Wireless Power Transfer systemwith Flying Capacitor Converter
for Current Harmonics Reduction
Rintaro Kusui
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Japankusui@stn.nagaokaut.ac.jp

Keisuke Kusaka
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Japan
kusaka@vos.nagaokaut.ac.jp

Abstract— A wireless power transmission system using aflying capacitor converter (FCC) as a primary power source has
been proposed to reduce current harmonics that cause loworder harmonic radiation noise. However, the diode rectifier on
the secondary side applies a square wave voltage to thesecondary transmit coil. Current harmonics are not sufficiently
reduced due to the harmonic content of the square wave. This
paper proposes a WPT system with FCC on both the primaryand secondary sides in order to reduce voltage harmonics
applied to both sides of the transmission coil. The proposedsystem reduces the odd-order harmonics of the primary andsecondary currents by more than 25 dB compared to theconventional system, as confirmed by simulations. In particular,
the 3rd harmonic is reduced by 37.2 dB, and the 5th harmonicis reduced by 35.1 dB.
Keywords—Wireless power transfer system, Flying-capacitor
converter, Current harmonics, Radiation noise

I. INTRODUCTION
Electric vehicles (EVs) are becoming more widespread toachieve carbon neutrality. EVs require frequent recharging
because the energy density of batteries is lower than that ofgasoline for conventional vehicles. Currently, wired chargers
are used to charge EVs. However, charging with a wired
charger requires complicated cable operations and carries therisk of electric shock or short-circuiting due to water intrusion
into the metal contacts, and so on. As a result, wireless powertransfer (WPT) systems are being actively studied to enableeasy and safe charging of EVs[1-3]. Although WPT systems
transmit power via weak magnetic coupling, the transmission
coils generate radiated emissions. Radiated emissions cancause electronic equipment malfunction and interference withwireless communications, and so on. For this reason, the WPTsystem must comply with the regulations established by eachcountry based on the guidelines of the Comité International
Spécial des Perturbations Radioélectriques (CISPR) and theInternational Commission on Non-Ionizing Radiation
Protection (ICNIRP)[4-5]. Reference levels for radiatedemissions for the WPT systems are specified in CSIPR11. In
particular, it is planned to reduce the reference levels byapproximately 30 dB in the range from 150 kHz to 30 MHz,corresponding to the low-order harmonic component of thetransmission frequency[6]. Accordingly, reduction methods
for the radiated emissions are required in WPT systems,
especially their lower harmonics.

Jun-ichi Itoh
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp

The leakage magnetic field of the WPT system is emitted
from the transmission coil. Many conventional WPT systems
have H-bridge power converters on the primary side and dioderectifiers on the secondary side[7]. The H-bridge inverter andthe diode rectifier output a square wave voltage with theamplitude of the DC voltage. The square-wave voltage haslarge low-order harmonics. As a result, currents with large
low-order harmonics flow through the transmission coils in
conventional WPT systems. These current harmonics are themain cause of the large low-order leakage field harmonics
from the WPT system.
Passive, active, and resonant shielding have been proposed
to reduce leakage magnetic fields using additional
windings[8-10]. These techniques add winding around themain winding. In passive shielding, the current flows in the
direction to counteract the leakage flux that interlinks the
additional short winding[8]. In active shielding, an additional
power supply is connected to the additional windings to carrycurrent that can cancel out the leakage magnetic field more
effectively[9]. In resonant shielding, a resonant capacitor isadded to the short winding to improve the shielding effect byreducing the impedance at the frequency being canceled[10].
However, the main purpose of these methods is to cancel out
the fundamental component. In other words, they are
ineffective enough to reduce the harmonic component ofradiation noise.
A WPT system with a flying capacitor converter (FCC)
connected only on the primary side has been proposed toreduce current harmonics in the transmission coil[11]. The
FCC outputs a stepwise sinusoidal voltage to the series circuitof the transmission coil and the resonant capacitor. The output
voltage of the FCC has very few voltage harmonics comparedto the square wave voltage. For this reason, the current
harmonics in the coil are reduced. However, this system has aconventional diode rectifier connected on the secondary side.
The diode rectifier outputs a square wave voltage with many
low-order harmonics. Thus, the current harmonics caused by
the square-wave voltage applied to the transmission coil on
the secondary side cannot be sufficiently reduced.
This paper proposes a WPT system that has FCCs not only
on the primary side but also on the secondary side. The FCC
on the secondary side also outputs a multi-level voltage withfewer low-order voltage harmonics than the square-wave
voltage. The new contribution of this paper is to propose the
WPT system with very few low-order harmonics oftransmission coils. The current harm onics on the primary andsecondary sides are significantly reduced by applying themulti-level voltage to the transmission coils. In other words,
the proposed system can reduce the radiated emission
harmonics than the conventional system. First, a current
analysis using an equivalent circuit shows the cause of current
harmonics in the WPT system. Then, the configuration of the
proposed system and the switching pattern to keep the flying
capacitor voltage balance are shown. Finally, the operation of
the proposed system is demonstrated by simulation. In
addition, the harmonic analysis shows that the proposed
method reduces the current harmonics that cause radiatedemission harmonics.

A. Current harmonics in the WPT system
Figure 1 shows the configuration of a conventional WPTsystem. Most conventional WPT systems have a two-levelfull-bridge inverter on the primary side and a diode rectifieron the secondary side, as shown in Fig. 1(a). As a result, asquare-wave voltage is applied to the compensation circuitand the transmission coil on the primary and secondary sides,
respectively. For this reason, a current with many low-orderharmonics flows in the transmission coils on both the primaryand secondary sides according to the resonance characteristicsof the transmission coils and the compensation circuit.
Ref.[11] has proposed a WPT system with an FCC and an
unfolder on the primary side instead of a full-bridge inverteras the primary side power supply, as shown in Fig. 1(b). In
this system, the FCC outputs a stepwise full-wave rectified
voltage. The unfolder switches the polarity of the FCC output
voltage to apply a multi-level sinusoidal voltage with few
harmonics to the transmission coil and compensation circuit.
As a result, this system reduces primary-side current
harmonics but has limited effect in reducing secondary-sidecurrent harmonics. The cause of this problem is discussed in
the current analysis using an equivalent circuit.
Figure 2 shows the equivalent circuit of a series-series (SS) compensation WPT system with resonant capacitors
connected in series with the primary and secondary coils,
respectively; V1 and V2 are the output voltages of the inverteror rectifier, and I1 and I2 are the primary and secondarytransmission coil currents. From Fig. 2, the circuit equation isexpressed as (1) from Kirchhoff's voltage law.

 I  1 
1   I2 j L2 +
jC2 

I1 =



1
jC2

L1

i2

Cout

L2

vac1

VDC2

vac2

(a) WPT system with inverter on the primary sideand diode-rectifier on the secondary side.
ifc 1

ifc (n 1)

VDC C1 C2 Cn 1
C1

C2
k

i1
Vo ut

L1

i2

Cout

L2

va c1

VDC2

vac2

(b) WPT system with flying-capacitor converteron primary side and diode-rectifier on secondary side.
Fig. 1. Conventional configuration of WPT system.
C1
C2

M

I1
V1

L1

L2

V2

Fig. 2. Equivalent circuit of S-S compensated WPT system.

j M
I2 = −V1 +j L1 +


1
jC1

V2

()

where  is the determinant of the impedance matrix of theequivalent circuit and is expressed as

1 
1 
2
2
 =  j L1 + j L2 +
 + M
j

C
j

C

1 
2 

()

j M

()

where L1 and L2 are the self-inductance of the primary andsecondary transmission coils, C1 and C2 are the primary andsecondary resonant capacitors, and M is the mutual inductance.
The transmission coil currents I1 and I2 are derived from (1)and expressed asj L2 +

i1
VDC

C2
k

ifc 2

II. CONFIGURATION OF PROPOSED WPT SYSTEM

1 j L1 + jC V1  
1
 =
V
 2
j M



C1

V1 −

j M
V2


()

The primary side voltage harmonics are reduced in theconventional configuration, but the secondary side voltage
harmonics are not. From (2) and (3), it is seen that each current
harmonic remains on the primary and secondary sides byleaving the voltage harmonics on the secondary side. Thus, itis necessary to reduce the voltage harmonics not only on the
primary side but also on the secondary side in order to reduce
both current harmonics sufficiently.
B. Proposed WPT system configuration
Figure 3 shows the configuration of the proposed WPTsystem. The proposed system has an FCC and an unfolder on
the primary side and an FCC and a diode rectifier on thesecondary side. In this paper, S-S compensation is used as thecompensation circuit of the WPT system. The primary-side
FCC outputs a stepwise full-wave rectified voltage as inconventional WPT systems with a single FCC. The unfolder

outputs a multi-level sinusoidal voltage by switching thepolarity of the FCC output voltage. The diode rectifier on thesecondary side supplies full-wave rectified current to the FCC
by switching the polarity depending on the polarity of thesecondary coil current. The secondary-side FCC outputs a
stepped full-wave rectified voltage that agrees with the phaseangle of the secondary coil current. As a result, a multi-levelsinusoidal voltage is applied to both the primary andsecondary sides of the transmission coil. In other words, theproposed system reduces the harmonics of the voltage applied
to the primary and secondary sides of the transmission coil,respectively. Therefore, the proposed system sufficiently
reduces current harmonics that cause harmonics in radiatedemissions.
III. SIMULATION RESULT
Table 1 shows the simulation conditions. Simulations are
performed for a conventional system with only an inverter anda diode rectifier, a conventional system with only the primaryside FCC, and a proposed system with FCCs on both theprimary and secondary sides. The FCC has a lower voltage
utilization ratio than the full-bridge converter due to the
stepped sinusoidal voltage output. For this reason, the DC
voltage is modified so that the fundamental amplitude of theoutput voltage is the same for all systems. The inductance ofthe transmission coils and the capacitance of the resonantcapacitors are the same for all systems. In addition, the FCC
has nine output voltage levels.
A. Operation of the conventional system
Figure 4 shows the simulation results of a conventional
WPT system with a full-bridge inverter on the primary side
and a diode rectifier on the secondary side. The waveforms
show the primary unfolder output voltage, the primarytransmission coil current, the secondary diode rectifier output
voltage, and the secondary coil current. The simulation resultshows that the power factor of the primary power supply isapproximately unity. From this, it is seen that the conventional
system operates under the resonance condition and the rated
condition. In addition, it is seen that both the primary andsecondary coil currents are distorted. In this system, a fullbridge inverter and a diode rectifier output a square-wave
voltage to a series circuit of a transmission coil and aresonance capacitor on both the primary and secondary sides,
respectively. As a result, the harmonic current that causes
current distortion flows through the transmission coil on the
primary and secondary sides according to the resonancecharacteristics of the transmission coil and the compensation
circuit.
Figure 5 shows the simulation results for a conventional
system with a 9-level FCC on the primary side and a dioderectifier on the secondary side. Fig. 5(a) shows the output
voltages of the power converter and the transmission coilcurrents on the primary and secondary sides, respectively. The
results show that the power factor is unity even when the FCC
is connected on the primary side. Accordingly, it is confirmedthat this system also operates under resonance and rated
conditions. The primary converter outputs a 17-levelsinusoidal wave voltage, unfolding the nine-level full-wave
rectified voltage output by the FCC. The primary current
harmonics are suppressed by the significant reduction ofvoltage harmonics due to the multi-level voltage output. As aresult, the primary current distortion on the primary side is
improved. However, voltage harmonics remain because theifc1 1

S11
ifc1 2

ifc 21

S12

ifc 1(n-1 )VDC1 Cfc 11 Cfc 12Cfc1 (n-1)

ifc 22S1 (n-1)

ifc 2(n-1)

S1n

Cfc 2(n-1 )Cfc 22 Cfc 21 VDC2
S2n
C1

C2
M

i1

L1

S2(n-1 )
L2

i2

va c1

vac2
S22
S21

Fig. 3. Proposed WPT system configuration with flying capacitor
converter on both the primary and secondary sides.
Table 1. Simulation and experimental conditions.
Prameters

SymbolInput/Output
DC voltage

VDC

Inv. (D. Rec.): 300

V

VDC2

FCC: 380

V

Rated output power

Pout

1 kW

Transmission frequencyf85.0 kHzValue

Self-inductance

L1,L2

451 mH

Resonant capacitors

C1,C2

7.78 nF

Flying capacitors

Cfc

65.0 mF

Coupling coefficient

k

0.275

-

Number of level for FCC

n

9

-

Unf olde r output voltage vac1
400
200
0
-200
-400
Primary side coils current iac1
50
-5Rec tifie r output voltage vac2
400
200
0
-200
-400
Seconda ry side coils current iac2
50
-510m s/div

Fig. 4. Operation waveform of conventional system with full-bridge
inverter on the primary side and diode rectifieron the secondary side.

diode rectifier outputs a square-wave voltage on the secondaryside. Thus, the secondary current harmonics cannot be
reduced, i.e., the secondary current distortion remains. Notethat voltage and current harmonics are analyzed in detail in
Section C, respectively. In order for the FCC to keep operating,the flying capacitor voltages must be balanced. Fig. 5(b)shows the simulation result of the flying capacitor voltage

Unf olde r output voltage vac1

Unf olde r output voltage vac1

400
200
0
-200
-400

400
200
0
-200
-400

Primary side coils current iac1

Primary side coils current iac1
5

5

0

0
-5

-5

Rec tifie r output voltage vac2

Rec tifie r output voltage vac2
400
200

400
200

0
-200
-400

0
-200
-400
Seconda ry side coils current iac2

Seconda ry side coils current iac2
5

5

0

0

-5

-5
10m s/div

10m s/div(a) Operation waveform(a) Operation waveform

400

400

200

200

0

47.5 V (380/8 V)
0.1s/div(b) Flying capacitor voltage
Fig. 5. Operation waveform of conventional system withflying capacitor converter on the primary side and dioderectifier on the secondary side.

over a long period. A nine-level FCC has seven flying
capacitors. Each voltage ideally has a value that is an integer
multiple of VDC/8. The simulation results confirmed that thevoltages of the seven flying capacitors maintain their nominal
values.

047.5 V (380/8 V)
0.1s/div(b) Flying capacitor voltage on the primary side
400

200

0

47.5 V (380/8 V)
0.1s/div

B. Operation of the proposed system
Figure 6 shows the simulation results of the proposed
WPT system with 9-level FCC on both the primary andsecondary sides. Fig. 6(a) shows the power supply output
voltages and the transmission coil currents on the primary andsecondary sides, respectively. The waveforms show that a 17level multi-level voltage is applied to the series circuit of thetransmission coil and the resonance capacitor on the primaryand secondary sides. In addition, the power factor of the
primary power supply in the proposed system is also unity. In
other words, it is confirmed that the proposed system transmits
the power under resonance conditions. The received power
and transmission efficiency decrease as the load power factor
decreases when the secondary side FCC output voltage phaseis different from the secondary side current phase. The
simulation results confirmed that the load power factor on thesecondary side is also unity. The proposed system meets thedesign specifications for these results without reducing thetransmission power. The primary and secondary sides
converter outputs a multi-level voltage with less low-orderharmonics. From Fig. 6(a), it is confirmed that the current(c) Flying capacitor voltage on the secondary side
Fig. 6. Operation waveform of the proposed system withflying capacitor converter on both the primary andsecondary sides.

distortion on both the primary and secondary sides can besignificantly improved by sufficiently suppressing the current
harmonics on both sides. In addition, the flying capacitor
voltage simulation results on the primary and secondary sides
are shown in Fig. 6(b) and (c). Similar to the conventional
system, the proposed system must also keep the balance of theflying capacitor voltage. The simulation waveforms show thatthe flying capacitor voltage is an integer multiple of 1/8 of theDC voltage on both the primary and secondary sides; it can be
confirmed that the proposed system also maintains the flying
capacitor voltage balance.
C. Current harmonics analysis
Figure 7(a) shows the harmonic analysis results of the
primary converter output voltage and Figure 7(b) shows the
harmonic analysis results of the rectifier output voltage. In

(a) Primary side(a) Primary side(b) Secondary side
Fig. 7. Harmonics analysis of power supply output
voltage on the primary or secondary side.

(b) Secondary side
Fig. 8. Harmonics analysis of transmission coil currentson the primary or secondary side.

Table 2. Harmonics analysis results of the each converter
outoput voltage at low-order harmonic components.

Table 3. Harmonics analysis results of the each coilcurrent at low-order harmonic components.
Number of order

Number of order
Configuration

Configuration
1st

3rd

5th

7th

9th

11th

Inv. – D. Rec. 51.6
Primary side
FCC – D. Rec. 51.6
[dBV]
FCC – FCC 51.6

42.1

37.6

34.7

32.5

30.8

4.37

2.07 -4.18 -9.65 3.47

4.37

2.07 -4.18 -9.64 3.48

Inv. – D. Rec. 51.6
Secondary side
FCC – D. Rec. 51.6
[dBV]
FCC – FCC 51.6

42.1

37.6

34.7

32.5

30.8

42.1

37.6

34.7

32.5

30.8

4.46

2.05 -4.19 -9.64 3.47

addition, Table 2 shows the values of the 11th and lower
voltage harmonics in the odd-order harmonics of thetransmission frequency. Similar to the simulation, theharmonics are analyzed for a conventional configuration withan inverter on the primary side and a diode rectifier on thesecondary side, a conventional configuration with an FCC on
the primary side and a diode rectifier on the secondary side,
and a proposed system with an FCC on both the primary andsecondary sides. Each configuration is analyzed and compared.
The analysis results show that the fundamental wave
amplitudes are almost the same in each configuration on boththe primary and secondary sides. In addition, from Fig. 7(a),an FCC on the primary side reduces the low-order harmonics
of the voltage by 25 dB or more compared to a configuration
without an FCC. In particular, the third harmonic is reduced

1st

3rd

5th

7th

9th

11th

Inv. – D. Rec. 14.4 -13.3 -21.5 -30.0 -31.5 -38.9
Primary side
FCC – D. Rec. 14.4 -22.4 -32.6 -38.9 -43.8 -48.2[dBA]
FCC – FCC 14.5 -50.3 -57.8 -67.3 -74.8 -63.8
Inv. – D. Rec. 14.4 -13.3 -21.5 -30.0 -31.5 -38.9
Secondary side
FCC – D. Rec. 14.5 -13.0 -22.7 -28.8 -33.3 -36.9[dBA]
FCC – FCC 14.5 -50.2 -57.8 -67.3 -74.8 -63.8

by 37.7 dB, and the fifth harmonic is reduced by 35.5 dB. On
the other hand, Fig. 7(b) shows that the voltage harmonics do
not change with or without an FCC on the secondary side. Thisis because each converter is controlled and operated
independently. Similarly, the voltage harmonics on thesecondary side are reduced when the FCC is connected to thesecondary side. The secondary FCC also reduces the lower
harmonics on the secondary side by approximately 25 dB.
Specifically, the third harmonic is reduced by 37.7 dB, and thefifth harmonic is reduced by 35.5 dB.
Figures 8(a) and (b) show the harmonic analysis results ofthe primary and secondary coil currents, respectively. In
addition, Table 3 shows the values of the current harmonics ofthe odd-order components of the transmission frequency. The
current harmonics are also analyzed and compared with threeconfigurations in the same way as the voltage. From theanalysis results, it is confirmed that the fundamental wave
component does not change in any configuration. These
results show that the proposed system does not change thetransmission power. From Fig. 8, the current low-orderharmonics are reduced by about 5 to 10 dB when FCC isapplied to the primary side only. In particular, the third
harmonic is reduced by 9.12 dB, and the fifth harmonic is
reduced by 11.2 dB. Also, the current harmonics on thesecondary side have significantly changed. It is seen that theconventional configuration with FCC on the only primary side
reduces the secondary current harmonics, which are mainly
caused by the secondary voltage harmonics. By contrast, theproposed configuration with FCC on the secondary side
reduces the low-order current harmonics on the primary sideby more than 25 dB compared to the conventional
configuration with an inverter on the primary side. In
particular, the third harmonic is reduced by 37.2 dB, and thefifth harmonic is reduced by 35.1 dB. In addition, thesecondary side current harmonics are reduced by 25 dB ormore as in the case of the primary side, especially the 3rd
harmonic is reduced by 37.2 dB, and the 5th harmonic is
reduced by 35.1 dB.
IV. CONCLUSIONA WPT system was proposed with FCC on the primaryand secondary sides to reduce the current low-order harmonics
in the transmission coil. The proposed system connects the
FCC and the unfolder or diode rectifier as primary or
secondary power sources. FCC significantly reduces coilcurrent harmonics by applying a stepwise sinusoidal voltage
to the transmission coil and compensation circuit. The
proposed system operation and current harmonic reduction
effect were verified by simulation. The proposed system
performed the same power transfer as the conventional system
under resonance conditions. Harmonic analysis results showthat FCC reduces voltage harmonics by more than 25 dB. In
particular, the third harmonic was reduced by 37.2dB and thefifth harmonic by 35.1 dB. The proposed system also reduced
low-order current harmonics by more than 25 dB. In particular,
the third harmonic was reduced by 37.2dB and the fifth
harmonic by 35.1 dB.

In future work, the reduction effects of the current
harmonics and the radiated emission harmonics will beverified by the prototypes with the proposed system.
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