Several-Hundred-kHz Single-phase to Commercial
Frequency Three-phase Matrix Converter
using Delta-Sigma Modulation with Space Vector
Yuki Nakata, Koji Orikawa and Jun-ichi Itoh
Department of Electrical, Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
nakata@stn.nagaokaut.ac.jp, itoh@vos.nagaokaut.ac.jp
Abstract—This paper discusses the pulse density modulation(PDM) control methods for a single-phase to three-phasematrix converter (MC) in the high-frequency application. This
converter outputs a commercial power grid frequency, i.e. 50
Hz or 60 Hz from the input of several-hundred-kHz frequency.
The proposed circuit achieves zero voltage switching operationby using the PDM control method. In this paper, two PDM
control strategies are compared between a conventional PDM
control method based on space vector modulation (SVM) andthe proposed PDM control method, which is combined with
SVM and a delta-sigma conversion. Also, the experimental
results of the proposed control method will be demonstrated
and discussed. As a result, the total harmonic distortion (THD)of the output voltage with the proposed PDM control method isimproved to 1.87% from 9.05% of the conventional PDM
control method.

I.

INTRODUCTION

In recent years, wireless power transfer systems havebeen actively researched [1-3]. There are two types ofwireless power transfer systems known as theelectromagnetic induction and a magnetic resonant coupling.
In the electromagnetic induction type, the frequency of thecoil for the transmission is low, and it can transmit highcapacity power with relative ease. However, the transmitting
efficiency decreases when the coupling is reduced byincreasing in the transmission distance. As a result, a large
coupling of the transmission coils is necessary in order toimprove the transmitting efficiency. Likewise, thetransmitting distance needs to become shorter. On the other
hand, the efficiency of the magnetic resonant coupling typeis over 90% at the intermediate distance which isapproximately 1 meter though the high frequency is used [1].
In the wireless power transfer system, the frequency of
the generated voltage at the receiving coil is from tens of
kHz to several MHz, which is identical to the power source
frequency. Accordingly, in order to connect this system to a

978-1-4799-5776-7/14/$31.00 ©2014 IEEEload, an interface converter which converts the received
power into a controlled output power is required. The
characteristic of this interface converter must have a highinput frequency (several hundred kHz) and a low output
frequency (50 Hz or 60 Hz) which is suitable for commercial
power grid. That is, an AC-to-AC converter is generally
clarified as the interface converter for this system. In general,back-to-back (BTB) system, which is constructed by a PWM
rectifier, a smoothing capacitor and a PWM inverter, is usedas this AC-to-AC converter. However, it is difficult to use
the PWM rectifier in the input side due to high-frequency
input. Additionally, the DC link voltage is smoothed byusing smoothing capacitor in BTB system. Unless the soft
switching technique is applied, the switching loss becomeslarge because of the hard switching.
On the other hand, matrix converters (MC) have been
attracted attentions as the AC interface converter for thewireless system, because it delivers advantages in terms of asize reduction and an energy saving owning to highefficiency [4-6]. The MC which has the several-hundred-kHzof high-frequency output has been researched. However, theimplementation of the control method utilizing thecharacteristics of high-frequency power source as shown
below for the MC with the high-frequency input has not beenreported.
The authors have proposed to use the single-phase to
three-phase MC in high-frequency as the interface converter.
A pulse density modulation (PDM) [7-10] control method isapplied to the converter by using the half cycle of the input
voltage as a pulse for PDM control. This converter achieves
an advantage that the switching loss can be decreased nearlyclose to zero by the switching at zero input voltage. The
PDM control based on space vector modulation (SVM) with
D-flip flop (conventional PDM control method) has been
proposed as one of the PDM for the converter [11-13].
However, the output voltage waveforms have distortion

when the modulation ratio is low and carrier frequency ishigh in the conventional PDM method.
This paper proposes a novel PDM method which is
combined with SVM and delta-sigma conversion in order toimprove the quality of the output voltage waveforms. The
proposed PDM method improves the performance comparedto the conventional PDM method. The reason is as follows;
the output voltage waveforms at the low modulation ratio
and high carrier frequency have distortion in theconventional PDM method, because the control resolution of
the output voltage becomes low, on the other hands, theproposed PDM method achieves high resolution by using
delta-sigma conversion synchronized with zero cross pointsof the input voltage. In order to confirm the effect of the
proposed PDM method, the conventional PDM method andthe proposed PDM method is compared based on theexperimental results.

High-frequency
power source
Transmission coil Receiving coilCommercial
grid

Power
converter
Wireless power transfer
Input voltage

High frequency

Output voltage

Low frequency

Figure 1. Wireless power transfer system.

This paper is organized as follows; first, theconfigurations of the proposed circuit are introduced; second,
the PDM control strategy using the conventional method andproposed method are discussed; finally, the validity of the
proposed method is confirmed in the experimental results.
II.

CIRCUIT CONFIGURATION

A. System Configuration
Fig. 1 shows a configuration of the wireless powertransfer system. The receiving coil voltage is a highfrequency AC, which has same as the frequency of thesource. In order to connect to the commercial grid, a single
phase AC to three phase AC converter is required as aninterface converter.
The interface converter inputs several-hundred-kHz
sinusoidal waveform, and outputs the low-frequency
waveform such as 50 Hz and 60 Hz. Hence, the PDM control
which uses a half cycle of the input voltage as a pulse can beapplied to the interface converter.
Therefore, the use of the matrix converter as an interface
converter for wireless power transfer system is proposed.
The matrix converter achieves high frequency by applying a
PDM control. The detail of PDM control is explained in next
chapter.
B. Single-phase to Three-phase Matrix Converter
Fig. 2 shows the circuit configuration of the proposed
single-phase to three-phase MC. This circuit is constructedby six bidirectional switches. Since this converter does not
require smoothing capacitors in the DC link, the lifetime of
the circuit is longer and the size is more compact than that of
the conventional system, which is constructed by a PWM
rectifier, smoothing capacitors and a three-phase PWM
inverter. Further, the efficiency of a MC is higher than theconventional system because the conversion number isreduced in comparison with the conventional system. In
addition, the proposed system can improve the efficiency interms of not only conduction loss but also the switching loss
in comparison with the conventional system. The proposed

Figure 2. Single-phase to three-phase matrix converter.

system reduces switching loss drastically because theswitching devices switch when the switch voltage is 0 V inthis system. As a result, this system achieves PDM control,
which uses a half cycle of the input voltage as a control unit.
Note that a snubber circuit is connected to the output sideof the converter as a protection circuit in the experimental
circuit. It is constructed by diodes, a small capacitor and a
resistor.
In addition, the voltage transfer ratio of the conventional
system, which has smoothing capacitor in DC link is 1. In
contrast, the voltage transfer ratio of the proposed singlephase to three-phase matrix converter is 0.637 as explainedin (1).

Vout =

2π⋅ Vin = 0.637 ⋅ Vin(1)

Where, Vout and Vin are the RMS value of the output voltage
vuv and input voltage respectively. Therefore, the voltage
transfer ratio of the proposed converter is lower than that of
the conventional system.
However, this drawback is not important in the wirelesspower transmission system. This system is supposed tomatch certain impedance because if it assumes that the inputof this system is secondary side of the wireless transfer

system. In this case, the input voltage of this systemincreases proportion to the impedance when the output
power becomes large. For example, assuming that thissystem outputs several-kW power, the input voltage becomesapproximately from 400 V to 500 V. Therefore, by assumingthat this system is used in wireless transfer system, theproposed single-phase to three-phase matrix converter can beused for the utility system operates as a step-down converter.

Figure 3. Configuration of the input filter.

C. Design of the Input Filter
The impedance matching is important on the circuit for
the high-frequency application in order to prevent thereflection of the power and achieve the high efficiency
transmission [3]. In this system, the input filter is connectedto the input side as an impedance matching circuit, which
can match the impedance of the voltage source and thecircuit. The design method which matches the impedance Zin
to 50 Ω is explained in this section because the general highfrequency power sources have 50 Ω of matching impedance.
Fig. 3 shows the configuration of the input filter. It isconstructed from a reactor Lf and a capacitor Cf. The
impedance of the load connected to the filter is expressed byresister Rload as shown in Fig. 3. The value of Lf and Cf aredetermined that the real part of the synthetic impedance
equals to 50 Ω and the imaginary part equals to 0 Ω in orderto achieve 50 Ω of the matching impedance. Lf and Cf arecalculated by (2) and (3), where, ω=2πf is the input voltage
angular frequency. Lf and Cf are 80 μH and 16 nF
respectively, when the frequency of f is 100 kHz, and Rload is
100 Ω. These values are used in the experiment.

Lf =C f Rload2

1 + (ωC f Rload ) 2

Cf =

III.

1
ω RloadFigure 4. PDM control waveform of the proposed circuit.

Rload
−1
50

(2)

(a) PDM signals generation block diagram based on SVM.

(3)CONTROL STRATEGIESA PDM control method is applied to the proposed system
in order to reduce the switching loss of the converter. PDM
controls the density and the polarity of the constant-width
pulse, and these pulse signals are used as the output unit.
Fig. 4 shows a view showing a frame format of the PDM
control waveform for the single-phase to three-phase MC.
Assuming that the single-phase to three-phase MC isconnecting to a wireless power transfer system as input
power source, it is receiving high-frequency sinusoidal
voltage as an input. Therefore the PDM control can beapplied to the proposed circuit by using the half cycle of the
input voltage as a pulse for PDM control as shown in Fig. 4.
A. PDM Control based on Space Vector Modulation
Fig. 5(a) shows the PDM signal generation block of aconventional PDM control method based on the SVM. The
selected vector signals generated from the SVM is the input(b) Space vector diagram.

(c) Switching pattern table.

Figure 5. Control block diagram of the conventional PDM method
based on SVM.

to the D flip flop (D-FF). The plus/minus detection signal
from the input voltage is used to detect the zero cross points
of input voltage, and this signal is an input to the CLK of the
D-FF. The output of the D-FF, “Q” is synchronized at theedge of plus/minus signal, which is the zero cross point of
the input voltage. After that, the switching signals whichcorrespond to the vectors in Fig. 5(b), are generated from
output signals of the D-FF using pattern table in Fig. 5(c).

∑Figure 6. PDM signals generation block diagram of the proposed PDM method combined with the SVM and delta-sigma conversion.

The “1” and “0” in the Fig. 5(c) show the output states ofeach arm. As a result, a PDM control which uses a half cycleof the input voltage as an output unit are obtained, and theswitching at approximately zero point of the input voltage isachieved. Furthermore, the switching signals are exclusive
NORed with the polarity of the input voltage, because it isnecessary to exchange the switching signals of the upper arm
and the lower arm depending on the polarity of the input
voltage.
Therefore, the switching patterns generated by SVM arequantized by the pulse whose width is half cycle of the input
voltage and the switching timing is synchronized with thezero cross point of the input voltage. The output voltage
waveforms become the PWM waveforms synchronized withthe zero cross point of the input voltage. As a result, thisPDM control method based on SVM can achieve theswitching at zero voltage.
In this method, the output voltage is controlled byregulating the on duty per one cycle of the carrier wave. As aresult, the output voltage ripple and distortion increase at low
modulation ratio. Hence high carrier frequency is needed inthis method in order to suppress the output ripple. However,when the carrier frequency is high and become close to the
input frequency, the output voltage control resolution
becomes low. It is because that the rate of a pulse widthversus one control cycle is large and the quantization error of
the output voltage becomes large when the carrier frequency
is high. Moreover, this method has low resolution at low
modulation ratio because of the same reason.
A new PDM method is proposed in order to suppress theoutput voltage distortion, and detail of the method is
explained in next section.
B. PDM Control based on Space Vector Modulation
combined with Delta-Sigma Conversion
In this section, a proposed PDM method, which is
combined with SVM and delta-sigma conversion, is
proposed in order to suppress the output voltage distortion.
Fig. 6 shows block diagram of the proposed PDM
method. The each phase command values vu*, vv* and vw*
are converted to each component of the command vector vα*
and vβ* by coordinate transformation. The command value(vector) is updated with a period of 100 μs (10 kHz). Thisfrequency corresponds to carrier frequency of theconventional PDM method. The error between eachcomponents of the command vector (vα*, vβ*) and output
vector (vα, vβ) are calculated, and integrated. The integrated
errors are compared with candidate vectors, and the closest
vector is selected and output. After that, switching patterns
are generated from selected vector in Fig. 5(b) using
switching table in Fig. 5(c). Furthermore, the switchingpatterns are exclusive NORed with the polarity of the input
voltage for the same reason as conventional PDM method.
The calculator and integrator of the errors operate insynchronization with zero cross points of the input voltage.
As a result, the control resolution remains nearly unaffectedby update cycle of the command values and modulation ratio
in this proposed PDM method, unlike conventional method.
In addition, this method achieves the advantages of“oversampling” and “noise shaping” techniques [14], andsuppresses the low order harmonics components. The
harmonic components because of quantization error occur
because this method quantizes the commands of the output
voltage. However, the power spectrum density of theharmonics from the quantization error spreads in the wide
frequency band, by sampling with substantially-larger
frequency than the fundamental frequency of the output
voltage commands (i.e. oversampling). The harmonics fromthe quantization error is distributed on the high frequency
side owing to a feedback circuit. As a result, low orderharmonics are suppressed, and the output voltage THD
becomes small. Therefore, it means that the output filter,
which is necessary to connect the utility system is smaller
than conventional method.
IV.

VERIFICATIONS OF THE PDM METHODSIn order to confirm the basic operation of theconventional method and the proposed method, the prototype
circuit is demonstrated in experiment with load condition.
Table 1 shows the experimental conditions.
A. Experimental Results with the Conventional PDM
MethodFig. 7(a) shows the operation waveforms of the proposed
circuit in the experiment with the conventional PDM
method. The result confirms that 50 Hz sinusoidal

TABLE I.

EXPERIMENTAL CONDITIONS

Input voltage

70.7 V (100 Vpeak)

Input frequency

100 kHz

Output line-line voltage

35 V

Output frequency

50 Hz

Load

Rload

25 Ω

Lload

5 mH

Carrier frequency of the SVM(Updating cycle of command)

10 kHz(100 μs)

Modulation ratio

0.5(a) Input and output operation waveforms.

waveforms are obtained on the output voltage and current.
However, from the output current waveform, the output
voltage has distortion because of the reason which is
explained in section III-A. Therefore, the output voltage
includes the low order harmonics.
Fig. 7(b) shows the extended view of the interval “A” in
Fig. 7(a). As a result, the output line-to-line voltage vuv
confirms that the switching of the MC is happened at
approximately each zero cross point of the 100 kHz
sinusoidal input waveform. Therefore, basic operation of theconventional PDM method is confirmed. However, theoutput current has the ripple of carrier frequency. In thismethod, the output voltage waveforms become PWM
waveforms because the PWM signals from SVM aresynchronized at zero cross points of the input voltage.
Therefore, the output current waveforms include the ripple ofthe carrier frequency.
Fig. 8 shows the harmonics analysis of the output voltage
and the input current from the experimental result with theconventional PDM method. From Fig. 8(a), the low-orderharmonic components of 50 Hz are included in the output
voltage, and the output voltage THD of 9.05% is obtained. In
addition, the output voltage includes the integral-multiple
harmonic nearly to the carrier frequency of 10 kHz, which isthe control cycle because the output voltage is controlled byregulating the on duty per one cycle of carrier wave in thismethod. Additionally, the integral-multiple harmonic nearly
to the 200 kHz is included in the output voltage and otherhigh-order harmonic components because the output voltage
has the fluctuation, which is twice of the input frequency.
Furthermore, from Fig. 8(b), the input current includes theintegral-multiple harmonic nearly closed to the carrier
frequency of 10 kHz and the input frequency of 100 kHz,and the input current THD is 55.2%.
From these results, it is confirmed that the output
waveforms have large distortion at the low modulation ratio
in this method because the resolution of the control becomeslow.
B. Experimental Results with the Proposed PDM Method
Fig. 9(a) shows the operation waveforms of the proposed
circuit in the experiment with the proposed PDM method.
The result confirms that sinusoidal waveforms of 50 Hz are(b) Extended each operation waveform.
Figure 7. Operation waveforms of the proposed circuitin the experiment with the conventional PDM control.

(a) Harmonics analysis of the output voltage.

(b) Harmonics analysis of the input current.
Figure 8. Harmonics analysis of the output voltage and the input current
with the conventional PDM control.

obtained on the output voltage and current. From the output
current, the output voltage does not have distortion becauseof the reason explained in section III-B.
Fig. 9(b) shows the extended view of the interval “B” in
Fig. 9(a). As a result, it is confirmed that the switching of the
MC is synchronized with each zero cross point of the 100
kHz sinusoidal input waveform from the output line-to-line
voltage vuv. The output current waveform has the smaller
current ripple in comparison with that of the conventional
method because the delta-sigma conversion operates per halfcycle of the input voltage and the output vectors in thismethod are changed per shorter period compared with theconventional method. From these results, the operation of the
proposed PDM method is confirmed.
Fig. 10 shows the harmonics analysis of the output
voltage and the input current from the experimental resultwith the proposed PDM method. From Fig 10(a), the loworder harmonic components of 50 Hz are not included in the
output voltage, and the output voltage THD of 1.87% is
obtained. In addition, the output voltage does not include theintegral-multiple harmonic nearly to the carrier frequency of
10 kHz, which is the control cycle. Additionally, the integralmultiple harmonic nearly to the 200 kHz is included in the
output voltage in the high-order harmonic components
because of the same reason as the conventional PDM
method. Moreover, the harmonics are distributed for the highfrequency side as explained in section III-B.
Furthermore, Fig. 10(b) shows that the input current has
the integral-multiple harmonic nearly closed to input
frequency of 100 kHz, and therefore the input current THD
is 49.8%. In this case, the input current does not include theintegral-multiple harmonic nearly closed to the updating
cycle of 10 kHz in contrast to the conventional PDM control
method.

(a) Input and output operation waveforms.

(b) Extended each operation waveform.
Figure 9. Operation waveforms of the proposed circuitin the experiment with the proposed PDM control.

From these experimental results, it is confirmed that theresolution degradation problem at low modulation ratio in
the conventional PDM method is solved by applying the
proposed method, and the output voltage waveforms are
improved.
C. Evaluation for THD and Switching Ripple of theConventional Method and the Proposed Method
Fig. 11 shows the output voltage total harmonic distortionsof the proposed circuit. From the result, the THD of theconventional PDM method increases when the modulation
ratio is low because of the reason which is explained in
section III-A. In the conventional PDM method, it isnecessary to use the proposed circuit over 0.8 of modulation
ratio in order to operate under 5% of THD. On the other
hand, the THD of the output voltage is under 5% at over 0.2
of modulation ratio in the proposed PDM method because of
the reason which is explained in III-B.
From these experimental results, it is confirmed that theoutput voltage at low modulation ratio is improved byapplying the proposed PDM method.

(a) Harmonics analysis of the output voltage.

(b) Harmonics analysis of the input current.
Figure 10. Harmonics analysis of the output voltage and the input current
with the proposed PDM control.

In addition, the output voltage waveform does not havethe integral-multiple components of 10 kHz as shown in theharmonics analysis. It indicates that the switching ripple ofthe output current is smaller in comparison with that of theconventional method. In other word, the value of theinterconnection reactor can be small if it assumes this system
connects to the commercial grid. The effect of the proposed
PDM method is confirmed by the simulation and thesimulation results are shown in Fig. 12.
Fig. 12 shows the grid voltage and current waveforms
when the conventional and the proposed PDM method areapplied. It assumes that the output of this converter connects
the three-phase 200 V commercial grid and the output poweris 1 kW. Fg.12 (a) shows the operation waveforms with theconventional PDM method and the interconnection reactor of
20 mH (= 15.7%) is connected. From Fig. 12(a), the current
flowing through the interconnection reactor includes theswitching ripple component when the conventional PDM
method is applied and the ripple factor is approximately 11%.
Furthermore, Fig. 12(b) shows the operation waveforms withthe proposed PDM method and the interconnection reactor of
5 mH (= 3.9%) is connected. The ripple factor of the current
flowing through the interconnection reactor is on the samelevel as that of the conventional PDM method and the ripple
factor is approximately 11%. From this result, it is confirmedthat the value of the interconnection reactor can be a quarterby applying the proposed PDM method. From these results,
the effect and validity of the proposed PDM method is
confirmed.

35
30
25
20
15
10
5
0

0.2

0.4

0.6

0.8

1

Figure 11. Output voltage total harmonic distortionsof the proposed circuit.

(a) Operation waveforms with the conventional PDM method
using the interconnection reactor of 20 mH (15.7%).

D. Efficiemcy Charasteristics
Fig. 13 shows the efficiency characteristics of the
prototype circuit with the conventional PDM control method
and the proposed PDM control method. The input and output
voltage conditions are as shown in table 2, and the output
power is controlled by changing the load value.
From the result, the maximum efficiency withconventional PDM control and with proposed PDM control
are 94.5% and 94.8% respectively at approximately 50-W
load. Furthermore, the efficiency decreases at heavy loadcondition. It is because that the output current becomes large
at heavy load, and the conduction loss becomes large.
In addition, the efficiency for the proposed PDM control
method is higher than that of the conventional PDM control
method at all measurement regions. Therefore, the proposed
PDM control method improves the output voltage
waveforms and THDs without the efficiency reduction.
V.

CONCLUSION

This paper discusses the PDM control methods for asingle-phase to three-phase MC in the high-frequency
application. Several-hundred-kHz frequency is inputted tothis converter, and the converter outputs a low frequency, i.e.
50 Hz or 60 Hz, for commercial power grid. The proposed
circuit achieves zero voltage switching operation by using
the PDM control method and obtains high efficiency. In thispaper, two PDM control strategies are compared between(b) Operation waveforms with the proposed PDM method
using the interconnection reactor of 5 mH (3.9%).
Figure 12. Grid voltage and current waveforms
connecting the commercial grid.

100
98
96
94
92
90
40

60

80

Figure 13. Efficiency of the proposed circuit.

[3]TABLE II.

EFFICIENCY MEASUREMENT CONDITIONS

Input voltage

176 V (250 Vpeak)

Input frequency

100 kHz

Output line-line voltage

90 V

Output frequency

50 Hz

Carrier frequency of the SVM(Updating cycle of command)

10 kHz(100 μs)

Modulation ratio

1.0

PDM control based on SVM and the proposed PDM method
which is combined with SVM and delta-sigma conversion,and suppress the distortion of the output voltage. Also, theexperimental results of the proposed system aredemonstrated with load condition and discussed. As a result,the THD of the output voltage with the conventional method
and the proposed method are 9.05% and 1.87% respectively,
when the modulation ratio is 0.5. Therefore, the validity ofthe proposed method has been confirmed for improvement of
the output waveforms.
In addition, the AC-to-AC converter for the highfrequency application is necessary in other case. For example,
the MC for high-frequency application can be applied totrans-linked converter, whose secondary side is connected tocommercial grid. For downsizing the converter, thetransformer for high-frequency link size is a majorbottleneck [15]. Therefore, the size of the transformer can besmall by higher frequency converter using high-speed
switching devices such as SiC and GaN.
In future work, the experiment will be conducted with aheavier load condition and the investigation about theefficiency of this circuit with both PDM methods.
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