Two-step commutation
for Isolated DC-AC Converter with Matrix Converter
Shunsuke Takuma*, and Jun-ichi Itoh
Department of Electrical, Electronics and Information Engineering, Nagaoka University of Technology, Nagaoka, Japan*E-mail: takuma_s@stn.nagaokaut.ac.jp

Abstract— This paper proposes a two-step commutation
method for a three-phase-to-single-phase matrix converter.
Conventional two-step commutation cannot be applied at all
operation regions because a commutation failure due to thedetection error of grid voltages still occurs. In the proposed
two-step commutation, by modulating only one of two
devices in a bi-directional switch and utilizing a zero vector
to let the switches naturally turn-off, the commutation
failures are avoided completely regardless of the voltage
detection error. From experimental results, it is confirmedthat the proposed two-step commutation has always safety
operation to avoid commutation failure. The input current
THD at 10 kW with the proposed two-step commutation is
improved by 37% in comparison with the conventional
four-step commutation.
Keywords— Two-step commutation, Current direction
estimation, Commutation failure.

I.

INTRODUCTION

A lot of studies on Electric vehicles (EVs) and Plug-in
hybrid vehicles (PHEVs) have been accelerated over the
past decade. Compared to the gasoline vehicle, EVs or
PHEVs still faces one of the main challenges, i.e. thelong battery charging time. In order to solve this problem,
high-power low-profile battery chargers are required [14]. In [5-9], isolated AC-DC converters using a matrix
converter as a medium frequency AC-AC converter
connected with the transformer at the primary side havebeen proposed. The matrix converter volume is expected
to be greatly reduced compared to other topologies which
employ a buffer capacitor because the buffer capacitor in
the high-power application such as the rapid battery
charger usually has to withstand a high current, which
increases the capacitor volume.
Generally, the matrix converters are required acommutation sequence at the switching timing of thepower devices to prevent short-circuit at a voltage source
and open-circuit at inductive components. The
conventional commutation method is separated into two
types, the voltage commutation method based on the
input voltage polarity and the current commutation
method based on the output current direction [10-13].
The voltage commutation works reliably if therelationship of the input voltages is accurately obtained.

These commutation sequences are the four-step
commutation which is divided into the four steps to avoid
the open-circuit and the short-circuit. Each step is turnedon or turned-off a switch into the two bi-directionalswitches depended on the voltage polarity or the current
direction. The commutation time which is longer than theswitching speed of the switching devices is inserted
among the first-step, the second-step, the third-step andthe fourth-step. Therefore, the four-step commutation
which is the voltage commutation or the current
commutation is a complex commutation algorithm which
greatly restricts the applicable control hardware. A life
time and a reliability of the switching devices are
decreased by the commutation failure which is based on
the detection error
In order to simplify the control hardware for thematrix converter, two-step commutation methods havebeen proposed [5-11]. Commutation time in the two-step
commutation is half of that in the four-step commutation.
This results in a short commutation time with a simpler
commutation algorithm. In particular, the two-step
commutation in [11] is achieved by zero vectors which isthe switching pattern of the additional circuit outputting
the zero voltage at the input terminal. Another two-step
commutation in [6-10] uses both the voltage polarity andthe current direction for the commutation. However, themain problem of these conventional two-step
commutations is that either the additional circuit isrequired or the commutation failures still occurs at thecritical area due to a detection error of the input voltage.
A solution for this problem is that the commutation
method is switched between the conventional two-step
commutation and the four-step commutation. However,this solution increases the number of switching step andrequires the implement of the two commutation methods.
If the switching pulses are shorter than the dead-time,
next commutation sequence starts before present
commutation period has been completed and it causes
input current distortions. In the low modulation index
region, the input current is distorted by the output voltage
error due to the conventional several-step commutation.
It is necessary to reduce the number of the commutation

step in order to reduce the output voltage error.
In this paper, the two-step commutation is proposed
for a three-phase to single-phase matrix converter inorder to improve the input current total harmonics
distortion (THD) in the low modulation index region. The
output voltage error is decreased by the proposed twostep commutation due to less commutation. In addition,
the commutation failure does not occur regardless of thevoltage detection error. The original idea of this paper is
to turning-on only one of two devices in the bi-directionalswitches based on the current direction and to use a
voltage vector which let the switches naturally turn-off.
Therefore, the proposed two-step commutation is
unnecessary to switch between the conventional two-step
commutation and another commutation method toprevent the short-circuit at the critical area. The
effectiveness of the proposed two-step commutation isevaluated with a 10-kW prototype thought experimental
results.
II.

Fig. 1. Isolated AC-DC converter with three-phase-to-single-phasematrix converter.

CIRCUIT CONFIGURATION AND CONTROL METHOD

Figure 1 shows the isolated AC-DC converter with thethree-phase to single-phase matrix converter. The
proposed circuit consists of a LC filter to eliminate
switching ripple component of the input current, a threephase to single-phase matrix converter with bi-directionalswitches, a medium frequency transformer, a dioderectifier, and a smoothing inductor in the output DC side.
In particular, the three-phase grid voltage is directly
converted to medium frequency single-phase voltage by
the matrix converter. Consequently, the volume of thetransformer is significantly minimized because thistransformer is operated with this medium frequency
single-phase voltage.
III.

TWO-STEP COMMUTATION METHOD

A. Problem of conventional commutation method
Figure 2 shows the equivalent circuit at each arm of
the matrix converter. The equivalent circuit consists ofthe three voltage sources (maximum-phase-voltage Vmax,
middle phase-voltage Vmid, minimum phase-voltage
Vmin), current source which represents as the current at
the transformer, and three bi-directional switches. Figure2(b) and 2(c) show the transition situation from Vmax toVmid with the four-step voltage commutation and theconventional two-step commutation. If the actual voltage
polarity does not agree with the detection voltage
polarity, the short-circuit via the grid occurs in thecommutation state of the four-step voltage commutation
or in the steady state of the conventional two-step
commutation after turning-on Smr
B. Principle of two-step commutation
Figure 3 depicts the principle of the proposed two-step
commutation, which is divided into two modes. Figure3(a) shows the transition from an input phase to another
input phase, whereas Figure 3(b) shows the transition
from zero-vector state to an input phase. As shown in Fig.
3 (a), when the matrix converter starts to transit from(a) Equivalent circuit(b) Four-step(c) Conv. two-step

Fig. 2. Conventional commutation step; If the acutal voltage does notagree with the detection voltage, the short-circuit occur by thecommutation failure
Vmax

Initial state

Vmax

Spl SprVmid

First stepSpl SprVmid
Sml SmrVmin

Spl SprVmid

Sml SmrVmin

Snl Snr

Second step

Vmax

Sml SmrVmin

Snl Snr

Snl Snr(a) Vmax to Vmid(b) Vz to Vmax
Fig. 3. Proposed commutation sequence. The commutation step isalways two-step by proposed sequence.

Vmax-phase to Vmid-phase in case of the positive output
current, only the switch Spr is on at Vmax-phase. At firststep, only the switch Smr at Vmid-phase turns-on. Then, at
second step, the switch Spr turns-off and the current
commutates from Vmax-phase to Vmid-phase. In thiscommutation mode, the short-circuit and the open-circuit
are avoided regardless of the voltage detection error by
the modulation of only one of two devices in the bidirectional switches. Therefore, the transition from an
input phase to another input phase without any
commutation failures is achieved. The initial state is on
state of Spl and then similar switching sequence areapplied when the output current direction is negative. The
initial state of the equivalent commutation model for eacharm is express by (1)S xl = 1
S xl = 0

S xr = 0iload > 0

S xr = 1

iload < 0x = p, m, n (1)where subscript x indicates p (Vmax-phase) or m (Vmidphase) or n (Vmin-phase) depend on the output line to line
voltage Vpr. If the output voltage of the matrix converter
is Vmax-Vmin, x of the upper side arm is p. In addition, x of
the lower side arm is n.
Figure 4 shows the output voltage error of thecommutation operation with the proposed two- step
commutation. The output voltage is delayed by one-steptime at the commutation from the high voltage phase to
the low voltage phase because the current flow does notchange until the second step. In contrast, the output
voltage error does not occur when the commutation fromthe low voltage phase to the high voltage phase because
the current flow changes after the first step. In last case,the output voltage is delayed by one-step time when thecommutation from the zero vector to any vector. The
reason is because the output voltage is zero when all
switches is turned-off at first step after the zero vector.
Figure 5 shows the proposed two-step commutation
sequence. The output voltage error due to the dead time isconsidered. The delay of one-step time occurs from thefirst step to the second step as shown in Fig. 2 (a) whenthe matrix converter transits from an input phase toanother input phase in the positive output current. In thetransition from the zero-vector state to another input
phase, all switches have to be turned-off at the first step.
Similarly, the delay of one-step time occurs from the firststep to the second step as shown in Fig. 2 (b).
Consequently, the compensation for the voltage error due
to the delay of one-step time of the proposed two-step
commutation is similar to that in the back-to-backconverter, which is significantly simpler than the output
voltage error compensation in the four-step commutation.
Figure 6 shows the half-cycle operation of one
switching period including commutation in sector I. The
relationship of phase-voltage is vr > vs > vt.
(i) Initial state: V1
Srp and Snt are on, whereas the output current direction
is positive. Therefore, Spr and Stn can only conduct thecurrent through the diode connected anti-parallel with theswitching devices.
(ii) Commutation state V1 to V2
At first step, Ssp is turned-on. The current flow does
not change because the R-phase voltage is higher than the
S-phase voltage.
At second step, Srp is turned-off. The output voltage ischanged from Vmax-phase to Vmid-phase. This matrix
converter successfully outputs vector V2(iii) Commutation state V2 to Vzero
At first step, Stp and Snr is turned-on, whereas theoutput current direction is still positive. At second step,
Ssp and Snt is turned-off. The output voltage polarity ischanged to be opposite of the output current. Thus, theoutput current quickly decreases to zero. When the output

Fig. 4. Output voltage error with proposed two-step commutation.

Fig. 5. Proposed two-step commutation sequence.

V1

V1⇒V2
Spr

Sps

Spt

Spr

Sps

Spt

Srp

Ssp

Stp

Srp

Ssp

Stp

Vmax
Vmid
Vmin

Vmax
Vmid
Vmin

Srn

Ssn

Stn

Srn

Ssn

Stn

Snr

Sns

Snt

Snr

Sns

Snt

Spr

Sps

Spt

Spr

Sps

Spt

Srp

Ssp

Stp

Srp

Ssp

Stp

V2

Vzero⇒V4

Vmax
Vmid
Vmin

Vmax
Vmid
Vmin

Srn

Ssn

Stn

Srn

Ssn

Stn

Snr

Sns

Snt

Snr

Sns

Snt

Spr

Sps

Spt

Spr

Sps

Spt

Srp

Ssp

Stp

Srp

Ssp

Stp

Vzero

Vzero

Vmax
Vmid
Vmin

Vmax
Vmid
Vmin

Srn

Ssn

Stn

Srn

Ssn

Stn

Snr

Sns

Snt

Snr

Sns

Snt

Spr

Sps

Spt

Spr

Sps

Spt

Srp

Ssp

Stp

Srp

Ssp

Stp

V4

Vzero⇒V4

Vmax
Vmid
Vmin

Vmax
Vmid
Vmin

Srn

Ssn

Stn

Srn

Ssn

Stn

Snr

Sns

Snt

Snr

Sns

Snt

Fig. 6. Transition situation during half cycle one switching period.

current reaches zero, the output voltage also becomes
zero, i.e. zero-vector state.
(iv) Commutation state Vzero to V4
At first step, Stp and Snr can safely turned-off because
the output current has become zero. At second step, Srn
and Spt is turned-on and the matrix converter outputs thenegative voltage.
In consequence, the proposed two-step commutation
operates the matrix converter without any commutation
failures regardless of the detection voltage error at the
input voltage.
IV.

INPLEMENT OF TWO-STEP COMMUTATION

A. Input current control for matrix converter
Figure 7 shows the space vector modulation (SVM)
applied to the three-phase to single-phase matrix
converter. The operation mode of SVM is divided byevery 60 deg. (Sector I, II, III, IV, V and VI) of the input
voltages. Output vectors which are close to the input
voltage vector are selected. In sector I, V1 and V2 areused during the first half of the control period as the
positive voltage, whereas V4 and V5 are used during thesecond half of the control period as the negative voltage.
Note that the zero vector Vz which outputs the zerovoltage, is decided by the sector. These duty reference T1,
T2, and Tz are calculated by
T1 =

T2 =

1 vα
A vβ

V 2α
V2 β

1 V1α
A V1β

vα
vβ





TZ = 1 − (T1 + T2 )  A =Fig. 7. Space vector modulation.

(2)

(3)

V1α
V1β

V2α 
 (4)
V2β 


B. Current direction estimation
Figure 8 shows the current estimation method toachieve the proposed two-step commutation. The current
direction estimation is required for reducing the current
sensor which has the high current ratio and the wide
bandwidth. The output current is synchronized with theswitching carrier by SVM. The switching signal for thezero vector is selected to reduce the output current up to
zero. In order to achieve the two-step commutation, thezero current timing at the output side is necessary until

Fig. 8. Estimation principle of current direction. The output current is
synchronized the switching carrier by SVM. Therefore, theoutput current direction is also same relationship.

end of the zero vector. The output voltage is clamped at
the grid voltage during the zero vector when the output
current thought via grid voltage. After that, the output
current and voltage are also zero. The current direction
estimation is achieved to keep the zero current at theoutput side until end of the zero vector.
C. Inplementation of proposed two-step commutation
Table I shows the switching table for the proposed
two-step commutation. The switching table depends on
the sector and the selected output vector. The switchingpulse of the same vector is changed by the sector.
According to the principle of the proposed two-step
commutation as shown in Fig. 3, the gate signals are

TABLE I. SWITCHING TABLE FOR TWO-STEP COMMUTATION.

θ
Fig. 9. Signal generation for proposed two-step commutation.

decided for the six bidirectional switches. For example,
the output vector V1 is selected in the sector I, Srp, Stp
and Stn are turned-on. Ssp, Srn and Ssn are turned-off.
Figure 9 shows the gate signal generation for the
proposed two-step commutation which requires thecomplex commutation algorism as the four-step
commutation
becausethe
proposedtwo-step
commutation only uses a switching table and the current
direction estimation. The one of two devices in the bidirectional switches is operated by the gate signals
depending on the current direction. Another one of thatis turned-off during half cycle of the switchingfrequency. Finally, the short-pulse in the gate signals ismasked because the short-pulse wide more than the sumof the raise time and the turn-on delay time required
between the switching and next switching on the threephase to single-phase matrix converter.
V.

TABLE II. EXPERIMENTAL CONDITION.
Element

SymbolValue

Three-phase AC voltage
Input frequency
Rated output power
Carrier frequency
Leakage inductanceTurn ratio of transformer

vac
f
Pout
fc
L1
N1:N2
Lf (%Z)
Cf (%Y)
L
C
td

200 V
50 Hz
10 kW
20 kHz0.4 µH
1:2.4
350 H(2.3%)
11 F(4.7%)
1.3 mH30 F
1.0 µs

Input filter
Output filter
Commutation time

EXPERIMENTAL RESULTS

Table II shows the experimental conditions for 10
kW. The switching devices at the three-phase to singlephase matrix converter uses IGBT (MITSUBISHI
ELECTRIC: CM400C1Y-24S). The one-step time td isdecided by the switching characteristics of IGBT. The
sum of the raise time and the turn-on delay time of this
IGBT is shorter than 1.0 μs. Therefore, the one-step timesets to 1.0 μs.
Figure 10 (a), (b) shows the experimental waveformsof the three-phase to single-phase matrix converter at 10
kW with the four-step commutation method based on thegrid voltage polarity (voltage commutation) and with theproposed two-step commutation method respectively.
The commutation failure applying the voltage
commutation occurs in the regions where therelationship of the grid voltages changes. As a result, thesurge current is approximately 220 A. Consequently, thelife time and the reliability of the switching devices isdecreased. In addition, the input current is distorted by
the commutation failure. The proposed method based on
estimation of the output current direction achieves toavoid short-circuit at the grid voltage. Consequently, theinput current distortion is low value by 2.9%. In addition,
surge current is always suppressed by the proposed twostep commutation.
Figure 11(a)-(b) show the experimental waveforms
with the four-step voltage commutation, and the extended
waveforms at high modulation index, respectively. The
input current has low THD by 4.9% and high-power(a) Four-step commutation(b) Two-step commutation
Fig. 10. Conparison of device current at matrix converter at rated 10
kW.

factor as 0.99. However, the output current does not zeroat zero vector.
Figure 12(a)-(b) show the experimental waveforms
with the proposed two-step commutation, and theextended waveforms at high modulation index,

(a)Input and output waveforms of matrix converter(b) Extended Fig 11(a)Fig. 12. Four-step voltage commutation with high modulation index (MI = 0.85) at rated power 10 kW.

(a)

Input and output waveforms of matrix converter(b) Extended Fig12 (a)Fig. 13. Proposed two-step voltage commutation with high modulation index (MI = 0.85) at rated power 10 kW.
16.0
14.0

Input current THD[%]

respectively. It is clear that the output current at the zero
vector state quickly decreases to zero. Therefore, thesurge voltage due to the output current does not occur
when all switches turn-off. It confirms from this resultthat the proposed two-step commutation method operates
the matrix converter without any commutation failures
regardless of the input voltage detection error.
Figure 13 shows the characteristics of the input current
THD with each commutation method at the highmodulation index. The input current THD of the
proposed two-step commutation is similar to one of theconventional four-step commutation. The commutation
step is decreased by the proposed two-step commutation
to keep the performance of input current control.
Figure 14(a)-(b) show the experimental waveforms
with the conventional four-step voltage commutation, andthe extended waveforms at low modulation index,
respectively. The input current is distorted by themasking of the short-pulse.
Figure 15(a)-(b) show the experimental waveforms
with the proposed commutation, and the extended
waveforms at low modulation index, respectively. It
confirms from this result that the proposed two-step
commutation method operates the matrix converter

12.0

Four-step voltage commutation

10.0

Two-step commutation

8.0
6.0
4.0
2.0

Modulation index 0.85

0.0
0.2

0.4

1p.u. = 10 kW

0.6
0.8
Input power [p.u.]

1.0

Fig. 11. Comparison of grid current THD at high modulation index. The
input current THDs of the proposed two-step commutation and theconventional four-step commutation are also same.

regardless of the modulation index.
Figure 16 shows the distortion characteristics of each
commutation methods at the low modulation index. The
input current THD of the proposed two-step commutationis 7.7% at 10 kW. In the low modulation index, theproposed two-step commutation has the highperformance in comparison with the conventional four-Input voltage vr 250[V/div]00Input current ir 50[A/div]
Output voltage vmc 500[V/div]00
Output current imc 100A/div(b)Fig. 14(b)10[ms/div]
Input and output waveforms of matrix converter(b) Extended Fig 14(a)Fig. 15. Four-step voltage commutation with high modulation index (MI = 0.30) at rated power 10 kW.
Input voltage vr 250[V/div]00Input current ir 50[A/div]
Output voltage vmc 500[V/div]00
Output current imc 100A/div(b)Fig. 15(b)10[ms/div]
Input and output waveforms of matrix converter(b) Extended Fig 14(a)Fig. 16. Proposed two-step voltage commutation with high modulation index (MI = 0.30) at rated power 10 kW.

step commutation at entire loads.

Figure 17 shows the output voltage error of each
commutation method. the output voltage error is lessthan 0.4% regardless of the modulation index. It isclear that the proposed two-step commutation method
is unnecessary to compensate the output voltage error.
Figure 18 shows the distortion characteristics of each
commutation methods against the modulation index at
rated 10 kW. The input current THD of the proposed
two-step commutation is 7.7% at 10 kW. The output
voltage range is extended by 36% in case of same input
current THD.
VI.

CONCLUSIONSIn this paper, the two-step commutation was
proposed in the three-phase to single-phase matrix
converter. Compared to the conventional two-step
commutation, the proposed two-step commutation isalways the safety operation regardless of the voltage
detection error. In addition, the commutation algorithmof the proposed two-step commutation is much simpler
than the conventional commutation. On the other words,
the simple control hardware is employed for the matrix
converter with the proposed two-step commutation. The

16.0
14.0

Four-step voltage commutation

12.0

37%

10.0

Two-step commutation

38%

8.0
6.0
4.0
2.0

Modulation index 0.3

1p.u. = 10 kW

0.0
0.2

0.4

0.6
0.8
Input power [p.u.]

1.0

Fig. 14. Comparison of grid current THD with each commutation
method at low modulation index. The input current THD is
improved by 37 % with the proposed two-step commutation incomparison with the conventional four-step commutation.

input current THD with the proposed two-step
commutation is improved by 38% at the low modulationindex.

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Fig. 17. Comparison of output voltage error.

14.0
12.0

Input current THD[%][1]

Output voltage error[%]

REFERENCES

10.0
8.0
6.0
4.0
2.0
0.0
0.1

0.3

0.5

0.7

0.9

Fig. 18. Comparison of grid current THD with each commutation method
at entire modulation index.