Power Decoupling Method Comparisonof Isolated Single-phase Matrix Converters
using Center-tapped Transformer with PDM
Nagisa Takaoka*, Hiroki Takahashi*, Jun-ichi Itoh**

Goh Teck Chiang, Takahide Sugiyama and Masaru Sugai*Dept. of Electrical Engineering
Nagaoka University of Technology** Dept. of Science of Technology Innovation
Nagaoka University of Technology
Nagaoka, Niigata, Japanntakaoka@stn.nagaokaut.ac.jp, thiroki@stn.nagaokaut.ac.jp,
itoh@vos.nagaokaut.ac.jp

Dept. of System & Electronics Engineering Dept. II
Power Electronics & Control Lab.
Toyota Central R&D Labs. INC.
tcgoh@mosk.tytlabs.co.jp, t-sugiyama@mosk.tytlabs.co.jp,
sugai@asca.tytlabs.co.jp

Abstract— This paper presents an isolated type of singlephase matrix converter topology for PHV/EV on-board battery
chargers. The proposed converter is comprised of a full bridge
inverter, a high frequency transformer and a matrix converter.
Due to the lack of DC link bus in matrix converter, in order tosuppress the power fluctuation, a power decoupling method
which only employs a center-tapped high frequency transformer
and a small LC buffer where requires no additional switches isapplied. On the other hand, the matrix converter applies PDM(Pulse Density Modulation) which achieve ZVS (zero voltage
switching) in order to generate a 50Hz/60Hz sinusoidal waveformat the grid side. As a result, this converter shows promisingfeatures small size and high efficiency. In this paper, by harmonic
analysis, the effectiveness of power decoupling method is
evaluated in two cases: the PDM based on the PWM as aconventional method and the PDM based on the delta-sigma
conversion. In the experimental results, the power decoupling
method with the PDM based on the delta-sigma conversion
reduces the DC bus current ripple by 84.8% comparing to thecase where the power decoupling method is not applied, while theoutput voltage distortion is reduced by 64.1% compared withthat of the PDM based on the PWM is applied.

composed of a diode rectifier and an inverter has been
proposed [2]. In order to reduce the power ripple component in
the DC bus current which is caused by the single-phase load in
this system, a high volume of bulky electrolytic capacitors is
required in the secondary converter, which causes difficulty indownsizing the on-board vehicle battery charger.

Keywords— matrix converter; isolated single-phase AC
converter; power decoupling; pulse density modulation

I. INTRODUCTION
An increasing focus on the reduction of CO2 has lead a
rapid expanding in the growth of PHV/EV. In order to sustain
such growth, a small size, high efficiency and bidirectionalenergy controlled on-board vehicle battery charger is actively
being researched [1]. An isolated type of DC to single-phase
AC converter is compulsory in order to achieve the safety
requirement in a PHV/EV. A conventional converter that isconstructed by a full bridge inverter as a primary converter, ahigh frequency transformer, and a secondary converter
978-1-4673-7151-3/15/$31.00 ©2015 IEEE

In order to reduce the power ripple component, circuit
topologies with power decoupling capability have been studied.
In [3], this method adds a current loop control which reduces aripple current into the existing voltage loop control system
without additional converters or energy storage components for
power decoupling. However, this system restricts downsizing
because a large capacitor or reactor which is consisted as acomponent of DC to DC converter is required as an energy
buffer. In other approaches, DC active filters have been
proposed, where these methods usually consist of a small
buffer capacitor as an energy buffer, a reactor to reduce theswitching ripple, and a DC chopper [4-8]. As a result, volume
reduction of the buffer capacitor is possible. However, thesecircuits restrict the high efficiency because in the tradeoff forpassive components, more switching devices are used for the
power decoupling.
On the other hand, a power decoupling method that utilizes
the center-tapped transformer with a small LC buffer in an
inverter has been presented [9]. This topology can compensate
the power ripple without any additional switching devices
however but then needs a DC-link smoothing capacitor in DC
link bus at the secondary side. Since this circuit needs to deal
with the isolated DC to single-phase AC converter by using a
diode bridge rectifier and a PWM (Pulse Width Modulation)
inverter, where the smoothing capacitors are required in the DC
bus link, light weight design is difficult in the AC/AC
conversion in the secondary side of the transformer.

The diode bridge rectifier and the PWM inverter system of
the secondary side raises large size, heavy in weight andshorter life-time because this system needs the smoothing
capacitors in the DC bus link. Many studies have shown thatthe topology of matrix converters promises to achieve higher
efficiency, smaller size and longer life-time [10-11]. The
topology of a matrix converter is employed between theisolated transformer and single-phase grid instead of theconventional diode bridge rectifier and inverter [12]. From theabove combination, the proposed on-board battery charger canachieve light weight by using small volume of LC buffer
circuit to achieve power decoupling, and also achieve higher
efficiency by applying ZVS (Zero Voltage Switching) in theswitching devices of the matrix converter.
This paper proposes an isolated single-phase matrix
converter with a PDM based on a delta-sigma conversion inorder to improve the effectiveness of the proposed power
decoupling method. The modulation method of a matrix
converter used in [12] is a PDM (Pulse Density Modulation)
based on a PWM [13-14]. This method can suppress aconversion loss because of enabling ZVS by synchronizing thegate pulses of the matrix converter with zero voltage term of
the secondary voltage of transformer. However, when the
carrier frequency ratio between the full bridge inverter and thematrix converter is not large enough or the modulation index of
the matrix converter becomes relatively low, the output voltage
distortion caused by the quantization error increases. The
output voltage distortion influences the power ripple
component in the DC bus current, and this decreases theeffectiveness of the power decoupling because the proposed
power decupling method cannot compensate the powerfluctuation of an effect on the output voltage distortion.
In the PDM based on the delta-sigma conversion, theresolution becomes independent on the carrier frequency ratio
and the modulation index of the matrix converter. Thus, this
proposed PDM method not only decreases the output voltage
distortion but also further reduce the power ripple by using the
proposed power decoupling method.
II. CIRCUIT TOPOLOGY
A. Conventional Converters
Fig. 1 shows a conventional isolated DC to single-phase
AC converter. The conventional circuit is comprised of a fullbridge inverter, a high frequency transformer and a rectifierinverter system. The full bridge inverter outputs a squarevoltage at a high frequency in order to reduce volume of thetransformer. The secondary rectifier converts the highfrequency voltage to a DC voltage and the PWM inverter
controls an output filter capacitor voltage with a feedback
control. When the load current is sinusoidal waveform andachieves the unity power factor, an instantaneous output power
pout is expressed by (1).

pout  2Vload sinot   2 I load sinot  Vload I load 1  cos 2ot   Pout 1  cos 2ot 





where, Vload is the load voltage (RMS), Iload is the load current(RMS), Pout is an output mean power and ωo is the output
angular frequency. A ripple component shown in the second
term of (1) should be bypassed in order to obtain a constantDC current of the DC bus. Hence, this system has to adopt abulky electrolytic capacitor Cdc and a inductor Ldc to absorb
the power ripple.
Fig. 2 shows an isolated DC to single-phase AC converterwith a DC active buffer circuit in [9]. This circuit comprises afull bridge inverter, a high frequency center-tapped transformer,
a DC active filter and a rectifier-inverter system. The converter
combines a full bridge inverter at primary side and a small LC
buffer circuit as a function of a DC active filter by using thecenter-tapped transformer. Therefore, the primary side of thissystem has two capabilities of the full bridge inverter and thebuffer circuit and absorbs the power ripple. This system
reduces a volume of a DC-link smoothing capacitor Cdc. In
addition, this circuit does not require additional switching
devices in comparison to the conventional circuit. However,this circuit still needs a large DC-link smoothing capacitor Cdc
and transforms the power in twice at secondary side of thetransformer because this system deals with the isolated DC tosingle-phase AC converter by using a diode bridge rectifier anda PWM inverter as described previously. Thus, this circuit
restricts a downsizing and high efficiency.
B. Proposed Converter
Fig. 3 shows the isolated DC to single-phase AC converter
Ibus
Ldc

iout iload

N1 N2
Lout

Vbus

Cdc

Full bridge Inverter

Diode rectifier

vout

Cout Rload

vload

PWM inverter

Fig.1
A conventional isolated DC to single-phase AC converter.
The conventional converter uses a bulky electrolytic capacitor Cdc and an
inductor Ldc to absorb the power ripple caused by a single-phase load.
Ibus
iout iload
N1 N2
Vbus

ibuf

Full bridge
Inverter

Lout
Cdc

Cbuf V
Cbuf
BufferDiodecircuit rectifier

vout

Cout Rload

vload

PWM
inverterFig.2 Previous isolated DC to single-phase AC converter with LC
buffer circuit. Thise converter need a DC-link smoothing capacitor Cdc at
DC bus in secondary side because the secondary converter is comprisedof diode rectifier and PWM inverter.

using a matrix converter and a small LC buffer which is
proposed in this paper. The matrix converter is employed as asecondary converter in order to eliminate the DC-linksmoothing capacitor, which is used in Fig. 2. When the matrix
converter applies in a secondary converter, this system cansuppress a conversion loss because of enabling ZVS bysynchronizing the gate pulses of the matrix converter with zerovoltage term of the secondary voltage of transformer. In
addition, a center-tapped transformer links the full bridge
inverter to the matrix converter for isolation and the power
decoupling which results in reducing the DC bus current ripple.
A buffer circuit including a buffer capacitor Cbuf and a buffer
inductor Lbuf is used in order to absorb the power ripple. It
should be noted that a charge and a discharge of the buffer
capacitor Cbuf to compensate the power ripple is implemented
at Cbuf. As explained above, the proposed converter achieves
higher efficiency, smaller size and longer life-time compared tothe conventional rectifier-inverter system.

Ibus

S1ap

Vbus
S1an

pout  Pbus 





pbuf  Pout cos2ot 

S2an

Cbuf

VCbuf
Buffer circuit

Cout Rload

vload

S2bn

Matrix converter

Fig.3
Proposed isolated DC to single-phase AC converter. The
secondary converter is comprised of a matrix converter in order to eliminate
DC-link smoothing capacitor.

vCbuf
VCmax
VCmin

Vbus

t

0

Ibus

vload
vload  2Vload sin o t 

t

0

ibuf

iload

charget0iload  2 I load sin o t 

t

0

t

0

＋



Lbuf

S1bn

Full bridge Inverter

iload

Lout

＋



iout

S2bp

vout

＋

pout  Pbus  pbuf 

N1 N2

S2ap

ibuf

Fig. 4 shows a principle of the power decoupling with Cbuf.
In order to yield a DC bus current without the ripple, a
relationship among the output power pout, a DC bus power Pbus
and a buffer power pbuf is defined as (2)-(4).


S1bp

t

0

discharge
pout

chargedischarge＝t0

Input powerpbus [W]t0

Buffer powerpbuf [W]t0

Output power
pout [W]Fig.4 A principle of the power decoupling with the buffer capacitor. A
buffer power to compensate the power ripple is charged or discharged at
Cbuf. As a result, a DC bus current without the ripple component is obtained.

applied to vary the voltage of buffer capacitor vCbuf which isused to absorb the power ripple caused by the single-phase load.
First, the buffer capacitor energy WCbuf is presented by using(4) and a voltage–current equation of a capacitor.

dvCbuf ttd
WCbuf   vCbuf ibuf d   vCbuf  Cbuf
t0
t0
d 


III. CONTROL STRATEGY
Fig. 5 shows a control block diagram of the proposed
converter. The current and voltage control in the proposed
method are implemented by PI controllers. The full bridge
inverter independently provides a differential mode voltage toexcite the transformer and a common mode voltage tocompensate the power ripple [12]. In contrast, the modulationof the matrix converter is discussed in the next chapter. Fig. 5
shows the control block diagram, the buffer current control is

pbuf

＝

where, a polarity of pbuf is defined as positive when Cbuf ischarged. In order to even out a DC bus current, the buffer
circuit has to reduce the ripple component of a paragraph 2 in
(1). Therefore, pbuf consists with the second term of (1). It
should be noted that the used capacitor is smaller than one in
the conventional converter because the power ripple iscompensated by varying a buffer capacitor voltage vCbuf not alarge capacitance. On the other hand, an inductor in the buffer
circuit is used for the current control for the power decoupling,which is equivalent to control of pbuf. The buffer current
control is carried out by the full bridge inverter. The fullbridge inverter outputs a differential mode voltage to excite
the transformer and a common mode voltage to compensate
the power ripple with the LC buffer independently, owing to
the center-tapped transformer [7]. Thus, the proposed
converter does not require additional switching devices for the
power decoupling and number of devices of the proposed
converter is the same as one of the conventional circuit.

pbus

＝



＝



  Pave cos 2 o d
t



t0

(5)

where, t0 is a start time of operation. The buffer capacitor
voltage vCbuf which needs to absorb the power ripple is derived
from (5).

Normalization of buffer voltage reference

ibuf*
vCbuf*PI

Fbuf (s)Kp_buf1+sTi_buf

vbuf*

sTi_buf
PI controller

FiltervCbuf

ibuf

Average voltage control ofbuffer capacitor

Buffer current control

vdif*
vcom*

1
Vbus

*

2 |vcom |
1

N2
Vbus
N1

Current control of output filter inductor
iout*

Kp_out*1+sTi_out vLout

sTi_out
PI controller

iout

1/x
vout

S1ap
S1an
S1bp
S1bn

Modulation offull bridge
inverter*vout**

Compensation of
secondary voltage
fluctuation of transformer

Modulationof matrix
converter

vload

S2ap
S2an
S2bp
S2bn

Fig.5 Control block diagram of the proposed converter. A buffer current control is for the power decoupling. An output filter current control is applied as aminor loop of the output filter capacitor voltage control that is originally required.

P
vCbuf  VC 0  ave sin2ot   sin2ot0 oCbuf2(6)

where, Vbus is the average DC bus voltage and Pave* iscalculated by load resistance.

Secondaryvoltage of thetransformerHigh
PDM signal
Low

Constant width

Output voltage*

ibuf  Cbuf



dvCbuf
dt

*



*
ave

P
2

cos 20 t 
*

Vbus
P
 ave sin2o t 4o Cbuf(7)

The output filter current control is applied as a minor loopof the output filter capacitor voltage control that is originallyrequired. The buffer capacitor voltage control is introduced inorder to avoid the divergence of the average voltage due todiscretization.
IV. MODULATION METHOD OF MATRIX CONVERTER
Fig. 6 shows a concept of the PDM method applied in thematrix converter as a secondary converter. The PDM treats the
input voltage waveform at high frequency as a pulse andsynthesize the output voltage with the density of the input
voltage pulses. In Fig. 6, a half cycle of the input voltage pulses
are used as the minimum unit of the output voltage waveform.
The switching devices in the matrix converter switch at thezero voltage term of the input voltage waveform. As a result,the matrix converter achieves ZVS which results in decreasing
switching loss.
A. PDM Based on PWM
Fig. 7 shows a block diagram of the PDM based on the
PWM, which is considered as conventional method in [7]. Firstof all, this PDM method yields a PWM pulse, which is

Fig.6
Concept of a PDM method applied in the matrix converter.
The PDM treats a half cycle of an input voltage waveform as a pulse
and synthesizes the output voltage with a density of the input voltage
pulses.

generated by triangle carrier comparison. In order to convert
the PWM pulse to a PDM pulse, the PWM pulse forciblysynchronizes with the zero voltage term of the secondary
voltage of the transformer by a D-FF (D flip flop). Then, thePWM pulse is synchronized with double edges of a primaryswitching signal S1bn because the double edges of S1bn agrees
with the zero voltage term of the secondary voltage of thetransformer. In addition, the gate signal of the matrix converter
is controlled according to the polarity of the secondary voltageof the transformer through CLK and EXNORs.
When the PDM based on the PWM is applied in the matrix
converter, the output voltage distortion increases because of the
problem with the resolution and the output voltage ripple. As aresult, the output voltage distortion which influences the power
ripple component in the DC bus current interferes in the power
decoupling. In the next paragraph the cause of the output
voltage distortion is explained.

Fig. 8 shows the relationship between the output voltage
reference vout* and the output voltage waveform with the PDM
in conventional method. Fig. 8 shows results when changing
vout* from 0.20 to 0.25, and 0.30 p.u.. The output voltage ripple
is high because the conventional PDM method outputs
concentrated pulses instead of distributed pulses in one carrier
period. Furthermore, when vout* =0.20 p.u., the pulse numberof the output voltage n in a half of the carrier period is 2. In
contrast, when vout* =0.25 and 0.30 p.u., n in a half of thecarrier period is 3. As a result, n in a half of the carrier period
wave is expressed by (8).

f trans

f sw

D Q
D-FF

S2ap
S2an

D Q
D-FF

S2bp
S2bn

Carrier
-1

CLK

S1bn

Double edge detection
Fig.7

Block diagram of the PDM based on the PWM.

(8)

(9)

If the output voltage reference is sinusoidal waveform, thelevel of pulse density of the output voltage is changed stepwise
by quantization. Then, Nres agrees with levels expressing thepositive output voltage and is proportional to the carrier
frequency ratio and α. In addition, Nres invariably is an integer
because Nres expresses the levels of the pulse density. From (9),if the carrier frequency ratio or α is lower, Nres of an output
voltage waveform is lower. As a result, the distortion against
the fundamental component of the output voltage is increased
with the quantization error. Especially, if α is lower, the term in
the generation of the quantization error becomes longer bydecreasing of dv/dt of vout*. Moreover, if the carrier frequency
ratio is small, the quantization error becomes higher by adecrease of the levels of the pulse density. Thus, if theresolution Nres is lower, the quantization error becomes higher
and the output voltage distortion is increased. Furthermore, due
to the PWM comparison method, high frequency transformer
pulse voltage is converted in a form of low frequency
concentrated pulse voltage in the output voltage of the matrix
converter, which results the output voltage ripple becomes
higher. The quantization error and the output voltage ripple
have a huge effect on the power ripple at primary side. On thebasis of these results, it is needed to apply a PDM method

Secondary voltage of the transformer[p.u.]

[V]

200
0
-200

[V]

where ftrans is the frequency of secondary voltage of thetransformer and fsw is the carrier frequency of the matrix
converter. It should be noted that n is rounded to an integer
because the PDM pulse exist only in the integer. In Fig. 8, forsimplicity ftrans and fsw are set as 10 kHz and 1 kHz
respectively. This makes the carrier frequency ratio become 10.
Thus, n becomes 2 while vout*=0.20 in a half of the carrier
period. In contrast, n which should be 2.5 becomes 3 while
vout*=0.25 in a half of the carrier period because theconventional PDM method do not consider number of digits
after the decimal point. This error is called as the quantization
error, which increases the output voltage distortion and it isinfluenced by the resolution Nres of the PDM. Consequently, n
is proportional to Nres which is expressed by (9) in this paper.
Besides, vout* is proportional to a modulation index α of amatrix converter.

N res 

vout*

[V]



f
n  trans vout *f swSynchronization
with CLK

1
0
-1
200
100
0
100
50
0
2.0

Carriervout*=0.20

Output voltage reference
vout*=0.25

vout*=0.30

Output voltage
n=2
n=3
Output voltage with LPF

4.0

n=3

6.0

[ms]

Fig.8
Waveform of matrix converter with the PDM based on the
PWM. The output voltage ripple is high because the concentrated bunchy
pulse is output in one carrier period in conventional PDM method. In
addition, the quantization error,which is generated by having no the plusefor vout* after the decimal, is high.

which reduces the quantization error and output voltage ripple
in order to improve the effect of the proposed power
decoupling method.
B. PDM Based on Delta-sigma Conversion
As a solution for the output voltage distortion, this paper
improves the distortion with applying a PDM based on a deltasigma conversion in the matrix converter.
Fig. 9 shows a block diagram of the PDM based on thedelta-sigma conversion, which is considered as the proposed
method [12]. A delta-sigma conversion is kind of Analogdigital conversions, which convert an analog signal into a
digital signal of 1 bit. First of all, the proposed PDM method
integrates the quantization error by comparing the quantized
output voltage reference vout* by ZOH (Zero Order Hold),which is synchronized with carrier peak of the matrix converter,and the quantizer outputs at 1 clock before. The output signalof the quantizer is changed when this integrated quantization
error exceeds a threshold. Due to the reason of switching
signals do not depend on the carrier frequency of the matrix
converter, the pulse density of the output voltage changes
continuously, which results in distributed pulses. Therefore, thePDM based on the delta-sigma conversion reduces theFig. 10 shows a relationship among vout*, the output voltage
vout and fsw with the PDM based on the delta-sigma conversion.
The carrier frequency ratio and vout* are the same as Fig. 8.
From Fig. 10, the output voltage pulse is continuously
generated independently on the carrier frequency of the matrix
converter. Especially, in the term of vout* =0.25 p.u., n in one
carrier period is 5 with the PDM based on the delta-sigma
conversion whereas n is 6 for the conventional PDM method.
In addition, the output voltage ripple is lower because theoutput voltage pulse is distributed in one carrier period.
Therefore, the PDM based on the delta-sigma conversion
reduces the quantization error as against the conventional PDM
method in this term. Moreover, comparing to the conventional
PDM method that outputs concentrated pulses, the output
voltage ripple becomes lower by the pulse is output
continuously in one carrier period in the proposed PDM
method. Thus, the PDM based on the delta-sigma conversion
reduces the quantization error and the ripple of the output
voltage. Moreover, the voltage error compensation improves
the DC bus current ripple with the proposed power decoupling
method because the proposed PDM method reduces the effects
on the power ripple at primary side by the output voltage error.

converter with the PDM based on the PWM. Fig. 12(a) shows aresult without the power decoupling method and (b) shows aresult with the power decoupling method. From 12 (a), it isunderstood that the buffer capacitor voltage does not varybecause the full bridge inverter does not output the common
DS modulator
Quantizer
ABS

S2ap
S2an

-1

z
0

S2bp
S2bn

Switching phase selector

Phase CLK
shifter

S1bn

Fig.9
Block diagram of the PDM based on the delta-sigma
conversion. This PDM method reduces the quantization error andimproves the output voltage distortion.

200
0
-200

V. EXPERIMENTAL RESULTS

[V]

1
0
-1
200
100
0

[V]

[p.u.]

Table 1 shows an experimental condition for the isolated
single-phase matrix converter with the PDM of conventional
and proposed method as drawn in Fig. 7 and 9. It should be
noted that the carrier frequency ratio is 10:1 and the output sideis R-L load without LC filter.
A. Power Decoupling with PDM Based on PWM
Fig. 11 shows the extended each waveform in experimental
result with the PDM based on the PWM. In the conventional
PDM method, the output voltage ripple is high by the output
voltage pulse is output continuously because the conventional
PDM method bases the PWM, which switch gate of thesecondary converter at once in a carrier period as shown in
Fig.11. Then, the voltage error is increased because the output
voltage ripple is high as described previously.

1
0



ZOH

Secondary voltage of the transformer[V]

quantization error and improves the output voltage distortion
because this PDM method has no resolution limits.

100
50
0

Output voltage reference

Carriervout*=0.25

vout*=0.20

vout*=0.30

Output voltage

Output voltage with LPF
3.0

4.0

5.0

6.0

[ms]

Fig.10 Waveform of matrix converter with the PDM based on the deltasigma conversion. The quantization error and the ripple of the output
voltage to apply the PDM based on the delta-sigma conversion.

Secondary transformer voltage vs [500 V/div]

Fig. 12 shows experimental waveforms of the proposed
0

TABLE I.

EXPERIMWNRAL CONDITION

DC bus voltage

350 Vdc

Rated power

410W

Load frequency

50 Hz

Buffer L (Lbuf)

2.0 mH

Buffer C (Cbuf)

200 mF

Grid connectedinductor L (Lout)

2.0 mH

Turn ratio oftransformer N2/N1

1.0

Load voltage

Carrier frequency ofCarrier frequency of
100 kHzfull bridge inverter
matrix converter
Natural angular
Natural angularfrequency of buffer 4000 rad/s frequency of filter
current control
current control
Damping factor of
buffer current control

0.7

Damping factor offilter current control

Output voltage vout [500 V/div]

100 Vpeak0

concentrated
0

10 kHz4000 rad/s
0.7Output voltage vout with LPF [100 V/div]

10 ms/div

Fig.11
Experimental waveforms of the PDM based on PWM as aconventional method. The output voltage ripple is high by the pulse is
output continuously because the conventional PDM method bases the
PWM, which switch gate of the secondary converter at once in a carrier
period.

mode AC voltage. As a result, without the power decoupling
method in the conventional PDM method, power ripple
component at 100 Hz is 57.4% in reference to the average DC
bus current. In contrast, the proposed power decoupling
method provides the common mode AC voltage to fluctuate thebuffer capacitor voltage. Therefore, the proposed method
reduces the 100 Hz component to 13.1%. However, the highorder distortion in the DC bus current persists by the effect,
which the output voltage THD is 4.33% in (b). The reason of
the output voltage THD is higher, which has the effect of thequantization error and the output voltage distortion cause of the
PDM based on PWM as described previously. Especially, theeighth-order harmonic distortion in the output voltage is higher
in Fig. 12(b). Therefore, a compensation reference shown (1)does not agree on the actual power ripple, which has the effectof the output voltage because the proposed power decoupling
method is based on the premise that the power ripple issinusoidal waveform without a distortion.
B. Power Decoupling with PDM Based on Delta-sigma
Conversion
Fig. 13 shows the extended each waveform in experimental
result with the PDM based on the delta-sigma conversion. The
pulse is output continuously with applying a PDM based on adelta-sigma conversion in the matrix converter in Fig. 13.
Therefore, the output voltage ripple is low. In additional, thevoltage error is reduced because the PDM based on the deltasigma conversion depends on the carrier frequency ratio
between the full bridge inverter and the matrix converter andthe modulation index of the matrix converter compared to theconventional PDM method as shown in Fig. 11.
Fig. 14 shows the experimental waveforms of the proposed
converter with the PDM based on the delta-sigma conversion.
Fig. 14(a) shows a result without the power decoupling methodand (b) shows a result with the power decoupling method.
From Fig. 14, it is understood that the output voltage THD is
reduced to 1.65% with the PDM based on the delta-sigma
conversion. Therefore, this PDM method can improve theoutput voltage distortion compared with the conventional PDM
method. Moreover, the proposed method can control Ibus almost
constant because this PDM method reduces the effect on the
power ripple by the output voltage distortion. Thus, the PDM
based on the delta-sigma conversion can further suppress thepower ripple compared with the conventional PDM method.
C. Comparison of Harmonic Analysis by two PDM Methods
Fig. 15 shows the harmonic analysis of the DC bus current.
It should be noted that the harmonic number is based on the
output frequency of 50 Hz. From the result without the power
decoupling method, the power ripple component at 100 Hz is
57.4% with reference to an average current. The proposed
power decoupling method with the PDM based on the PWM
reduces the 100 Hz component to 13.1% because the buffer
capacitor voltage fluctuation absorbs the power ripple at 100
Hz. However, the 100 Hz component of the power ripple on
the DC bus current remains because the quantization error andthe output voltage ripple have a huge effect on the power ripple
at primary side when the PDM based on the PWM is applied in
the matrix comverter. Thus, when the quantization error of theoutput voltage waveform is reduced, the ripple for the

DC bus current Ibus 2 A/div
0

Buffer current ibuf 5 A/div

0

Buffer capacitor voltage VCbuf 100 V/div0

Output voltage (LPF) vout 100 V/div

4 ms/div(a)Without the power decoupling method.

DC bus current Ibus 2 A/div
0

Buffer current ibuf 5 A/div

0

Buffer capacitor voltage VCbuf 100 V/div0

Output voltage (LPF) vout 100 V/div

4 ms/div(b) With the power decoupling method.
Fig.12
Experimental waveforms with the PDM based on the PWM.
The proposed power decoupling method provides the common mode AC
voltage to fluctuate the buffer capacitor voltage.

Secondary transformer voltage vs [500 V/div]0

Output voltage vout [500 V/div]00

Output voltage vout with LPF [100 V/div]

10 ms/div

Fig.13
Experimental waveforms of the PDM based on the deltasigma conversion as a proposed method. The pulse is output
continuously with applying a PDM based on a delta-sigma conversion in
the matrix converter.

harmonic component of the DC bus current can be reduced asshown in Fig. 12. In contrast, in the power decoupling methodwith the PDM based on the delta-sigma conversion, the 100 Hz
component is reduced to 8.75% because the PDM based on thedelta-sigma conversion reduces the effects on the power ripple
at primary side by the output voltage error. Then, the PDM
based on the delta-sigma conversion with the proposed power
decoupling method reduces the 100 Hz component of the DCbus current by 33.5% compare to the PDM based on the PWM
with power decoupling method. As a result, these experimental
results verified the effectiveness of the proposed power
decoupling with PDM based on the delta-sigma conversion.
VI. CONCLUSION
This paper proposed an isolated single-phase matrix
converter with the PDM based on the delta-sigma conversion
in order to futher improve the effectiveness of the power
decoupling method. The proposed system is expected toachieve smaller size compared to the conventional rectifierinverter system because in the proposed system the bulky
electrolytic capacitor is not required. In addition, this paper
clarified the cause of the output voltage distortion when the
PDM based on the PWM is applied. As a solution for the
output voltage distortion, this paper decreases the output
voltage distortion by applied the PDM based on the deltasigma conversion. From the experimental results, the proposed
power decoupling method reduces the DC bus current ripple by
84.8%. In addition, the proposed system reduces the output
voltage distortion by 64.1%. Thus, the validity of the proposed
voltage error compensation method is confirmed.

DC bus current Ibus 2 A/div

00

Buffer current ibuf 5 A/div
Buffer capacitor voltage VCbuf 100 V/div0

Output voltage (LPF) vout 100 V/div

DC bus current Ibus 2 A/div
0

Buffer capacitor voltage VCbuf 100 V/div

[3]

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Output voltage (LPF) vout 100 V/div

4 ms/div(b) With the power decoupling method.
Fig.14
Experimental waveforms with the PDM based on the deltasigma conversion in a steady state. The DC bus current do not have little
harmonic component.
60

Hamonic component[%](100%: DC current component)[2]

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Buffer current ibuf 5 A/div

0

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4 ms/div(a)Without the power decoupling method.

50

Without
系列3 the power decoupling method

40

系列2

30

With the power decoupling method and系列1

20

With the power decoupling method andthe PDM based on PWM
the PDM based on delta-sigma conversion

Reduced by 84.8%

100
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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