Three-phase Wireless Power Supply System Using Matrix Converter
Jun-ichi Itoh, Koki Yamanokuchi, Shunsuke Takuma, Keisuke Kusaka
Nagaoka University of Technology
1603-1 Kamitomioka-cho, Nagaoka city Niigata, Japan
Tel.,Fax: +81 / (258) – 47.9533.
E-Mail: koki_yamanokuchi@stn.nagaokaut.ac.jp, takuma_s@stn.nagaokaut.ac.jp,
kusaka@vos.nagaokaut.ac.jp, itoh@vos.nagaokaut.ac.jp

URL: http://itohserver01.nagaokaut.ac.jp/itohlab/index.html

Keywords«Matrix converter», «Three-phase system», «Wireless power transmission»

Abstract
This paper proposes a three-phase wireless power transfer (WPT) system with three-phase to threephase matrix converter to integrate the transmission coils with the power converter on the transmission
side suitable for high temperature operation. The proposed system expands a lifetime of the WPT system
due to eliminates a electrolytic capacitor. Furthermore, the space installed the WPT system is saved. A
novel hybrid commutation method, which is suitable for the WPT system with a resonant characteristic,is employed to avoid the commutation failure of the matrix converter. The strategy of the proposed
hybrid commutation is based on an estimation of the current direction considering to the resonant
characteristic and the elimination of the commutation in the critical area. The proposed commutation
method achieves AC input-current THD of 4.7% with the resonant three-phase load without any current
sensor on the high-frequency side. Furthermore, the proposed WPT system achieves a maximum systemefficiency of 88.2% under condition of 400-V AC input 400-V DC output and 4-kW output power.

Introduction
In recent years, wireless power transfer (WPT) systems using resonance compensation methods forbattery chargers in applications of electric vehicles (EVs) are actively studied [1]-[3]. In order to expand
a driving ranges of EVs, a onboard battery is expected to increase, leading to the increase in the charging
power of the WPT systems. However, the increase of the output power causes an increase of copper loss
on the transmission coil and magnetic leakage flux. A three-phase WPT system using 12 coils has been
proposed as a solution to the above problems. In [4], the effective current per winding is reduced relative
to single phase by using high-frequency three phases, leading to the reduction of the copper loss. More
important, it is possible to suppress the leakage magnetic field by arranging the coils opposite to eachother in this method. However, the heat generated in the transmission coil decreases the life of smoothelectrolytic capacitors. Thus, it is necessary to install the transmission coil and the power converter
separately, leading to a problem of a size increase of the system.
On the other hand, a matrix converter is known as a power converter that directly converts AC into
AC of required amplitude and frequency [5]-[6]. Since the matrix converter does not require a smoothelectrolytic capacitor, it is more suitable for driving at high temperatures than a system using a rectifier.
Thus, the circuit arrangement where the power converter is integrated into the transmission coil ispossible. Nevertheless, there are several issues that the matrix converter is applied to the high-frequency
power supply such as commutation. As conventional commutation methods for the matrix converter, acurrent commutation or a voltage commutation are generally applied used. However, it is necessary todetect the direction of the output current to determine the commutation sequence and the compensation
for commutation errors [7]. In applications such as WPT where the output side is high-frequency suchas 20kHz or 85kHz, it is difficult to detect the current direction without time delay.

This paper proposes a commutation method for the matrix converter applied in the high frequency
three-phase WPT system. The proposed method estimates the output current direction using thecharacteristic that the output power factor of the matrix converter with the resonant load isapproximately unity when the matrix converter operates near the resonant frequency. As experimental
results, it is confirmed that the proposed WPT system is directly converted from low-frequency AC tohigh-frequency AC without any commutation failures. It is also confirmed that the system efficiency of
up to 88.2% is achieved under the condition of 400-V AC input and 400-V DC output.

Proposed three-phase WPT system with matrix converter
Fig. 1 shows the three-phase WPT system using a matrix converter. The proposed three-phase WPTsystem consist of the three-phase matrix converter, the wireless transmission part, the three-phaserectifier and the snubber circuit. The three-phase matrix converter is operated at around 20 kHz. The
wireless transmission coils uses the three-phase WPT system with 12 solenoid coils proposed in [4].
Note that the snubber circuit that is connected with the input and output of the matrix converter
suppresses the overvoltage caused by the open-circuit.
Fig. 2 shows the arrangement and coupling of transmission coils in a three-phase WPT system. The
copper loss is reduced by using a three-phase 12-coil WPT system, since the current flow per winding
is reduced compared to a single-phase WPT system. Furthermore, the leakage magnetic field is canceledby arranging two solenoid coils differentially coupled magnetically. Furthermore, the mutual inductance
Ma, Mb, Mc where is unnecessary because it does not contribute to power transmission is cancelled bytransmission coils arranged 120 degrees away from the other phase. Hence, the three-phase PWT systemwith 12 solenoid coils is more suitable for high power WPT.
In this paper, the S / S method where the resonant capacitors are inserted in series respectively in the
primary side and the secondary side of the WPT coil is used. The resonant capacitors and the selfinductance of each coil are designed to resonate at the transmission frequency. Consequently, the power
factor seen from the power supply is improved, and the copper loss generated in the transmission coiland the conduction loss of the power converter are reduced. In this paper, the transmission frequency of
Vsnubber

vr

R

ir

U1

Sru
Ssu
Stu

Cf

V1

Srv
Ssv
Stv

S

Srw
Ssw
Stw

T Lf

Cu1 iu1
vuv1
Cv1

W1

iu2 Cu2 U2

Lu1A

Lu2A

Lu1B

Lu2B

Lv1A
Lv1B

Lw1B
Lw1A

Lv2B

Lw2A
Lw2B

Iload

vuv2
V2

VDC

Lv2A
Cv2

Cw2W2

Cw1

Fig. 1. Three-phase wireless power transfer installed matrix converter.
iw1 w
iw2
w2
1
Lv1B
Lw1A

Ma1

iu1

Lu1B
Mc1
Lv1A

Lw2A

Mb1

u1

Ma2

iu2

Lu2B
Mc2

Lu1A

Lv2A

Lw1B

iv1

Lv2B

v1

Mb2

u2

Lu2A
Lw2B

iv2

v2

Fig. 2. Connection and placement of transmission coils in Fig. 1.

Rthe WPT system is set to 20 kHz with the consideration of the high power capacity of the system power.
The proposed commutation method suppresses the commutation failure by using the resonancecharacteristic which the output power factor of the matrix converter is approximately unity when thetransmission frequency equals the resonance frequency.

Virtual AC / DC / AC conversion method
In this paper, a virtual AC / DC / AC conversion method is used to control the matrix converter [8].
Fig. 3 shows the circuit configuration of the matrix converter. The output voltage are shown in (1) using
the input voltages of the matrix converter.
 vu   S ru   vv    S rv
v w   S rw

S su
S sv
S sw

S tu  vr  
S tv   v s 
S tw   vt (1)where Smn is the switching function in the matrix converter (m:r,s,t, n:u,v,w). Smn = 1 when Smn is turned
on, and Smn = 1 when Smn is turned off.
Fig. 4 shows the circuit configuration of the indirect matrix converter. The indirect matrix converter
is consisted of a rectifier and an inverter. The input / output relationship is the same as the input / output
relationship of the matrix converter. The switching function of the matrix converter is determined by
combining the switching function of the rectifier and the inverter shown in the right side of (2).
 S ru S rv S rw

S su
S sv
S sw

S tu   S up 
S tv    S vp
S tw   S wp

S un 
  S rp
S vn  
S rn
S wn  

S sp
S sn

S tp 

S tn 

(2)where Sij is the switching function in the rectifier and the inverter (i:r,s,t,u,v,w, j:p,n). Sij = 1 when Sij isturned on, and Sij = 1 when Sij is turned off. Thus, the control is considered separately as a virtual current
source rectifier and a virtual voltage source inverter. The virtual current source rectifier is operated witha space vector modulation [9]. Meanwhile, the virtual inverter is operated with a single pulse operation
for reducing the number of switching [10]. The generated switching pulses for the PWM rectifier andthe inverter are combined for the control of the matrix converter. Note that the zero-vector of the current
Sru
Ssu

U

Srv
Ssv

V

Stv

Load

Input filter

Stu

R
S
T

Srw
Ssw

W

Stw

Fig. 3. Matrix converterRST
Srn Ssn Stn Sun Svn Swn
Fig. 4. Indirect matrix converter

U
V
W

Load

Input filter

Srp Ssp Stp Sup Svp Swpsource rectifier and the timing of the vector change of the voltage source inverter are synchronized for
reducing the number of switching.
Fig. 5 shows the vector diagram and switching patterns for the virtual rectifier. The input current
command is expressed with zero vectors I7, I8, and I9 and nearest two input current vectors from the
input current command vector. Note that three-zero vectors are selected so that the maximum phase of
the input phase voltage absolute value keeps the ON state for reducing the number of switching times.
Moreover, the zero-vectors are divided and placed at the bottom and peak of the carrier. The input
current command duty d1, d2 and d0 are shown in (3) using the input current command.
 I    I 1  
 I     I 1 1   1

I 2
I 2
1

I 0   d 1  
I 0  d 2 
1   d 0 

(3)where I and I are the  axis components of the input current command vector, Iab is the  axis
components of the each input current vector (a:,, b:0,1,2). d1 and d2 are shown in (4) by applying
Kramer's formula shown by (3).
I 1 I 0
I
I
d 

0

2

I 0

I 2

I 1

I 2

I 1

I 2

, d 

I 1

I 0

I 1

I 2

I 1

I 2

(4)

The sum of the input current command duty is 1, as shown in (3). Therefore, the duty of zero-vector d0
is shown in (5) using the d1 and d2 represented by (4).
(5)
d 0  1  d1  d 2
Fig. 6 shows the vector diagram and switching patterns for the voltage source inverter. The voltage
source inverter is driven with a single pulse operation. In the single pulse operation, an adjacent output
voltage vector from the voltage command is used for reducing the switching loss. Using the single pulse
operation, the number of switching is reduced in comparison with the PWM. On the other hand, thesingle pulse operation has many low order harmonic components. However, the input impedance is highI 010I2 001010
100 I3

iin*

I7
001
100 I4

I1 100
001
I

I8 I9

100
I6 010

001
010
100
010
001
I7 =
I =
I =
100 8
010 9
001
I5

 S rp S sp S tp I 1   S rn S sn S tn 
1 0 0 
0 0 1 ON OFF OFF   OFF OFF ON 

Fig. 5. Space vector for virtual current source PWM rectifier.
010
V
101 3
011
V
100 4

v
V2

110
001

vout*

100
V1
011
v

Sector001
V5110

V6 101010

S vp S wp SV1   upS un S vn S wn 
1 0 0 
0 1 1 ON OFF OFF 

 
ON 
 OFF ON

Fig. 6. Space vector for voltage source inverter.

except at the resonant frequency in the WPT system. Therefore, the low output current distortion rate(THD) is maintained even if single pulse operation is used for the voltage source inverter.
In this control method, the voltage commutation failure region is separated from the current
commutation failure region by setting the control frequency to an integral multiple of three with respect
to the resonance frequency. The commutation method will be described from the next section.

Conventional commutation method
The matrix converter has problems such as reliability decline, power loss increase and noise increase
due to the commutation failures such as the short-circuit of the voltage source and the open-circuit of
the current source. For this reason, the matrix converter requires the commutation sequence at theswitching timing of the power devises to prevent a commutation failure. There are two commutation
methods: the voltage commutation and the current commutation [11]-[12]. The voltage commutation
determines the commutation sequence based on the information of the detected input voltage. In thevoltage commutation, the input voltage may be shorted when the voltage crosses each other owing to
the voltage detection delay or the voltage detection error. There is a risk of power device destruction by
the current of the short-circuit, but the protection of the power devices against the short-circuit is very
difficult. Furthermore, the input current is distorted because the commutation failure of the voltage
commutation and the commutation error for the commutation timing. The commutation error
compensation using the output current direction detection is required in order to the input current
distortion by the commutation error is suppressed. On the other hands, the current commutation method
determines the commutation sequence based on the output current direction. In the current commutation,
the current source side may be opened at the output side when the current direction detection has anerror owing to the detection delay or the current detection error, leading to surge voltage. However, it isdifficult to detect the current direction without delay in applications where the output of matrix converter
such as WPT system is high-frequency over 10 kHz. In other words, the commutation method that
requires the conventional output current direction detection is not suitable for the WPT system. Thus, a
new commutation method is proposed to estimate the output current using the resonance characteristics.
Fig. 7 shows the input and output waveforms of the matrix converter when only the four-step voltage
commutation is applied. The right side in Fig. 7 is enlarged waveforms in the red square on the left side.
In Fig. 7, the commutation failure of the voltage commutation occurs near the changing of the input
voltage magnitude relationship, and the input current is distorted. In order to reduce the commutation
failure, the hybrid commutation has been proposed. The matrix converter commutates with both thevoltage commutation and the current commutation. In particular, around the output current zero-crossing,the voltage commutation is used because the current commutation has high possibility to have acommutation failure. On the other hand, the current commutation is used around the input-voltage
2000Input voltage [V]

vs

-200
10
0

vt

vr

Input current [A]

is

-10
400
200
0
-200
-400

it

ir

Output voltage [V]Output current [A]

10
0
-10

200

Input voltage [V]

vr
vs
vt

0
-200
10

Input current [A]

ir
is
it

0
-10
400
200
0
-200
-400

Output voltage [V]

vwu
vuv
vvw

Output current [A]

10
0
-10
20ms

2ms

Fig. 7. Simulation of voltage commutation.

iw
iu
iv

crossing. However, the problems of the voltage commutation and the current commutation does not be
solved due to the output current direction detection is necessary also in the hybrid commutation. For thisreason, it is difficult to use the conventional hybrid commutation for the WPT systems with the matrix
converter.

Proposed commutation method
In this proposed control method, the current commutation failure region and the voltage commutation
failure region are completely separated when the output power factor of the matrix converter is one.
Therefore, four-step voltage commutation independent of the output current information and four-stepvoltage commutation independent of the input voltage information are suitable. For this reason, theproposed hybrid commutation is four-step commutation the resonance characteristics of WPT using theresonant capacitor.
Fig. 8 shows a U-phase switching pattern and a voltage commutation period TV when the input
voltage magnitude relationship switches from R-phase to S-phase. TV is expressed by (6),cos 1 PFout 
2f R



dz
4 fc

 TV 

1
 3Td
12 f R(6)

where PFout is the output power factor of the matrix converter, fR is the resonant frequency of thetransmission coil, fc is the carrier frequency, dz is the zero voltage period in one carrier period, and Td isthe commutation step time. Note that the input voltage ripple is considered to be negligibly small. Whenthe resonant frequency and the output frequency of the matrix converter are equal, the output power
factor of the matrix converter is approximately unity, and the output voltage command and the output
current are in phase. Thus, the output current direction is estimated from the output voltage command.
In consideration of this characteristic, the proposed commutation method uses voltage commutation in
the area where current zero crossing is expected. On the other hand, current commutation is used for thecommutation patterns where the commutation failure of the voltage commutation occurs. For example,
the voltage commutation is used for phase-U in the period of ±TV when the output voltage command ischanging from sector five to six as shown in Fig. 8.
First, the conditions of the left side of (6) is explained in detail. The commutation failure issuppressed without the current sensor on the output side by applying the voltage commutation to a periodof ± TV where the current zero crossing is expected. However, if there is a positional deviation of the
Sector

1

2

3

4

5

6

1
Carrier 0.5
0
Sru
Ssu
Stu

iu

iv

Commutation 1 (V)methodU，V，W 0 (C)
dz
4fc

1
12fR

iw

TV
Voltage commutation
failure pattern

All phase current
commutation period

Fig. 8. Suppression of commutation failure when input voltage phase changes from R to S.

WPT coil, the resonant frequency changes. This may reduce the output power factor of the matrix
converter. Thus, TV needs to be larger than the possible maximum output phase shift between the output
voltage command and the output current.
Next, the conditions of the right side of (6) is explained. The matrix converter controls the input
current so that the input power factor is one. Thus, when the zero voltage period is divided into carrier
peak and bottom, a commutation failure pattern of the voltage commutation occurs at the center of thecarrier as shown in Fig. 8. Thus, the commutation failure of the voltage commutation is suppressed bymaking all phase current commutation near the center of the carrier taking into consideration of thecommutation time.
Fig. 9 shows the input and output waveforms of the matrix converter when the proposed commutation
is applied. The right side in Fig. 9 is enlarged waveforms in the red square on the left side. The
commutation failure due to the voltage commutation (Fig. 7) is suppressed. Furthermore, since no surge
occurs at the output current zero crossing, it is confirmed that the commutation failure because thecurrent commutation is suppressed.

Experimental result
Table I shows the experimental parameters of the WPT system. The proposed WPT system with thematrix converter, which employs the proposed commutation method, is tested in the circuit
200
0
-200
10
0

Input voltage [V]

vs

vt

vr

Input current [A]

is

-10
400
200
0
-200
-400

it

ir

Output voltage [V]Output current [A]

10
0
-10

200

Input voltage [V]

vr
vs
vt

0
-200
10

Input current [A]

ir
is
it

0
-10
400
200
0
-200
-400

Output voltage [V]

vwu
vuv
vvw

Output current [A]

10
0
-10
20ms

2ms

Fig. 9. Simulation waveforms of proposed commutation.

Table I: Experimental parameters.
Item
Grid line voltage
Resonant frequency
Carrier frequency
Load Voltage
Rated power
Filter inductance
Filter capacitancePrimary inductance
Secondary inductancePrimary capacitance
Secondary capacitance
Diodes
SiC-MOSFETs

SymbolValue
Vrs,Vst,Vtr
400 V
fR
19.8 kHzfc
59.4 kHz
VDC
400 V
P
5.4 kWLf
2.2 mHCf
4.4 mF
212 mH
Lx1y
212 mH
Lx2y
152 nFCx1
152 nF
Cx2
VS-20ETF06-M3
BSM00003A

iw
iu
iv

configuration shown in Fig. 1. Here, x are u, v, w and y are A and B, respectively, which are constants
shown in Fig. 2.
Fig. 10 (a) shows the input and output waveforms of the matrix converter, whereas Fig. 10 (b) showsthe enlarged waveform near the center of Fig. 10 (a). Under this condition, an input current THD of
4.7% is achieved, satisfying the grid constraints. Furthermore, as compared with Fig. 8, since the input
current distortion is suppressed even if the magnitude relationship of the input voltage is changed, it isconfirmed that the commutation failure of the voltage commutation is suppressed. As shown in Fig. 10(a) and (b), since no surge occurs in the output voltage of the matrix converter during the period of theoutput current zero crossing (b), the suppression of the commutation failure of the current commutationis also confirmed. Note that several the input current distortions occur at intervals other than when the0

500 V/div

Grid voltage Vr

0

10 A/div

Grid current Ir
Matrix converter output voltage

Vuv1

500 V/div

Matrix converter output current

Iu1

10 A/div00

4 ms/div(a) Waveforms of matrix converter with TV = 1.6 µs
00Grid voltage Vr

500 V/div

Grid current Ir

10 A/div0
Matrix converter output voltage

Vuv1

500 V/div

Matrix converter output current

Iu1

10 A/div

0

20 ms/div(b) Enlarged waveforms near the center in Fig. 9 (a)0Rectifier input voltage Vuv2

500 V/div

Rectifier input current Iu2

10 A/div

Load voltage VDC

250 V/div

Load current Iload

5 A/div

000

20 ms/div(c) Waveforms of rectifier on secondary side
Fig. 10. Operation waveforms of WPT system with proposed commutation method.

input voltage magnitude relationship alters compared with the simulation waveform of Fig. 9. These
distortions are caused by the difference between the command pulse and the actual pulse due to the delayof the controller and the turn-on/turn-off characteristics of the switching devices. Fig. 10 (c) shows the
waveform on the secondary side of the WPT system. Since both VDC and Iload are positive, it indicatesthat the power is being transmitted to the receiving side in the WPT system.
Fig. 11 shows the efficiency of the WPT system with the matrix converter at the input voltages of
400 V. It is confirmed from Fig. 11 that the maximum system efficiency of 88.2%, i.e. the efficiency
from the input of three-phase AC to the DC load and the matrix converter efficiency 95.0%, i.e. theefficiency between the input and output of the matrix converter are achieved. This system efficiency
satisfies the standardization of ISO [13], where the system efficiency of 85.0% or more is required.

Conclusion
In this paper, the control method of the three-phase WPT system using the matrix converter and thetransmission coil figuration were proposed to realize the high power WPT system suitable for hightemperature operation. In the proposed method, the output current was estimated from the output voltage
command using the impedance characteristics of the WPT system, and the voltage commutation wasapplied around the output current zero crossing. As the experimental results, it was confirmed that thethree-phase WPT was driven by the matrix converter with the proposed commutation method without
any current sensor on the high-frequency side. In addition, the system efficiency of 88.2%, i.e. theefficiency from the input of three-phase AC to the DC load, was achieved under condition of 400-V AC
input. 400-V DC output and 4-kW output power.

References[1] N. Xuan Bac, D. M. Vilathgamuwa and U. K. Madawala, "A SiC-Based Matrix Converter Topology for
Inductive Power Transfer System," in IEEE Transactions on Power Electronics, vol. 29, no. 8, pp. 4029-4038,
2014.
[2] G. Lovison, D. Kobayashi, M. Sato, T. Imura, and Y. Hori, "Secondary-side-only Control for High Efficiency
and Desired Power with Two Converters in Wireless Power Transfer Systems," IEEJ Journal of Industry
Applications, vol. 6, no. 6, pp. 473-481, 2017.
[3] H. Ishida, T. Kyoden, and H. Furukawa, "Effectiveness of Convolutional Perfectly Matched Layer in Timedomain Numerical Analysis of Low-frequency Wireless Power Transfer," IEEJ Journal of Industry Applications,vol. 8, no. 1, pp. 131-139, 2019.

100
90

Efficiency  [%]

80
70
60
50

Rectifier Efficiency

40

Transmission coils
Efficiency
Matrix converter
Efficiency

30
20
10
0

System efficiency
0.5

1

1.5

2

2.5

3

3.5

Output power P [kW]Fig. 11. Efficiency of WPT system.

44.5

[4] K. Kusaka, K. Furukawa and J. Itoh, "Radiative Noise Reduction Technique Using 12 Coils Suitable for HighPower Inductive Power Transfer," 2018 IEEE Energy Conversion Congress and Exposition (ECCE), pp. 61796186, 2018.
[5] Y. Hayashi, H. Motoyama and T. Takeshita, "Wireless Power Transfer System Using Three-phase to Singlephase Matrix Converter," 2018 International Power Electronics Conference (IPEC-Niigata 2018 -ECCE Asia), pp.
356-362, 2018.
[6] J. Afsharian, D. Xu, B. Wu, B. Gong and Z. Yang, "The Optimal PWM Modulation and Commutation Scheme
for a Three-Phase Isolated Buck Matrix-Type Rectifier," in IEEE Transactions on Power Electronics, vol. 33, no.
1, pp. 110-124, 2018.
[7] K. Kato and J. Itoh, "Improvement of Input Current Waveforms for a Matrix Converter Using a Novel HybridCommutation Method," 2007 Power Conversion Conference - Nagoya, pp. 763-768, 2007.
[8] J. Itoh, T. Mura and H. Takahashi, "Investigation of switching loss reduction for the matrix converter based on
virtual AC/DC/AC conversion using space vector modulation," 2012 IEEE 13th Workshop on Control andModeling for Power Electronics (COMPEL), pp. 1-6, 2012.
[9] J. W. Kolar, M. Baumann, F. Schafmeister and H. Ertl, "Novel three-phase AC-DC-AC sparse matrix
converter," APEC. Seventeenth Annual IEEE Applied Power Electronics Conference and Exposition, vol.2, pp.
777-791, 2002.
[10] J. Itoh and T. Masuda, "Loss reduction for matrix converter with hybrid six step operation in flywheel energy
storage system," 2017 IEEE 12th International Conference on Power Electronics and Drive Systems (PEDS), pp.
709-714, 2017.
[11] J. Mahlein, J. Igney, J. Weigold, M. Braun and O. Simon, "Matrix converter commutation strategies with andwithout explicit input voltage sign measurement," in IEEE Transactions on Industrial Electronics, vol. 49, no. 2,
pp. 407-414, 2002.
[12] P. Nielsen, F. Blaabjerg and J. K. Pedersen, "Novel solutions for protection of matrix converter to three phaseinduction machine," IAS '97. Conference Record of the 1997 IEEE Industry Applications Conference ThirtySecond IAS Annual Meeting, vol.2, pp. 1447-1454, 1997.
[13] ISO, "Electrically propelled road vehicles -- Magnetic field wireless power transfer -- Safety andinteroperability requirements, " ISO/PAS 19363, 2017