Experimental Verification of High Frequency
Link DC-AC Converter using Pulse Density
Modulation at Secondary Matrix Converter.
Jun-ichi Itoh, Ryo Oshima and Hiroki Takahashi
Dept. of Electrical, Electronics and Information Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
ryo_oshima@stn.nagaokaut.ac.jp

Abstract— This paper verifies an isolated DC-AC power
converter using a single phase to three phase matrix
converter in experiment. A matrix converter does not
require the large reactors and the large smoothing
capacitors in a DC-link part. Furthermore, the proposed
control method enables zero voltage switching of the matrix
converter by implementing a phase shift control on the
primary inverter and a pulse density modulation on thesecondary matrix converter. In this paper, the fundamental
operation of the converter is demonstrated by theexperiment. From the experimental results, the total
harmonic distortion in the output voltage is less than 5% in
the entire range. In addition, a maximum efficiency of
90.9 % is achieved at an output power of 1.5kW.
Keywords— dc-ac converter, high frequency link
converter, pulse density modulation, zero voltage switching.

I.

INTRODUCTION

Recently, from the view point of global warming andenvironmental problems, the renewable energy systems
are focused on. However, in a renewable energy system,
especially a wind turbine and a photovoltaic cell, a powerfluctuation occurs owing to the meteorological conditions.
Therefore, an energy storage system using a battery isnecessary in order to suppress the power fluctuation.
The battery energy storage system requires a 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 failureand noise. However, an isolation transformer designed
for the commercial frequency is bulky and heavy. Hence,in order to reduce the volume of the isolation transformer,
a high frequency AC link converter has been researched.
In past works, two typical high frequency link DC-AC
converter topologies have been proposed. First one
consists of a high frequency isolated DC-DC converter
and a three-phase inverter for the grid connection [1-4].
This circuit configuration reduces the volume of theisolation transformer because the full bridge inverter
operates in the DC-DC converter at the high frequency.
However, the DC link capacitors between the rectifier

and three-phase inverter are bulky in order to smooth theDC link voltage. Thus, it is difficult to reduce the volumeof the system and to realize long lifetime. Moreover, thetotal efficiency decreases because of three times power
conversion.
Second one is the high frequency link converter with amatrix converter for the secondary power conversion inorder to reduce the volume of the capacitor [5-7]. This
circuit topology has advantages as follows: (i) the
number of power conversion is reduced to two times.
Thus, the efficiency is higher than the former type. (ii)
The system achieves smaller size and long lifetime
because the DC-link capacitor is not required. However,when PWM (pulse width modulation) control is used tothe matrix converter in the secondary side, the switchingloss of the matrix converter is increased because of a hardswitching. Moreover, the conduction loss of the inverter
is increased because the freewheeling current flows at theinverter while the matrix converter outputs zero vectors.
This paper proposes an isolated DC-AC converter
which adopts a matrix converter with pulse density
modulation (PDM) and the suppression control offreewheeling current. By using the PDM, zero voltage
switching (ZVS) is achieved. Then, the fundamental
operation of the proposed circuit is demonstrated in thesimulations and the experiments. The remainder of thispaper is organized as follows. First, the circuit
configuration of the high frequency link converter is
described. Second, the control scheme is explained indetail. Third, a problem of freewheeling current occurs at
the primary inverter and the suppression control offreewheeling current are explained. Fourth, afundamental operation of the proposed method is shownin simulation. Finally, the operation of the proposed
circuit is demonstrated under the condition of an input
DC voltage of 200 V and an AC link frequency of 50
kHz. In addition, the efficiency and the total harmonic
distortion (THD) of the output voltage are evaluated inorder to clarify the validity of the proposed system.

II.

CIRCUIT CONFIGURATION

Fig. 1 shows the configuration of the conventional
circuit. The conventional circuit comprises a bidirectional
DC-DC converter with an isolation transformer such as
dual active bridge converter [8-9]. However, the twostage topology requires the bulky DC capacitors in orderto smooth the DC link voltage.
Fig. 2 shows the main circuit configuration of the
proposed DC-AC converter with the matrix converter.
The proposed circuit comprises a full bridge inverter withphase shift control at the primary side of the transformer
and the single-phase to three phase matrix converter at
the secondary side. It is noted that the PDM is applied tothe matrix converter only. The proposed system achieves
high efficiency because the number of the power
conversions is reduced owing to the matrix converter. In
addition, the advantages of the matrix converter are long
lifetime and the reduced volume owing to the absence ofthe large DC-link capacitor and an initial charge circuit.
However, it is difficult to reduce the switching loss due tothe hard switching when the conventional PWM method
is applied to the matrix converter.
In order to reduce the switching loss of the matrix
converter by implementation of ZVS, the PDM is applied
to the matrix converter. In addition, for simplicity of the
PDM, the primary inverter provides three-level voltage
including zero voltage with the phase shift control. As aresult, the matrix converter achieves ZVS when theswitches turn in the zero voltage periods and acommutation scheme of the matrix converter is simplified.
III.

TPD 

N1:N2

Vbat

D
(1)2  f c _ inv

where, fc_inv is carrier frequency of the primary inverter.
B. Pulse density modulation method based on space
vector modulation
Fig. 5 shows a control block diagram of a PDM for thematrix converter. This control is composed of space
vector modulation (SVM), a clock (CLK) generator for

U
V
W

vs

vp

Isolation Rectifier
Inverter transformer

InverterFig.1. High frequency link DC-AC converter with rectifier andinverterSap Sbp

Sup Svp Swp

N1:N2

Vbat

vuv

vs

vp

San Sbn

U
VW

Sun Svn Swn

Isolation
1f-3f matrix
Transformer
converter
Fig.2. High frequency link DC-AC converter with matrix converter
Inverter

10Carrier 1
Carrier

+

Sap
San

-

Phase Carrier 2
delay

Command
[0.5]

+

Sbp
Sbn

-

Fig.3. Control block diagram of the inverter.

CONTROL STRATEGIES

A. Phase shift control
Fig. 3 shows a control block diagram of the phase shift
control for the primary inverter. This control is composedof a carrier generator, a phase delay circuit, and two
comparators. Duty ratio D of the primary inverter toadjust the input voltage of the matrix converter iscontrolled by the phase delay.
Fig. 4 shows an operation principle of the phase shift
control for the primary inverter. The inverter outputs
three-level voltage including zero voltage by the phaseshift control. Therefore, the matrix converter achieves
ZVS if the matrix converter turns in the zero voltage
period generated by the primary inverter. Actually, thephase delay is achieved by adjusting carrier delay time
TPD given by (1).

DC-link
capacitor

DC-DC converter

Carrier 1
Zero voltage period
Carrier 2

Invertergate pulse

Sap
San
Sbp
Sbn

Primary
voltage vp

D

Fig.4. Operation principle of the phase shift control for the primary
inverter.
Outputvoltage
SVM signal
PDM signal
reference u
Sup,Svp,Swp
D
Q
v
3
3
3
Space
D-FF
Sun,Svn,Swnw
Vector3
1
Modulation
Switchingsignal generator
0
Carrier
CLK CLK
Double edge
Sbp, Sbn
generator
detection
Fig.5. Control block diagram of the matrix converter.

the PDM, a delay (D-FF) and a switching signal
generator. In order to generate the gate signal by the
PDM, the D-FF is used to quantize the duty references
generated by the SVM. Moreover, the CLK to drive the
D-FF is synchronized with the zero voltage periods
owing to the phase shift control in order to achieve the
PDM and ZVS easily.
Fig. 6 shows operation waveforms of the PDM whichenables ZVS of the matrix converter. The PDM controls
the density and the pole of the constant width pulse. In
addition, these pulse signals are used as the minimum
unit of the output voltage waveform [10]. It should be
noted that the input voltage of the matrix converter(secondary voltage of the transformer) is high frequency
square waveform. Therefore, a half cycle of the input
voltage is used as one pulse of the PDM. Then, the halfcycle period of the input voltage is detected easily by thegate pulses Sbp and Sbn of the primary inverter. As a result,the PDM and the ZVS of the matrix converter are
implemented without switching loss by the control
scheme in Fig. 5.

Secondaryvoltage vsD

Zero Voltage Switching

CLK
SVM signal
PDM signal
Matrixconvertergate pulse

Sup
Sun
Svp
Svn
Swp
Swn

Outputvoltage vuv
Fig.6. Operation principle of the pulse density modulation for thematrix converter.

Sap Sbp

Sup Svp Swp

N1:N2

Vbat
vs

vp

SUPPRESSION CONTROL OF FREEWHEELINGCURRENTThis chapter describes a problem and the principle of afreewheeling current mode at the primary side. In
addition, a suppression control of freewheeling current ispresented in order to improve system efficiency.
Fig. 7 shows operation modes of the DC-AC converter.
The red line (state 1) in Fig. 7(a) shows a current pathwhen the primary inverter outputs positive voltage andthe matrix converter selects (100) vector. It should be
noted that this case is not the freewheeling current mode.
In the state 1, the transformer current contributes toprovide the DC battery power to the load because theprimary inverter outputs positive voltage.
In Fig. 7(b), the red line shows a current pathway
when the matrix converter chooses a vector except thezero vector though the primary inverter outputs zerovoltage. This paper defines this mode as the freewheelingcurrent mode. The problem of the freewheeling current
mode means increasing conduction loss of the primary
inverter and copper loss of the transformer. The principleof the increasing losses is following. In this state, the DC
battery power is not transmitted to the load because theprimary inverter outputs zero voltage. However, theprimary and the secondary current of the transformer
flow since the matrix converter selects a vector not thezero vector and the load is inductive. As a result, acurrent pathway in the primary side is constructed and the
conduction loss of the primary inverter and the copper
loss of the transformer are generated although thetransmitted power from the DC battery to the load is zero.
Therefore, the freewheeling current mode needs to be
suppressed in order to improve the system efficiency.
Fig. 7(c) shows the principle of the suppression
method of the freewheeling current mode. The

VW
Sun Svn Swn

San Sbn

IV.

vuv

U

(a) The output current pathway when the DC-AC converter supplies
electric power from the source to the RL load. (State 1)

Sap Sbp

Sup Svp Swp

N1:N2

Vbat
vs

vp

vuv

U
V
W
Sun Svn Swn

San Sbn(b) The current pathway when the matrix converter supplies electric
power while the inverter outputs zero vector. (State 2)

Sap Sbp

Sup Svp Swp

N1:N2

Vbat
vp

vs

vuv

U
V
W

San Sbn

Sun Svn Swn(c) The current pathway after changed the output current pathway.
(State 3)
Fig.7 Switching transition of the DC-AC converter

TABLE ISIMULATION AND EXPERIMENTAL CONDITIONS
Element
SymbolBattery voltage
Vbat
Carrier frequency of inverter
fc_inv
Carrier frequency of matrix converter
fc_mc
Modulation frequency of matrix converter
fm_mc
Turn ratio
N1:N2
Duty of primary voltage
D
Load power
Pload

Value
200 V
50 kHz
5 kHz
50 Hz
1:2
0.9 p.u.
3 kW

suppression method focuses on the output voltage in thefreewheeling current mode. In Fig. 7 (b), the output
voltage is zero because the primary inverter outputs zerovoltage though the matrix converter chooses a vector
except the zero vector. Therefore, the freewheelingcurrent mode is equivalent to the zero vector of thematrix converter. In addition, if the matrix converter
selects the zero vector, the secondary current of thetransformer does not flow. It results in reducing the
conduction loss of the primary inverter and the copper
loss of the transformer. Hence, in order to prevent the
freewheeling current mode, the matrix converter should
select the zero vector while the primary inverter outputs
zero voltage such as Fig. 7 (c).

Filtered output voltage vuv [V]Output current iu [A]

0.30

time[s]Fig.8. The input and output waveforms of the secondary matrix
converter in simulation.
Secondary voltage of the transformer vs [V]SIMULATION RESULTS

Table I lists the simulation parameters. The DC-AC
converter outputs three-phase voltage of 200V and 50 Hz
for the grid connection. However, the simulation is
implemented with a RL load for simplicity.
Fig. 8 shows the input and output waveforms of thematrix converter with the proposed method in simulations.
It should be noted that the cut-off frequency of the low
pass filter to observe the output voltage waveform is 1
kHz. As shown in figure, it is confirmed that the output
current of the matrix converter is sinusoidal waveform.
Then, the output current THD is 2.79%.
Fig. 9 shows the enlarged waveform of Fig. 8. The
secondary voltage of the transformer is three-level
voltage of 50 kHz. In addition, the output voltage
waveform consists of the secondary voltage pulses of thetransformer and the density of the pulses is controlled by
the PDM. Thus, the operation of the PDM in the matrix
converter is confirmed.
Fig. 10 shows the efficiency characteristic for the
output power in simulation. It is noted that this loss
simulation calculates only semiconductor losses on the
proposed circuit. The efficiency is 97.8% at the
maximum point. Moreover, the efficiency is greater than
95% in the entire range. Therefore, it is confirmed thatthe high efficiency is obtained by ZVS.
VI.

Output voltage vuv [V]Output voltage vuv [V]Filtered output voltage vuv [V]Output current iu [A]time[s]Fig.9. Enlarged waveforms of Fig.8.

10099
Efficiency[%]

V.

Secondary voltage of the transformer vs [V]

98
97

96
95
94
0

1000

1500 2000 2500
Output power[W]

3000

3500

Fig.10. Efficiency characteristics except the transformer obtained from
R-L load experiment that is subjected to the output power insimulation.
Input voltage Vbat 250V/div

EXPERIMENTAL RESULTS0

A. Fundamental operation
In order to confirm the fundamental operation of the
proposed method, the proposed circuit is demonstrated
with the 3-kW prototype circuit in experiment. The
experimental conditions are same as the simulation.
Fig. 11 shows the input and output waveforms of thematrix converter in experiment. As the result, the output
current is sinusoidal and the output current THD is
obtained by 4.28%.
Fig. 12 shows the enlarged waveforms of Fig. 11ff.
From the result, it is confirmed that the secondary voltageof the transformer is 50kHz and three-level, which has

500

Secondary voltage of the transformer vs 500V/div0
Output voltage vuv 500V/div0
Output current iu 20A/div
0
10ms/div

Fig.11. Experimental waveforms of input and output of the DC-AC
converter.

B. Effectiveness of the suppression control offreewheeling current
Fig. 15 shows the primary voltage and current of thetransformer regarding the suppression control of thefreewheeling current mode in experiment. Fig. 15 (a)shows a result without the suppression control and Fig.
15 (b) shows a result with the control. It should be notedthat the duty ratio D of the primary inverter is set to 0.5
p.u. to observe its difference easily. From Fig. 15 (a),the primary current flows while the primary inverter
outputs zero voltage because of the freewheeling current
mode. However, as shown Fig. 15 (b), the primary
current of the transformer does not flow during the zerovoltage period because the suppression control forces
the matrix converter to select the zero vector while theprimary inverter provides zero voltage. The voltage andcurrent fluctuation in Fig. 15 is caused by a LC
resonance due to the capacitance between primary sideand secondary side of the transformer and wiring
inductance.
Fig.16 shows the efficiency characteristic withrespect to the output power with RL loads. A dotted line
shows the efficiency characteristic with the suppression
control of freewheeling current and the solid line shows
efficiency characteristic with the suppression method.
From the results, the efficiency without the suppression
control of freewheeling current mode is 89.8% at
maximum point. However, the suppression control offreewheeling current improves the efficiency. The
maximum efficiency with the suppression control is
obtained by 90.9 %. Especially, the suppression control ismore effective in light load region because the exciting
current of transformer is reduced. Therefore, thesuppression control of the freewheeling current improves
the efficiency of 4.4% at a maximum. Thus, the validityof the suppression control of the freewheeling current
mode is confirmed.
Fig.17 shows loss analysis results at the maximum
efficiency point and the rated power in experiment withthe suppression control of freewheeling current. Then, theInput voltage Vbat 250V/div
Secondary voltage of the transformer vs 500V/div

00

Output voltage vuv 500V/div0
Output current iu 20A/div
020μs/div

Fig.12. Enlarged waveforms of Fig.10.
Gate voltage of the U-phase upper arm Sup 25V/div
0
Gate voltage of the V-phase lower arm Svn 25V/div
0
Secondary voltage of the transformer vs 500V/div0
Output voltage vuv 500V/div
04μs/div

Fig.13. Experimental waveforms when the gate signals are changed in thezero voltage period.

12
Output voltage THD[%]the zero voltage period. In addition, the output voltage
waveform consists of the secondary voltage pulses of
the transformer. Moreover, the density of the pulse iscontrolled by the PDM. Thus, the PDM of the matrix
converter is confirmed.
Fig. 13 shows the ZVS operation of the matrix
converter in the proposed system. From the results,
when the secondary voltage of the transformer is zerovoltage, the switching of the matrix converter isimplemented and the ZV is achieved.
Fig. 14 shows output voltage THD characteristic forthe output power. As shown in Fig. 13, the output
voltage THD is 3.76% at the minimum point and lessthan 5% all of the output power range. Therefore, theproposed system can be connected to the grid if theinterconnection inductors are set to several percent of
the rated power capacity.

10

8
6
4
2
0
0

500

1000

1500 2000 2500
Output power[W]

3000

3500

Fig.14. THD characteristics of output voltage obtained from R-L load
experiment that is subjected to the output power.

rated power is 3kW and the maximum efficiency is
obtained at 1.5kW.
It should be noted that matrix converter loss includes
the snubber loss. Then, snubber voltage is 880V at the
rated power because the snubber absorbs the leakage
inductance energy of the transformer and commutation
failure of the matrix converter. As a result, the snubber
loss is obtained by 12.9W and accounts for 35% of thematrix converter loss. However, if the commutation
sequence is modified, it is possible to reduce the snubber
loss because the snubber voltage increase is suppressed.
Consequently, the efficiency improvement of DC-AC
converter will be expected.
On the other hand, the main loss of the DC-AC

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Primary voltage of the transformer 250 V/div

０

Primary current of the transformer 20 A/div

4µsec/div(a) Without the suppression control of freewheeling current.
Zero voltage period０Primary voltage of the transformer 250 V/div

０

Primary current of the transformer 20 A/div

4µsec/div(b) With the suppression control of freewheeling current.
Fig.15 Experimental waveforms of primary voltage and current of
the transformer with the suppression control of freewheelingcurrent.
With suppression control of freewheeling current
92.5

90
Efficiency[%]VII. CONCLUSION
This paper verified the isolated DC-AC converter
using a matrix converter in simulations and experiments.
The matrix converter in the proposed system employs the
PDM and achieves ZVS by combination with the highfrequency inverter with the phase shift control. From thesimulation result, it is confirmed the fundamental
operation and the maximum efficiency of proposed DCAC converter of 97.8% is obtained. In addition, a 3-kW
prototype of the proposed circuit was tested. From theexperimental results, the ZVS operation and the PDM of
the matrix converter were confirmed. Moreover, theoutput voltage THD is less than 5% in the entire range.
Besides, the efficiency characteristics with respect tothe output power is evaluated. In addition, a loss analysisof the experimental result is implemented. A maximum
efficiency of 90.9 % is achieved at 1.5kW output powerwith the suppression control of freewheeling current. It is
confirmed that the efficiency of 1 % is improved byapplying the suppression control of freewheeling current.
And, from the loss separation results, the inverter loss isthe main loss of the DC-AC converter.
In the future work, in order to achieve the highefficiency of DC-AC converter, it will be performed thesoft switching at the inverter. Finally, the prototype
circuit will be connected to the grid and evaluated inexperiment.

Zero voltage period

87.5

Without suppression controlof freewheeling current

85
82.5
80

77.5
75
0

500

1000

1500 2000 2500
Output power[W]

3000

3500

Fig.16 efficiency characteristics of the DC-AC converter obtained
from R-L load experiment that is subjected to the output power.

400
350

Inverter loss

300
Loss [W]converter is the inverter loss at both maximum efficiency
point and the rated power. Therefore, it is necessary to
reduce the inverter loss in order to improve the efficiencyof the DC-AC converter. As a method to increase theefficiency, soft switching technique will be introduced in
the future.

250
200Transformer loss

150
100
Matrix converter loss

50
0
1590
3017
Output power[W]Fig.17 Loss analysis results of the DC-AC converter with the
suppression control of freewheeling current.

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