Isolated DC to Three-phase AC Converter
using Indirect Matrix Converterwith ZVS Applied to All Switches
Shunsuke Takuma, Koji Orikawa, Jun-ichi Itoh

Ryo Oshima, Hiroki Takahashi

Dept. of Science of Technology Innovation
Nagaoka University of Technology
Nagaoka, Niigata, Japan
takuma_s@stn.nagaokaut.ac.jp
orikawa, itoh@vos.nagaokaut.ac.jp

Dept. of Electrical Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
ryo_oshima@stn.nagaokaut.ac.jp
thiroki@stn.nagaokaut.ac.jp

Abstract-- This paper proposes a Zero Voltage Switching(ZVS) method for an isolated DC to three-phase AC converter
using an indirect matrix converter at the secondary side of thetransformer. Phase-shift control is applied to the inverter at the
primary side of the transformer, while Pulse Density Modulation(PDM) is employed to the indirect matrix converter at thesecondary side. The inverter at the secondary side achieves ZVS
by synchronizing the gate pulses with the zero voltage period of
the input voltage. As a result, the proposed method reduces
switching losses of both two converters. The validity of the
proposed method is confirmed by experiment with a 3-kW
prototype. From the experimental results, the snubber loss
generated by the leakage inductance which satisfies theconditions for ZVS is small and almost constant against theoutput power. It is concluded that the efficiency of the entire
range of load with proposed control is improved by 2% incomparison to the isolated DC-AC converter using matrix
converter. In addition, the loss of the inverter at primary side is
reduced by 64.5% at rated output.

by high frequency drive. However, the circuit configuration
which uses rectifier and inverter at the secondary side of thetransformer requires the electrolytic capacitor at DC-link.
Therefore it becomes large volume and short-life span.

Keywords— indirect matrix converter ; isolated DC-AC
converter ; pulse density modulation

For further improving the efficiency, the Zero Voltage
Switching (ZVS) method and the suppression control of thefreewheeling current for an isolated DC to three-phase AC
converter using a matrix converter at the secondary side of thetransformer has been studied [11]. ZVS is realized bysynchronizing the pulse density modulation (PDM) signal
generated by the space vector modulation (SVM) with the zerovoltage periods of the input voltage of the inverter at thesecondary side. Besides, a soft switching technique for the
inverter at the primary side is also required to further improvethe efficiency. In order to achieve high efficiency, previous
studies have shown that the isolated DC to three-phase AC
converter realizes the soft switching operation on the primary
and the secondary converter by using the auxiliary resonant
circuit [12]. However, the number of components is increased
due to the auxiliary resonant circuit using two capacitors andtwo auxiliary resonant inductors. Thus, the control methods for
reducing switching loss without passive components arenecessary. In [13], the number of switching devices of the DCAC converter using an indirect matrix converter is reduced to
14 compared with that using the matrix converter. However,the control at the secondary side of this topology is PWM using

I. INTRODUCTION
Recently, from the view point of global warming andenvironmental problems, renewable energy generation systems
have been actively researched. However, in renewable energy
generation system, power fluctuation occurs because of
meteorological conditions. Therefore, an energy storage systemusing a battery is necessary in order to suppress the powerfluctuation. This energy storage system requires an isolated
DC-AC converter to connect the grid and the battery. In
addition, the DC-AC converter requires the isolation by atransformer in order to protect the system from failure andnoise. However, an isolation transformer in the converter
designed for the commercial frequency is bulky and heavy.
Hence, in order to reduce the volume of the transformer, a highfrequency link DC-AC converters have been researched [3-10].
In [1-5], the system consists of high frequency inverter,transformer, the rectifier and the inverter has been suggested.
This converter is possible to reduce the volume of transformer
978-1-4673-7151-3/15/$31.00 ©2015 IEEE

In order to remove the electrolytic capacitor at the DC-link
for downsizing and long life time, a high frequency link DCAC converter which employs a matrix converter as AC tothree-phase AC converter at the secondary side of transformer,
has been investigated [8-10]. In comparison to the conventional
circuit, this circuit consists of an isolation DC-DC converter
and an inverter. Therefore, the number of times of power
conversion is decreased. As a result, high efficiency is achieved.
this topology. However, the control at secondary side ofthis topology is PWM using modified signal, and switchingloss increase. The control methods for reducing switching loss
without passive components are necessary components arenecessary.

modified signal. Therefore, the switching loss is increased.
The control methods are necessary for reducing switching loss
without passive components.
This paper proposes a ZVS method for the isolated DC to
the three-phase AC converter which uses an indirect matrix
converter at the secondary side of the transformer in order toachieve high efficiency without additional passive components.
In the proposed method, ZVS of the inverter at the primary sideis achieved by the drain-source capacitance of the primary
MOSFETs and the leakage inductance of the transformer. In
addition, in order to obtain the transformer current which
satisfies the conditions for ZVS, a matrix converter in theconventional circuit is replaced with an indirect matrix
converter. By this replacement, the primary inverter andsecondary rectifier is same configuration as the conventional
isolated DC-DC converter. Then, the discharge or charge of thedrain-source capacitances at the MOSFETs of the inverter isaccomplished before those MOSFETs turn on [14]. To besummed up, the diode rectifier of the indirect matrix converterat the secondary side makes the inverter at the primary sideachieves ZVS. Moreover, PDM is applied to the indirect matrix
converter in order to achieve ZVS for MOSFETs at thesecondary side. As a result, ZVS is achieved on all switches
without additional passive components in the proposed circuit.
In experiments, the fundamental operation of the proposed
ZVS method is demonstrated and the efficiency is evaluated inorder to clarify the validity of the proposed converter. In
addition, relationship between the snubber loss and the leakage
inductance which satisfies the conditions for ZVS is clarified.
II. CIRCUIT CONFIGULATION
Fig. 1 shows the circuit configuration of the conventional
high frequency link DC-AC converter. The circuit comprises ofa full bridge inverter at the primary side of transformer and thesingle-phase to three-phase matrix converter at the secondaryside. This paper employs a ZVS method based on LC
resonance of the inverter at primary side. This configuration
can reduce the number of power conversion and does not
require a bulky reactor and an electrolytic capacitor as a DClink capacitor. Therefore, high-efficiency, downsizing and long
lifetime can be realized. The leakage inductance of thetransformer is used as resonance inductor. However, theconventional circuit can achieve ZVS for only one leg of theinverter because the pole of transformer current is changed byoperation of the matrix converter before that leg of the inverter
turns on, as mentioned in chapter IV. In order that theconventional circuit achieves the ZVS, additional passive
components are required to form an auxiliary resonant
commutated pole inverter in the primary side. Therefore, thispaper replaces the matrix converter with an indirect matrix
converter in order to achieve ZVS without additional passive
components.
Fig. 2 shows the configuration of the proposed DC-AC
converter with an indirect matrix converter. The proposed
circuit comprises a full bridge inverter at the primary side of
the transformer and a single-phase to three-phase indirect
matrix converter at the secondary side. The proposed circuit
includes an isolated DC-DC converter. Therefore, it is obvious

idc
vpa

is
Cds

Spa

Spb

Vdc

Sau

Sav

Saw

Sua

Sva

Swa

vs

vuv

Cds

Sub

Svb

Swb

vnb

Sbu

Sbv

Sbw

Cds
vpb

L1 N1:N2

iinv

vinv
vna

Cds

Sna

Snb

U
V
W

iu

Fig. 1. Conventional isolated DC to three phase AC converter with amatrix converter in consideration of drain-source capacitances at the
primary side and transformer parameters.
idc
vpa
Spa
Vdc

irec
Cds
Spb

Cds
Dsnu
vpb
D
D
ap
bp
L1 N :N is
1

iinv

vs

vinv
vna
Sna

Cds
Snb

2

Cds
vnb

vrec

Spu Spv Spw U
vuv iu V
W

Csnu Rsnu
Dan Dbn

Snu Snv Snw

Fig. 2. Proposed isolated DC to three-phase AC converter with anindirect matrix converter. The proposed circuit achieves ZVS on all
switches.

that the inverter at the primary side achieves ZVS in the samemanner with past works about isolated DC-DC converters [6].
In addition, PDM used in the conventional circuit is applied tothe inverter part of the indirect matrix converter in order toachieve ZVS at secondary side. As a result, the proposedsystem achieves high efficiency because the proposed systemachieves ZVS is accomplished at both the primary and thesecondary inverters. In addition, the features of indirect matrix
converter which is long life time and reduced volume owing to
the absence of the large DC-link capacitor and initial charging
circuit are not required. The control method of the inverter at
primary side is the phase-shift control same as the one of theconventional circuit. Ignoring the effects of transformer
magnetizing inductance Lm and load inductance L1 forsimplicity, the condition of the transformer current Iinv_lim toachieve ZVS in each arms of the inverter at primary side isgiven by (1).

I inv _ lim ≥ Vdc

2C ds
L1

(1)

III. CONTROL METHOD OF INVERTER AT PRIMARY SIDE
Fig. 3 shows the control block diagram of the phase-shift
control for the inverter at primary side. This control iscomposed of a carrier generator, a phase delay circuit, and two
comparators. Duty ratio D of the primary inverter to adjust theinput voltage of the matrix converter is controlled by the phasedelay. This inverter outputs three-level voltage including zerovoltage by the phase-shift control. Therefore, the indirect
matrix converter achieves ZVS if the indirect matrix converter
is turned on in the zero voltage period generated by the inverter
at primary side. The phase delay is achieved by adjusting thecarrier delay time TPD given by (2).

TPD =

D
2 f c _ inv(2)

where, fc_inv is the carrier frequency of the inverter at primaryside. In addition, the designing for the dead-time is importantbecause it is necessary to discharge the drain-source
capacitances during the dead-time period. In this paper, thedead-time tdead1 is given by (3) according to [14].

Fig. 3. Control block diagram of the inverter at primary side. This diagram
is based on a phase-shift control.

Inverter voltage vinv [V]
200
0
-200

t dead 1 =π
2

2 L1C ds

40

(3)

Transformer current iinv [A]20pole of transformer
current changes

0-20

IV. MODULATION METHOD OF INVERTER AT SECONDARY SIDE

-40

A. Problem of conventional circuit
The conventional circuit can only achieve ZVS at one legof the primary inverter. In this section, the reason of thisproblem is explained.

200

Fig. 4 shows the simulation result of the conventional
circuit. It should be noted that PDM in [11] is used as themodulation method of the matrix converter. This PDM
commutates the matrix converter switches during the zerovoltage period of the output voltage of the inverter at primaryside. This achieves ZVS for all switches of the matrix
converter. On the other hand, it is understood from Fig. 4 thatthe drain-source capacitance of Snb is discharged immediately
after the output voltage of the inverter becomes zero because
the pole of the transformer current is negative when Snb turns
on. As the result, Snb achieves ZVS because the terminal
voltage of vnb dropped zero. However, after a switching of thematrix converter, the pole of the transformer current changes
from negative to positive. Thus, the terminal voltage vpa does
not drop zero because the drain-source capacitance of Spa is notdischarged before Spa turns on. Therefore, Spa cannot achieve
ZVS. The same problem occurs when the pole of thetransformer current changes from positive to negative.
Therefore, if the matrix converter is applied to the converter atsecondary side, only one leg of the primary inverter at primaryside can achieve ZVS. In this paper, indirect matrix converter
is applied to the converter at secondary side in order to achieve
ZVS in both legs of the inverter at primary side.
B. Operation principle of isolated DC-AC converter withindirect matrix converter
Fig. 5 shows simulation waveforms of the proposed circuit.
It is understood from Fig. 5 that, in the proposed circuit, thepole of the transformer current does not change during zerovoltage period. This is because the pole of input current of the

1.0
0.5
0.0

Gate signal of Spa at the inverter
Terminal voltage vpa [V]Hard switching

100
0
1.0
0.5
0.0

Gate signal of Snb at the inverter
Terminal voltage vnb [V]

ZVS

200
100
0
1.0
0.5
0.0
1.0
0.5
0.0
1.0
0.5
0.0

Gate signal of Sau at the matrix converter
Gate signal of Sav at the matrix converter
Gate signal of Saw at the matrix converter
1.0 s

Fig. 4. Inverter waveforms, terminal voltages and gate signals of
MOSFETs with the conventional circuit in simulation. Spa of the inverter at
primary side cannot achieve ZVS because a pole of the transformer current
is changed by the matrix converter.

secondary inverter is always kept positive by the operation of
the rectifier at secondary side. Therefore, the pole of thetransformer current does not depend on the switching of theinverter part of the indirect matrix converter. The current poleis determined by the provided voltage of transformer leakage
inductance. In other words, the pole of the transformer current
depends on the output voltage of the primary inverter, and thepole changes only after a zero voltage period. As the result, thedrain-source capacitances of Snb and Spa are discharged before
Snb and Spa turn on and ZVS is achieved in both legs.

The input current at secondary inverter is positive, whenpower factor of load is over 0.866. In case of negative, the ZVS
condition at the primary inverter cannot be satisfied. However,
the energy storage systems as mentioned as applications in thispaper achieve ZVS because it is operated at the unity power
factor. When the output of the inverter at the secondary side iszero vector periods, the primary current of the transformer
becomes 0 A. Therefore, the condition for achieving ZVS
calculated by (1) is not achieved. The pole of the transformer
current at conventional circuit depends on switching of thematrix converter at secondary side. As a result, theconventional circuit cannot achieve ZVS on one leg of theinverter at primary side.
C. Modulation method for secondary inverter of indirect
matrix converter
The PDM is applied to the inverter at secondary side. The
PDM provides a sinusoidal output voltage by adjusting thedensity of high frequency input voltage pulses of the inverter atsecondary side. In addition, the inverter at secondary sideachieves ZVS by synchronizing the gate pulses with the zerovoltage period of the input voltage. Thus, the PDM is suitable
for the proposed circuit.
Fig. 6 shows the control block diagram of a PDM for the
inverter part of the indirect matrix converter. This control iscomposed of a space vector modulation (SVM), a clock (CLK)
generator for the PDM, a delay (D-FF). In order to generate thegate signal by the PDM, the D-FF is used to synchronize thegate pulses generated by the SVM with the zero voltage
periods of the input voltage of the inverter at secondary side.
Zero voltage periods of the inverter at primary side aredetermined by condition of the upper and lower arm of Aphase and B-phase respectively. Hence, the CLK to drive the
D-FF is synchronized with the zero voltage periods generated
by the phase-shift control. As the result, the secondary inverter
achieves ZVS simply by the PDM.
D.Relationship between the leakage inductance and thesnubber loss
The leakage inductance of the transformer and the drainsource capacitance of the primary MOSFETs are used in orderto achieve ZVS. From (1), the area which achieves ZVS isextended with increasing the leakage inductance. However, thecurrent path followed to the DC link is blocked by zero vector
periods of the SVM signal at the secondary inverter withindirect matrix converter. When the SVM signal is zero vector
periods, the DC link is opened. Therefore, the surge voltage
occurs by stored energy in the leakage inductance when thecurrent of leakage inductance is blocked.
In order to suppress the surge voltage of switches, asnubber circuit is connected to the DC link or the switches inparallel. The snubber circuit consists of a snubber diode, asnubber capacitor and a snubber resistor. Therefore, thesnubber loss occurs in the snubber resistor.
Hence, snubber loss increases with the increasing theleakage inductance while the area which achieves ZVS of theinverter at primary side is extended.

Inverter voltage vinv [V]
200
0
-200
40
20
0

Transformer current iinv [A]pole of transformer
current changes

-20
-40
1.0
0.5
0.0

Gate signal of Spa at the inverter
Terminal voltage vpa [V]

ZVS

200
0
1.0
0.5
0.0
200

Gate signal of Snb at the inverter
Terminal voltage vnb [V]
ZVS

0
1.0
0.5
0.0
1.0
0.5
0.0
1.0
0.5
0.0

Gate signal of Sau at the matrix converter
Gate signal of Sav at the matrix converter
Gate signal of Saw at the matrix converter
1.0 s

Fig. 5. .Inverter waveforms, terminal voltages and gate signals of
MOSFETs with the proposed circuit in simulation. The proposed
converter achieves ZVS of all switches on the inverter at primary side.

Fig. 6. Control block diagram of the inverter on indirect matrix
converter. This diagram is based on a PDM and achieves ZVS on the
inverter at secondary side.

V. EXPERIMENTAL VERIFICATIONCONVERTER

OF

ISOLATED

DC-AC

In order to confirm the fundamental operation of the
proposed method, the proposed circuit is demonstrated with 3kW .
Table I lists the experimental conditions. The DC-AC
converter outputs a three-phase voltage of 200V and 50 Hz

with RL loads. The dead time of the primary inverter isdesigned by (3)Fig. 7 shows the measured waveforms of input and output
voltage of the matrix converter in experiment. As the result, theoutput current is sinusoidal waveform at 50 Hz.

TABLE I.

EXPERIMENTAL CONDITIONS.

Fig. 8 shows the extended waveforms of Fig. 7. It is
confirmed from Fig. 8 that the secondary voltage of thetransformer is three-level square waveform at 50 kHz, which
has the zero voltage period. This confirms the operation of thephase-shift control for the inverter at primary side. Moreover,from the output line voltage, it is understood that the density ofthe pulse is controlled by the PDM. Thus, the PDM of theindirect matrix converter is confirmed.
Fig. 9 and Fig. 10 show the gate-source voltage and thedrain-source voltage of Snb and Spa at rated load and 33% load
respectively. In Fig. 9, the gate-source voltage rises after thedrain-source voltage drops to zero due to the resonancebetween the drain-source capacitance and the leakage
inductance of the transformer. Therefore, the ZVS of theinverter at primary side is achieved. However, it is understoodform Fig. 10 that at 33% load, the ZVS of Spa is not achieved.
The reason is that because the transformer current at the 33%
load becomes 0A and this value dissatisfy the condition forachieving ZVS calculated by (1).
Fig.11 shows the gate-source voltage of the U-phase upperarm Sup and the V-phase lower arm Svn, the output line voltage.
During the zero voltage on the secondary voltage of thetransformer, U-phase upper arm Sup and V-phase lower arm Svn
are switched simultaneously. Therefore, ZVS is achieved. As
described in Fig.6, it is confirmed that the SVM signal issynchronized with the period of the zero voltage of thesecondary side voltage of the transformer.
Fig. 12 shows snubber losses against the output power at
the leakage inductance are 0.4 μH and 1.6 μH, respectively. An
air core inductor is connected to the primary side oftransformer in series. Total inductance of on the primary sideof the transformer is adjusted by varying the inductance of the
air core inductor. From the results, the snubber loss is increased
with the increasing the leakage inductance. However, theincreasing of the snubber loss is small. In addition, the snubber
loss against the variation of the output power is almost constant.
Therefore, it is confirmed that the leakage inductance isdesigned according to only ZVS condition from (1) without
considering the snubber loss.
Fig. 13 shows the efficiency characteristic with respect tothe output power with RL loads. The cross denotes theefficiency of the conventional DC-AC converter with a matrix
converter and the circle denotes efficiency of the proposed DCAC converter with an indirect matrix converter. From theresults, the efficiency of the conventional circuit is 90.3% at
the maximum point. In contrast, the maximum efficiency withthe proposed circuit is 93.0 %. As a result, the proposed circuit
improves the efficiency of the entire range by 2%. However,
the efficiencies of both converters are low at 1-kW output
power because the transformer current becomes smaller thanthe value for achieving ZVS. As a result, the switching loss ofFig. 7. Input and output waveforms of the proposed converter at the rated
power in experiment.

Fig. 8. Extended waveforms of Fig. 7.

the inverter at primary side increases at 1-kW output power due
to the incomplete ZVS.
Fig. 14 shows the loss analysis result at the maximum
efficiency point in experiment of the conventional and the
proposed circuits. From the result, the proposed method
reduces the total loss by 30.5% in comparison to theconventional circuit. In addition, the inverter loss at primaryside is reduced by 64.5%. This is because all switches of the
primary inverter achieve ZVS. Thus, the validity of the
proposed method is confirmed. However, total loss oftransformer and indirect matrix converter loss of proposed
circuit is greater than that loss of conventional circuit. This
reason is because experimental circuit which use matrix
converter in Fig. 1 as secondary inverter. By comparison withproposed circuit in Fig.2, experimental circuit at secondary sideincrease two switching devices on current path. Hence, total
losses at secondary side are same loss as conventional circuit inconsideration of the conductor losses.
VI.

Fig. 9. The gate to source voltage and drain to source voltage of Spa and Snbof the inverter at primary side on rated power.

CONCLUSION

In this paper, in order to achieve high efficiency without
any additional passive components, a ZVS method for theisolated DC to three-phase AC converter using an indirect
matrix converter at secondary side of the transformer is
proposed. The proposed method achieves ZVS of all switcheson the primary inverter by applying a phase-shift control to theprimary inverter. On the other hand, the inverter part for theindirect matrix converter achieves ZVS by using the PDM
based on SVM. Furthermore, experiments were conducted toverify the validity of the proposed method. As the result,snubber loss against the change output power is almost
constant. Therefore, the leakage inductance is designed
according to only ZVS condition. The proposed circuit
improves the efficiency of the entire range by 2%. As a loss
analysis result, the proposed method reduces the total loss by
30.5% in comparison to the conventional circuit.

Fig. 10. The gate to source voltage and drain to source voltage of Spa and Snbof the inverter at primary side on 33% rated power.

In the future work, the prototype circuit will be connectedto the grid and evaluated in experiment.

Fig. 11. The gate to source voltage of Sup and Svn of the inverter atsecondary side.

REFERENCES

Leakage inductanceH
7.5

Leakage inductance
0.4 H

7.0

Carrier frequency
of inverter fc_inv =50 kHz

6.5

Carrier frequency ofmatrix converter fc_mc =5 kHz

6.0

500

0

1000

1500

2000

2500

Output power[W]Fig. 12. Relationship between snubber loss and leakage inductanceWith indirect matrix converter

94
92
90
88
86

With matrix converter

84
82

R-L load experiment

80
0

500

1000

1500

2000

2500

3000 3500

Output power[W]Fig. 13. Efficiency characteristics of the conventional and the
proposed converters

Conventional
matrix converter type450
387.0W

400
350
Power loss [W]

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8.0

[1]

300

Proposedindirect matrix
converter typeTransformer andmatrix converter
loss

269.0W

250
200

94.5W
7.8W

150
100
50
0

Inverter loss

266.2W

20.6W

Snubber loss
100.2W

3043

148.3W

3085

Output power [W]Transformer andindirect matrix
converter loss

Fig. 14. Loss analysis results of the conventional and the proposed
converters at 3 kW-load.