−1Z2 − M)Z−1L

The Balance of three-phase is maintained when negativephase and zero phase of output voltage become zero. It iswhen Eq.(16) is given as input voltage. Negative phase andzero phase are calculated as Eq.(17). This is replaced asEq.(18) whereψ is a complex number.

V1 =

1λλ2

V · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (16)

[Vnegative

Vzero

]=

[1 λ λ2

1 1 1

]Ω

1λλ2

· · · · · · · · · · (17)

ψ

1λλ2

= Ω 1λλ2

· · · · · · · · · · · · · · · · · · · · · · · · · · · (18)

λ means 120 degree rotation as shown in Eq.(19).

λ = −12+

√3

2j · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · (19)

However, it is difficult to satisfy this qualification because thecontrol of transmitter voltage and receiver voltage is needed.So, degree of collapse of three-phase is evaluated as rate ofvoltage unbalancing.

The rate of voltage unbalancing,kub, is 100 percentage ofnegative phase and positive phase, which is calculated byEq.(20)∼ Eq.(21). VU

VV

VW

= 1 1 1λ2 λ 1λ λ2 1

Vpositive

Vnegative

Vzero

· · · · · · · · · · · (20)

kub =

∣∣∣Vnegative

∣∣∣∣∣∣Vpositive

∣∣∣ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·(21)

3


V+U+ W+ U+ V- W+

Reve

rsal

Three rectangular coils are adjusted Unipolar V-minus

Fig. 5. The configuration of Unipolar-Type and V-minus Type

Canceling of magnetic flux is significant.

Unipolar

Fig. 6. Canceling of magnetic flux of Unipolar and V-minus

U+ V+ W+

U+ V+ W+

Transmitter

Receiver

ZLoad

[1]Wiring of Unipolar

U+ V- W+

U+ V- W+

Transmitter

Receiver

ZLoad

[2]Wiring of V-minus

Fig. 7. Wiring of Unipolar and V-minus

Phase U

Phase V

Phase WSmoothing Capacitor

Fig. 8. Three-phase converter

5.3 Rectified voltage ratio For EV applications,three-phase power is charged to smoothing capaciter. Aver-age voltage after rectified by rectifier Fig.8 is evalued. Inthis case, rectified voltage ratio is defined as the ratio ofsmoothing capaciter voltage and voltage amplitude of sin-wave source.

6. Experiment and Simulation

6.1 Conditions The shapes of transmitter and re-ceiver coils are designed as 1600× 900 mm consided fromnormal size EV. The size of one-phase coil is 1600× 300

Fig. 9. Manufactured coils

mm. table.2 shows the values of each parameter.The coils are made by copper wire. The sectional area

of the wire is in 2.0 mm unit(average inner radius is 1.8mm, coating thickness is 0.8mm, conductor resistance is 9.91

4


Table 2. spec of coils

Phase U Phase V Phase WNumber of turns 15 15 15

size [m] 0.30×1.60 0.30×1.60 0.30×1.60

Tra

nsm

itter

Self Inductance [µH] 523.50 509.12 510.39

Capacitance [nF] 6.6791 6.8870 6.8677Q factor 258 255 244

Resistance [Ω] 1.090 1.050 1.217Number of turns 15 15 15

size [m] 0.30×1.60 0.30×1.60 0.30×1.60

Rec

eive

r

Self Inductance [µH] 513.29 512.08 514.00

Capacitance [nF] 6.8378 6.8467 6.8211Q factor 257 255 256

Resistance [Ω] 1.058 1.075 1.070

1.6m

Setted on

the base of EV

Varied in

the road

0.9 m

1.6m

Horizontal gap

Fig. 10. Coil size of equipments

Ω/km). As the core of coils, expanded polystyrene is used.Vertical gap between transmitter coil and receiver coil is set

as 200 mm considering it is supposed to gap between roadand bottom of vehicle. Considering that moving EV mis-alignes in the cross direction to movement, the x axis is setas horizontal misalignment of transmitter coil to receiver coil.The y axis is set as efficiency and rate of voltage unbalancing.

In the prior reserch of single phase WPT, it is showed thatload of the receiver effects the efficiency. In order to max-imize the efficiency, changing the receiver load by DC-DCconverter is studied(13). In this paper, the loads of three-phaseof receiver is changed to same resistance by which the effi-ciency is the highest.

Resonance frequency is 85 kHz, which is promoted to stan-dardize for dynamic charging for EV(14).

6.2 Experiment equipments Experiment equipmentis shown in Fig.11. It is consisted of resonator coil, load, astand which supports receiver coils. The 4ch signal genera-tor whose impedance is 50Ω is used as power source. Sinwaves are generated by three-phase inverter Fig.12 so thattheir phase difference is 120 degree as 10Vp−p. Power ana-lyzer and oscilloscope are used to collect data.

6.3 Simulations and experiment result Mutual in-ductances between coils are measured by LCR meter. Simu-lation has done by using each value.

The results are shown in Fig.13, Fig.14, and Fig.15. It isfound that proposed the V-minus type, is suitable for improv-ing efficiency and reducing the rate of voltage unbalancing.

Using V-minus type, magnetic flux canceling is lower, the

Fig. 11. Institution of experiment

Fig. 12. Three-phase inverter

0 0.05 0.1 0.15 0.2 0.25 0.30

20

40

60

80

100

horizontal misalignment [m]

effi

cien

cy [

%]

Unipolar[calc]Unipolar[meas]Vminus[calc]Vminus[meas]

　

Fig. 13. Simulation result of horizontal misalignmentvs efficicency

0 0.05 0.1 0.15 0.2 0.25 0.30

20

40

60

80

100

120


rate

of

volta

ge u

nbal

anci

ng [

%]

Unipolar[calc]Unipolar[meas]Vminus[calc]Vminus[meas]

　

Fig. 14. Simulation result of horizontal misalignmentvs rate of voltage unbalancing

induced voltage and the rectified voltage will be higher thanusing Unipolar type. Furthermore because difference of thephase of alternating magnetic flux is only 60 degree, disturb-ing by other phases is lowered, and voltage unbalancing oc-curs less than using Unipolar type.It is shown that proposedmethod is superior to achieve efficient and lowering of volt-age unbalancing.

5


0 0.05 0.1 0.15 0.2 0.25 0.30

1

2

3

4

5

6


rect

ifie

d vo

ltage

rat

io

Unipolar(calc)Unipolar(meas)Vminus(calc)Vminus(meas)

　

Fig. 15. Simulation result of horizontal misalignmentvs rectified voltage

When horizontal gap is bigger than 0.2 m, rate of voltageunbalancing of V-minus became higher than that of Unipolarit is because when horizontal gap is bigger, zero phase be-comes ruling of receiver voltage. Positive phase and negativephase will be similar to zero, and rate of voltage unbalancing,which is rate of positive phase and negative phase, fluctuateseasily.

7. Conclusion

In this paper, the V-minus, a new method of three-phaseWPT was proposed and its advantages were demonstrated.V-minus works more efficiently even there is horizontal gap.However, using unsymmetric shape coil, the rate of voltageunbalancing is still high. Therefore, in the further, controllingprimary and secondary parameters to increase the efficiencyand lower the rate of voltage unbalancing will be considered.

As one of the performance criteria, rectified voltage wasevalued in this study. But considering that the voltage of thesmoothing capaciter was measured in an unloaded condition.Another future works will be evaluating the system perfor-mance in the condition that the load resistance is controlledto have the maximum transfer efficiency.

References

( 1 ) S. Li, C. Mi:“Wireless Power Transfer for Electric Vehicle Applications”,JESTPE 2014-02-0205 (2014)

( 2 ) M. Kato, T. Imura, T. Uchida, Y. Hori,“Loss Reduction in Antenna for Wire-less Power Transfer by Magnetic Resonant Coupling,” in EVTeC’11 pp. 1-5(2011)

( 3 ) M. Kato, T. Imura, Y. Hori:“New characteristics analysis considering trans-mission distance and load variation in wireless power transfer via magneticresonant coupling”, Intelec 2012, 2012.10, pp.1-5 (2012)

( 4 ) A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, M.Soljacic, “Wireless Power Transfer via Strongly Coupled MagneticReso-nances”ScienceExpress, Vol.317, No.5834, pp.83-86, 7 June (2007)

( 5 ) Y. Tanikwa, M. Kato, T. Imura, Y. Hori:“Fundamental Experiment of Mag-netic Resonance Coupling Three-phase Wireless Power Transfer”, Intelec1349-1377 (2013)

( 6 ) Y. Tanikawa, M. Kato, T. Imura, and Y. Hori, ”Experiment of Magnetic Res-onant Coupling Three-phase Wireless Power Transfer,” in The 27th Interna-tional Electric Vehicle Symposium and Exhibition (2013)

( 7 ) T. Imura: “Equivalent Circuits for Repeater Antennas Used in Wirelss PowerTransfer via Magnetic Resonance Coupling”, Denki Gakkai Ronbunshi, Vol.131-D, No.12, December 2011, pp1373-1382 (2011)

( 8 ) K. MIWA,J. KANEDA, N. KIKUMA, H. HIRAYAMA, K. SAKAKIBARA ：“A Consideration of Arrayed Transmitting Coils in Wireless Power Transferwith Magnetically Coupled Resonance” IEICE WPT 2012-09 pp.1-4(2012)

( 9 ) Grant A. Cvie, John T. Boys, Michael L. G. Kissin and Howard G. Li:“AThree-Phase Inductive Power Transfer System for Roadway-Powered Vehi-cles”, IEEE Transactions On Industrial Electronics, VOL. 54, NO. 6, DE-

CEMBER (2007)(10) Grant A. Cvie, John T. Boys:“Inductive Power Transfer”, Proceedings of the

IEEE, VOL. 101, NO. 6, Junn (2013)(11) M. Hirokazu, N. Yasuhiko, I. Kouichi：“3-phase Contactless Power trasnfer

System Taking Account of Mutual Inductance” IEEE Transactions on PowerElectronics pp1039-1040 (2010)

(12) M. Hirokazu, N. Yasuhiko, I. Kouichi: “Robustness of Three-Phase Contact-less Power Transfer System for Horizontal Displacement” IEEE Transactionson Power Electronics pp1378-1379 (2010)

(13) Y. Moriwaki，T. Imura，Y. Hori: “A Study on Reduction of Refflected PowerUsing DC/DC Converter in Wireless Power Transfer System via MagneticResonant Coupling”(in Japanese),IEEJ, JIASC, Vol.2, ppII-403-II-408(2011)

(14) SAE International: “Wireless charging advances with selection of 85-kHzcharging frequency” http://articles.sae.org/12647/ (2015)

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