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Analysis and Experiment on Harmonic CurrentDistortion in Wireless Power Transfer System

Using a Diode Rectifier

Katsuhiro Hata, Takehiro Imura, and Yoichi HoriThe University of Tokyo,

515, Kashiwanoha, Kashiwa, Chiba, 2778561, JapanPhone: +81-4-7136-3881, Fax: 81-4-7136-3881

Email: hata@hflab.k.u-tokyo.ac.jp, imura@hori.k.u-toyko.ac.jp, hori@k.u-tokyo.ac.jp

AbstractWireless power transfer (WPT) via magnetic reso-nance coupling provides highly efficient mid-range transmission.Its transmitting power can be controlled using a diode rectifierand a DC-DC converter on the secondary side. Previous researchreplaces the load and the rectifier circuit with an equivalentload resistance or a fundamental harmonic sine wave voltagesource to analyze the charging power of WPT. In such a casehowever, the effect caused by the rectifier circuit becomes unclearbecause the harmonic components are neglected. As a result,the theoretical charging power and its true value have an errordue to the harmonic current distortion. In this paper, a novelWPT circuit model is proposed for the analysis of the harmoniccurrent distortion on the secondary side. The proposed modeluses the secondary voltage as the input variable of transferfunctions and makes clear the effect caused by the rectifier circuit.Experiments demonstrate that the harmonic current distortion isincreased with the increase in the secondary voltage. These resultsaccord with the analysis using the proposed model and verify theeffectiveness of the proposed model.

KeywordsWireless power transfer, Magnetic resonance cou-pling, Diode rectifier, Harmonic current distortion.

I. INTRODUCTION

Electric vehicles (EVs) have environmental advantages andthe capacity for advanced motion control due to the fastresponse time of their electric motors [1]. However, EVs needto be charged frequently due to their limited mileage percharge. Charging operations should be simplified to reduce theburden on the user.

Wireless power transfer (WPT) can mitigate complicatedcharging operations and apply dynamic charging to EVs in mo-tion [2], [3]. WPT via magnetic resonance coupling provideshighly efficient mid-range transmission and it has robustness tomisalignment between a transmitter and a receiver [4], [5]. Itstransmitting efficiency and its charging power are determinednot only by the parameters of the transmitter and the receiverbut also by the load [6]. The load condition can be controlledusing a diode rectifier and a DC-DC converter on the secondaryside [7], [8]. As a result, the transmitting efficiency can bemaximized [9], [10] or the charging power can be controlledon the secondary side [11][13].

Many papers on the modeling of the WPT circuit use anequivalent load resistance, which includes the load and therectifier circuit [14][16]. A previous study [17] has proposed

RL

V1

Power source Load

V2

I1

I2

C1

C2

R2

L2

R1

L1

Lm

Transmitter and Receiver

(a) Equivalent circuit of magnetic resonant coupling.

RLV1

Power source Load

V2

I1

I2

C1

C2R

2R1 L1-Lm

Lm

Transmitter and receiver

L2-L

m

(b) Ttype equivalent circuit.

Fig. 1. Equivalent circuit of the wireless power transfer system.

a fundamental mode equivalent circuit, which replaces theload and the rectifier circuit with a fundamental harmonicsine wave voltage source. Furthermore, the WPT circuit modelconsidering the discontinuous mode of the diode rectifierhas been represented [18], [19]. However, the actual load isreplaced by an equivalent load resistance or a fundamentalharmonic sine wave voltage source. As a result, the effectscaused by the diode rectifier cannot be made clear because theharmonic components are neglected. This causes an error inthe theoretical charging power of WPT.

This paper proposes a novel WPT circuit model, whichis expressed by multi-input, multi-output (MIMO) transferfunctions using the secondary voltage as the input variable.The proposed model can analyze the harmonic current dis-tortion caused by the rectifier circuit because the load is notapproximated by any elements. Experiments show that thecharging power control on the secondary side using the dioderectifier has the potential for causing the harmonic currentdistortion. This result is analyzed using the proposed modeland the effectiveness of the proposed model is verified.

0

0.5

1

1.5

2

2.5

0

0.2

0.4

0.6

0.8

1

1 10 100 1000 10000 100000

Ch

agin

g p

ow

erP

[kW

]

Tra

nsm

itti

ng e

ffic

ien

cy

Load resistance RL []

P

Fig. 2. Load resistance vs. transmitting efficiency and charging power.

II. WIRELESS POWER TRANSFER VIA MAGNETICRESONANCE COUPLING

A. Characteristics at resonance frequency

A series-series circuit topology is used for the wirelesspower transfer circuit and its equivalent circuit is shown inFig. 1 [20]. The transmitter and the receiver are characterizedby the inductances L1, L2, the series-resonance capacitors C1,C2, and the internal resistances R1, R2, respectively. Lm is themutual inductance between the transmitter and the receiver.V1 is the RMS voltage of a power source and its angularfrequency is expressed as 0. The transmitter and the receiverare designed to satisfy the following equation.

0 =1L1C1

=1L2C2

(1)

When the load resistance is RL, the voltage ratio AVand the current ratio AI between the secondary-side and theprimary-side are expressed as follows:

AV =V2V1

= j0LmRL

R1R2 +R1RL + (0Lm)2(2)

AI =I2I1

= j0Lm

R2 +RL(3)

where V2, I1, and I2 are the RMS values of the secondaryvoltage, the primary current, and the secondary current, re-spectively. Then, the transmitting efficiency is expressed asfollows:

=(0Lm)

2RL(R2 +RL){R1R2 +R1RL + (0Lm)2}

(4)

and the charging power P is described as follows:

P =(0Lm)

2RL

{R1R2 +R1RL + (0Lm)2}2V1

2. (5)

Fig. 2 shows the load resistance RL versus the transmittingefficiency and the charging power P . The parameters of thetransmitter and the receiver, which are used in this work, aregiven in TABLE I. The amplitude of V1 is equal to 100 V. is maximized if RL is given as follows:

RLmax =

R2

{(0Lm)2

R1+R2

}. (6)

0

0.5

1

1.5

2

2.5

0

0.2

0.4

0.6

0.8

1

1 10 100 1000 10000

Ch

argin

g p

ow

er P

[kW

]

Tra

nsm

itti

ng e

ffic

ien

cy

Secondary voltage V2 [V]

P

Fig. 3. Secondary voltage vs. transmitting efficiency and charging power.

TABLE I. PARAMETERS OF TRANSMITTER AND RECEIVER.

Primary side Secondary side

Resistance R1, R2 1.14 1.19 Inductance L1, L2 637.9 H 638.4 HCapacitance C1, C2 4002 pF 3996 pFResonant frequency f1, f2 99.6 kHz 99.6 kHz

Mutual inductance Lm 81.5 H (gap: 200 mm)

Outer diameter 448 mm

Number of turns 56 turns

P is maximized if RL is expressed as follows:

RLPmax =(0Lm)

2

R1+R2. (7)

B. Charging power control on the secondary side

The load resistance RL is determined by the amplitudeof the secondary voltage V2, which can be controlled by theDC-DC converter on the secondary side. Fig. 3 shows thesecondary voltage V2 versus the transmitting efficiency andthe charging power P . If the maximum efficiency is achieved,V2 satisfies the following equation [9].

V2max =

R2R1

0LmR1R2 + (0Lm)2 +

R1R2

V1 (8)

Charging power control can be achieved by secondaryvoltage control [12], [13]. However, it is effective only if V2is controlled below the maximum secondary voltage V2max,which is expressed as follows:

V2max =0LmR1

V1. (9)

Then, the equivalent load resistance RL goes to infinity andthe voltage ratio AV becomes saturated [6]. The maximumpower is obtained when V2 is given as follows:

V2Pmax =0Lm2R1

V1 =V2max

2. (10)

For efficient transmission, it is important to define theoperating range of V2 to be below V2Pmax. As a result, the

Receiver

Transmitter

DC-DC

converter

Rectifier

M

Battery

Power source

Motor drive

Electric vehicle

Ground facility

Fig. 4. System configuration of wireless charging for electric vehicle.

Idc

Vdc C

L r

E

IL

LmC1 C2R2

L2

R1

L1V1

Power source Transmitter and receiver Rectifier DC-DC converter Battery

V2

I1 I2

VS

P

d

Fig. 5. Circuit diagram of the wireless charging system.

reference voltage V2, which obtains the desired power P , isgiven as follows [13]:

V2 =

(0LmV12R1

)(

0LmV12R1

)2 {R1R2 + (0Lm)

2}P R1

. (11)

C. Effect of the diode rectifier

Fig. 4 shows a system configuration of wireless chargingfor an EV. Assuming that the voltage control of the DC-DCconverter is designed properly, the charging power controlcan be achieved. The circuit diagram of the wireless chargingsystem is shown in Fig. 5. In this paper, the motor drive systemis neglected as this is a fundamental study.

The secondary voltage is generated by the diode rectifier.If the absolute value of the secondary voltage exceeds theamplitude of the DC link voltage Vdc, the rectifier is conductedand the absolute value of the secondary voltage becomes thesame amplitude as Vdc, where the forward voltage of the diodeis ignored. Furthermore, if the amplitude of Vdc is much low

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