Optimum Inductance for Isolated DC to Three-phase AC Converter
using Indirect Matrix Converter
Shunsuke Takuma * Hayato Higa * Koji Orikawa * Jun-ichi Itoh**Nagaoka University of Technology
This paper proposes a Zero Voltage Switching (ZVS) method for an isolated DC to three-phase AC converter using an indirectmatrix converter at the secondary side converter. The secondary side inverter employs the pulse density modulation in order toachieve ZVS on all switches at the secondary side. On the other hand, ZVS at the inverter side at the primary side is achieved bythe leakage inductance of the transformer. However, there is a trade-off relationship between the switching loss and the sum of thesnubber loss at the secondary side and the copper loss of an additional inductor connected to the transformer in series for ZVS. In
this paper, the efficiency characteristic in terms of the leakage inductance is evaluated. From the experimental results, the validityof the proposed circuit is confirmed by a 3-kW prototype.
Keywords Indirect matrix converter, Zero voltage switching, DC-AC converter
Snubberirec circuit

1. Introduction

Sap

Energy storage systems require a DC-AC converter forconnecting the grid and batteries. Such converters necessary to beisolated by a transformer in order to protect from failures and noises.
However, the transformer for commercial frequency is bulky andheavy. Therefore the high frequency AC link converter has been
researched for down-sizing the transformer [1]-[2].
The authors have proposed the isolated DC-AC converter which
adopts the indirect matrix converter using the pulse density
modulation in order to improve the efficiency [3]. This proposed
circuit achieves ZVS by using the pulse density modulation.
The leakage inductance of the transformer is required to achieve
ZVS at primary inverter. However, the effect of varying the leakage
inductance for ZVS range has not evaluated. In this paper, theefficiency characteristic in terms of the leakage inductance isevaluated.

2.

Relationship between leakage inductance andZVS

Fig. 1 shows the circuit configuration of the DC-AC converterwith the indirect matrix converter. This circuit is divided into thefull bridge inverter which adopts the phase shift control at theprimary side of the transformer and the indirect matrix converter atthe secondary side.
PDM used in the conventional circuit is applied to the indirect
matrix converter in order to achieve ZVS at the secondary side. Asa result, the proposed system achieves high efficiency because boththe primary and the secondary inverters of the proposed systemachieves ZVS. Ignoring the effects of the transformer magnetizing
inductance Lm and the load inductance L for simplicity, thecondition of the transformer current Iinv_lim which achieves ZVS ineach arm of the inverter at the primary side is given by (1).

I inv _ lim  Vdc

2Cds
Lt

(1)

where, Vdc is the input DC voltage, Cds is the drain-source
capacitance of MOSFET in the inverter at the primary side, and Lt

Scp Sdp

Sbp
Cds

isv1
SanSbnCds

Sup Svp Swp

Cds
Ll

VDC

PU

Dsnu

VW

v2
N1:N2

Scn Sdn

Csnu Rsnu

Cds
N

Sun Svn Swn

Fig.1. DC-AC converter with indirect matrix converter.
Table 1. Experimental conditions.
Element
Symbol Value
Input DC voltage
Vdc
200 V
Output line voltage
Vrms
200 V
Carrier frequency of inverter
fc_inv
50 kHzCarrier frequency of indirect matrix converter fc_imc
5 kHz
Output frequency
Turn ratio
Duty of primary voltage
Load resistanceLoad inductance
Rated power
Drain to source capacitance of MOSFET
Winding resistance
Leakage inductance
Magnetizing inductance
Dead time of primary inverter
Dead time of secondary converter

fout
N1:N2
DRL
Cds
R1
L1
Lm
tdead1tdead250 Hz
1:2
0.9 p.u.
12.9 W
3 mH
3 kW
2.94 nF
39.0 mΩ0.40 µH
4.58 mH
125 ns
100 nsis the sum of the leakage inductance in the transformer and theinductance of an air-coil inductor connected to the primary side of
the transformer in series.
From (1), it is understood that ZVS range is extended byincreasing the leakage inductance. On the other hand, the increaseof the snubber loss is small even though the total inductance value
Lt is changed. From calculations results, the difference of thesnubber loss between the total inductance of 0.8 H and 2.4 His only 1.2 W at the rated output power. Therefore, the efficiency inthe heavy load region is not affected by the leakage inductance.

Experimental Results

Table 1 shows the experimental conditions. The experimentswith a prototype circuit are conducted in order to confirm the ZVS.
By inserting an air-coil inductor, total inductance whichcorresponds to the leakage inductance is changed. The inductanceof air-coil inductor is 0.4 H and 2.0 H while the original leakage
inductance is 0.4 H.
Fig. 2 (a), (b), (c) and (d) show the gate-source voltage and thedrain-source voltage of Sap and Sbn when the total inductance whichcorresponds the leakage inductance is 0.8 H and 2.4 H,
respectively. When the total inductance is 2.4 H, the minimum
current which achieves ZVS is smaller than that of when the total
inductance is 0.8 H. From Fig. 2(a) and (b), the extension of area
witch achieves ZVS is confirmed.
Fig. 3 shows the efficiency characteristic with two different total
leakage inductances. In order to minimize the effect of copper loss
in the air-coil inductor, the length of the air-coil inductor is same.
Fig. 4 shows the efficiency characteristic at rated output powerof 3 kW. The iron loss of transformer is changed due to the voltagedrop on the additional inductor of the transformer. Therefore, theefficiency is different between two conditions. However, themaximum difference of the efficiency is only 0.3%. As aconclusion, the efficiency characteristic is not changed by the total
inductance which corresponds to the leakage inductance.
Fig. 5 shows the snubber loss at the secondary side of thetransformer. From the results, the snubber loss increases with theincreasing the total inductance. However, the increase of thesnubber loss is small against the variation of the output power.
Hence, the change of the snubber loss does not affect the efficiency
of prototype circuit.

Gate-source voltage 25V/div

Gate-source voltage 25V/div

Hardswitching

ZVS

400ns/div

400ns/div

Drain-source voltage 100V/div

Drain-source voltage 100V/div(a)Sap (Total inductance: 0.8 H) (b)Sap (Total inductance: 2.4 H)
Gate-source voltage 25V/div
Gate-source voltage 25V/div

Hardswitching

ZVS
400ns/div

400ns/div
Drain-source voltage 100V/div

Drain-source voltage 100V/div(c)Sbn (Total inductance: 0.8 H)(b)Sbn (Total inductance: 2.4 H)Fig.2. Gate-source voltage and drain-source voltage of Sap and Sbn ofinverter in primary side at 2.1 kW.

96.0
Total inductance
2.4 H

95.5
Efficiency [%]

3.

95.0
Total inductance
0.8 H

94.5
94.0
93.5

0

1000

2000

3000

Output power[W]Conclusion

Fig.3. Efficiency characteristics.

This paper experimentally verified the effect on the efficiency
characteristic by total inductance which corresponds to the leakage
inductance of the transformer. The minimum value of the inverter
output current which achieves ZVS in primary side inverter isextended by increasing the total inductance. From the experimentalresults, it is confirmed that ZVS is achieved at the output power of
2.1 kW when the air-coil inductor of 2.0 H is inserted. Theswitching loss at the primary side is decreased by ZVS. The
efficiency the rated output power is not affected even though thetotal inductance is changed because the change of the snubber loss
is very small compared to the output power.
In the future work, the ZVS range at the primary side of theproposed circuit in terms of the output power will be derived.

96.0

Efficiency [%]4.

Carrier frequency of inverter

fc_inv =50 kHz

95.5

Carrier frequency ofindirect matrix converter

fc_imc = 5 kHz

95.0

Linearization

94.5
94.0
Rated output power = 3 kW

93.5
0.0

0.5

1.0

1.5

2.0

Total inductance value[H]

Fig.4. Comparison of efficiency at rated power.

[1]

[2]

[3]

[4]

K. Inagaki, T. Furuhashi, A. Ishiguro, M. Ishida, S. Okuma, Y. Uchikawa :“A Waveform Control Method of AC to DC converters with High-Frequency
Links”, IEEJ Trans. D,Vol.110, No.5, pp.525-533 (1990)
K. Inagaki, S. Okuma : “A High Frequency Link DC/AC Converter using aThree Phase Output PWM Controlled Cycloconverter”, IEEJ Trans.
D,Vol.112, No.6, pp.545-552 (1992)
S. Takuma, R. Osima, H. Takahashi, K.Orikawa, J.Itoh: "Isolated DC toThree-phase AC Converter using Indirect Matrix Converter with ZVSApplied to All Switches", ECCE2015, Vol. , No. , pp. 4678-4684 (2015)
Y. Nakata, J. Itoh : “Pulse Density Modulation Control using Space Vector
Modulation for a Single-phase to Three-phase Indirect Matrix Converter”,
IEEE ECCE 2012, Raleigh, P3905, pp. 1753-1759 (2012)

Snubber loss [W]References

109876543210☐Total inductance = 2.4 H＋Total inductance = 1.6 H●Total inductance = 0.8 H
Carrier frequency of inverter fc_inv =50 kHz
Carrier frequency offc_imc = 5 kHz
indirect matrix converter
1000
2000
3000
Output power[W]Fig.5. Comparison of snubber loss

2.5