Hybrid Commutation Methodwith Current Direction Estimation
for Three-phase-to-single-phase Matrix Converter
Shunsuke Takuma and Jun-ichi Itoh
Department of Electrical, Electronics and Information Engineering
Nagaoka University of Technology, NUT
Nagaoka, Niigata, Japan
takuma_s@stn.nagaokaut.ac.jp, itoh@vos.nagaokaut.ac.jp
Abstract—This paper proposes a hybrid commutation method
for a three-phase-to-single-phase matrix converter. Commutation
failures in the voltage commutation method result in an increaseof grid current distortion (THD), whereas the commutation
failures in the current commutation method lead to an increasein snubber capacitor voltage. The proposed commutation method
combines the voltage and current commutation methods in orderto suppress the commutation failure effects. In particular, thecurrent commutation is operated based on the original estimation
method for the high-frequency output current. As experimental
results, the proposed commutation method improves the gridcurrent THD by 64%, whereas the snubber capacitor voltage isreduced by 13%.
Keywords—Hybrid commutation,
Current direction estimation;I.

four-step

commutation,

INTRODUCTION

The 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 PHVs still faces oneof the main challenges, i.e. the long battery charging time. In
order to solve this problem, high-power low-profile battery
chargers are required [1]-[4]. In ref. [5]-[9], isolated AC-DC
converters using a matrix converter as a high-frequency ACAC converter connected with the transformer at the primaryside are 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 highpower application such as the rapid battery charger usually has
to withstand a high current, which increases the capacitor
volume.
Generally, the matrix converters require a commutation
sequence at the switching timing of the power devices in orderto prevent short-circuit at a voltage source and open-circuit at acurrent source. In Ref. [10]-[13], the conventional
commutation method is separated into two types, the voltage
commutation method based on the voltage polarity and thecurrent commutation method based on the current direction.

The voltage commutation can work reliably if the relationshipof the input voltages are accurately obtained. However,commutation failures may occur when two of the input voltage
values are almost similar, i.e., at the critical area where therelationship of the input voltage alternates. Consequently, theinput current distortions occur due to the commutation failures
when the voltage commutation is applied at the critical area.
In Ref. [14], the hybrid commutation method between thevoltage commutation and the current commutation has been
proposed for a three-phase-to-three-phase matrix converter inorder to reduce the number of the commutation failures. In thishybrid commutation method, the detection of the current
direction is required for the current commutation. However, in
the application of the three-phase-to-single-phase matrix
converter connected with the transformer at the primary side,
the matrix converter outputs a high-frequency current, thedirection of which is difficult to be detected accurately with ageneral current sensor.
In this paper, the estimation method for the high-frequency
current direction of the single-phase-to-three-phase matrix
converter is proposed. The purpose of this paper is the
reduction of the number of the commutation failures. The
original contribution in this paper is the high-frequency current
direction estimation based on the carrier of the space vector
modulation (SVM). The remainder of this paper is organized asfollows; in section II, the configuration of the three-phase to
single-phase matrix converter is explained, then in section III
the control and analysis for the high-frequency output voltageof the three-phase to single-phase matrix converter are
explained. The principle of the current estimation method andthe proposed hybrid commutation is explained in section IV.
After that, experimental proposed hybrid operations arepresented in section V. In addition, a comparison of thecharacteristics among the voltage and current commutation
method is carried out. Finally, the advantages of the proposed
commutation are clarified based on these results. the input
current THD is 2.9% at 10 kW with the proposed hybrid
commutation.

II.

CIRCUIT CONFIGURATION

Figure 1 shows the conventional AC-DC converter with a
PWM rectifier and an inverter. An Electric capacitor is often
used at DC link. Therefore, an initial charge circuit for a DC
capacitor is required. Interconnected inductors are required tocontrol input current. These passive components are necessary
for the operation of the conventional AC-DC converter.

III.

CONTROL METHOD

Fig. 1. Conventional AC-DC converter with PWM rectifier and inverter.

Csnu Rsnu
orL

Snubber circuit
itr

Srp’ Ssp’ Stp’

iload

Ll

vpr

C

i m LmSrn’ Ssn’ Stn’3 -1 Matrix converter

Load

vr
vs
vt

Input filter

Figure 2 shows the isolated AC-DC converter applied withthe three-phase-to-single-phase matrix converter. The
relationship of the input voltages (vr, vs, vt) is required to
employ the voltage commutation, whereas the information of
the output current direction itr is necessary for the current
commutation. However, due to the detection delay and the gain
error of the voltage or current sensor, these commutations
usually occur at the intervals when the input voltage polarity
changes or at the zero crossing of the output current. The
commutation failures with the voltage commutation shortcircuit the input side of the matrix converter, which increases
the input current distortion. On the other hand, thecommutation failures with the current commutation abruptly
opens the output side, which increases the snubber capacitor
voltage. Therefore, the hybrid commutation method between
two commutation methods is proposed in order to reduce thecommutation failures.

Diode rectifierFig. 2. AC-DC converter with three-phase to single-phase matrix
converter. The snubber circuit is absorbed the energy of leakage
inductance when the commutation failure occur.

Figure 3 shows the space vector modulation (SVM) to
apply the three-phase to single-phase matrix converter. The
SVM is based on the detection of six 60° intervals (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 are used 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. In thiscontrol method, the output single-phase voltage has highfrequency same as switching carrier. Note that the zero vector
V7, V8, and V9 which output the zero voltage, is decided by
sector. These duty reference T1, T2, and Tz are calculated by(1–3).

T1 =

1 vα
A vβ

V 2α
V2 β

(1)
Fig. 3. Space vector modulation.

T2 =

1 V1α
A V1β

vα
vβ


V
TZ = 1 − (T1 + T2 )  A = 1α

V1β


V2

V2

(2)
V2α 

V2 β 


V1

V1
V7

t V9

V8

V4 V7

1/fsw
(a) Method I

V9

V4
V5

V5

(3)

In Figure 2, the switching from the bidirectional switch toanother one is only six times per one cycle of the switching
carrier. Because, the switching loss is increased when the

t

V9

1/fsw
(b) Method II

Fig. 4. High-frequency output voltage waveforms in sector I.

switching time is larger than six times. The select of output
vector is two methods.
Figure 4 (a) and (b) illustrate the output voltage waveforms
in sector I. In case of Method I, the output voltage waveform isa point symmetry. On the other hand, the output voltage
waveform is a line symmetry by applying Method II. In two
Method, the voltage-time product is same under the
instantaneous voltage as constant DC. Therefore, an ideal
voltage source and high switching frequency is required for thecondition which equal to voltage-time product between
Method I and Method II.
Figure 5 (a) and (b) show the switching patterns of Method
I and II in sector I. In Method I, V8 is used as zero vector. The
commutation from Srp to Ssp and Stn to Ssn is selected, when the
output vector is changed from V1, V2 to V8. In other words,
the switching device after the commutation does not selected at
next commutation. As a results, the switching pulse that isshorter than the commutation time is reduced and the input
current distortion is also reduced. However, Method I has aproblem. Focus on the filter capacitor Ctr, it is discharged
during V1 and V4. V2, V8, and V5 are selected after V1
outputs. However, there is only V7 between V4 and V1. As aresult, the filter capacitor has the switching ripple component
and 300 Hz component. Because, the periods of V2, V5, andV8 depend on duty reference of T1, T2, and Tz. It means that
output voltage at the high-frequency transformer has 300 Hz
components. Therefore, it is possible to conduct the large
current by the saturation of the transformer. In order tosuppress low order harmonics components of the input current,
the filter capacitors value should be large. However, it also
increases a volume of the filter C.
In Method II, in order to solve the problem of Method I, theoutput vector is placed to be the symmetrical waveform. The
zero vector is used V9 to connect V2 and V4. Consequently,
the filter capacitors are discharged or charged every switching
periods. Therefore, the output voltage does not include 300 Hz
component in comparison with Method I. The high-frequency
transformer is not affected by the low order harmonics
components. In this paper, the commutation and the current
estimation is discussed based on Method II.
IV.

COMMUTATION METHOD

A. Voltage commutation
The voltage commutation requires only the input voltage
polarities. The voltage detection of the input side is always
equipped to measure the voltage condition. Therefore, theadditional voltage sensor is not required for the voltage
commutation. However, the voltage commutation has somedisadvantage. One is that the commutation failure is caused bydetection error of the input voltage polarity in nearly two line
to line voltages.

(a) Method I
Fig. 5. Switching pattern in sector I

Figure 6 shows the equivalent commutation model for amatrix converter. The initial state of the switching devices on
the commutation model is following:
S1a, S1b : ON

S2a, S2b : OFF

the steady state after the commutation is following:

Fig. 6. Commutation model.

(b) Method IIS2a, S2b : ON

B. Current estimation for current commutation
The current commutation method requires only the current
direction not the instantaneous current value. Therefore, thedirection of the high-frequency current can be estimatedwithout the fast-response-time current sensor. The estimation
principle for the current direction is based on the control
method of the matrix converter. The high frequency of theoutput voltage is determined by the carrier of SVM and the
duty reference. The output voltage has positive and negative
periods during one cycle of the carrier. Similarly, the output
current direction also has positive and negative periods during
one cycle of the carrier.
Figure 7 shows the relationship between the carrier of SVM
and the estimated current direction. At the beginning of the half
carrier period, the current direction alternates duringcommutation after the zero voltage period. Therefore, theoutput current direction of matrix converter at single-phaseside changes sign after the half carrier period.
Figure 8(a) and (b) show a four-step commutation with thecurrent commutation in order to prevent an open-circuit. Whenthe current direction does not change during commutation, thecurrent commutation succeeds, and no surge voltage occurs at
the output side of the matrix converter. Therefore, the snubber
capacitor voltage does not increase.
Figure 8(c) and (d) show the commutation failure with thecurrent commutation. The problem is that the commutation
after the zero voltage period itself changes the current
direction. Therefore, the commutation failure occurs regardlessof the result of the proposed current direction estimation. In the
1st step of the proposed commutation, the output of the matrix
converter is opened and the output current is abruptly blocked.
Thus, a surge voltage occurs and is absorbed by the snubber
circuit which protects the matrix converter. Consequently, thesnubber capacitor voltage increases due to the commutation
failures with the current commutation method. The current
commutation failures can be reduced by employing the voltage
commutation method at the commutation after the zero voltage
period, i.e., the hybrid commutation method.
C. Proposed hybrid commutation method
Figure 9 shows the hybrid commutation between thevoltage commutation and the current commutation, which has
the four-step commutation. In the critical area, the current
commutation is applied to avoid a grid from a short circuit. On
the other hand, the voltage commutation is applied in the
uncritical area because the surge voltage is caused by thecurrent commutation in entire area. Proposed commutation is
to avoid commutation failure. However, the output voltage ofthe three-phase to single-phase matrix converter of two
commutations has the voltage error by each commutation. The
amplitude of the input current is affected by the error of output
power because the input current is decreased when output
voltage is increased under the constant output power. Therefore,
the error compensation is required for the constant output
voltage against same duty reference.

Carrier
Transformer voltage

S1a, S1b : OFF

V2
V1
0
V4
V5

N⇒P

Transformer
current

P

Estimation N
direction

Positive

P

P⇒N
N
Negative

N
P

Fig. 7. Estimation principle of current direction. The output voltage is
syncnonized the switching carrier by SVM. Therefore, the output current
direction is also same relationship.

(a) iload > 0(b) iload < 0(c) iload >0 to iload <0(d) iload <0 to iload >0

Fig. 8. Four-step commutation with current commutation method. Whencurrent direction is changed, the current commutation is failure.

Fig. 9. Proposed commutation method. In the critical area, the current
commutation is applied to avoid short-circuit. In the uncritical area, thevoltage commutation is applied to reduce the surge voltage.

D. Output voltage error of hybrid commutation method
Figure 10(a) and (b) show the output voltage error of thethree-phase to single-phase matrix converter with the voltage
commutation method in each current direction. If the current
direction is positive, the output voltage is changed from v1 to v2
at the second step. In comparison with the ideal step without
commutation, the period of v2 is decreased by one
commutation step. Figure 9(b) shows the error voltage under
the negative current direction and same voltage relation as
Figure 9(a). In the second step, the load current remains to flow
with v1. At the third step, the output voltage is changed byturning on of S2b.

1

2

3

4
S1a

S1b

S1b

S2a

S2a

S2b

S2b

Vout

v1

Vout

v2

(T1 > T 2 )T1 ' = T1
T2 ' = T2 − Td
T ' = 1 − (T '+T ' )
1
2
 Z
,

Figures 12(a) and (b) show the output voltage error with thecurrent commutation method in positive current direction. If v1
is larger than v2, the output voltage is changed from v1 to v2 at
the third step. In comparison with the ideal step without
commutation, the period of v2 is decreased by two
commutation steps. Figure 11(b) shows the error voltage whenv2 is larger than v1. At the second step, the output voltage ischanged by turning on of S2a.
Figures 13(a) and (b) show the output voltage error with thecurrent commutation during one cycle. The error compensationof the current commutation is expressed as following:

3

4

v2

Error

(a) iload > 0. v1 > v2(b) iload < 0. v1 > v2

Fig. 10. Output voltage error by voltage commutation.

(a) T1 > T2

(4)

(T1 < T2 )

2

v1

Error

Figure 11(a) and (b) show the output voltage error with thevoltage commutation method during one cycle. According to
Figure 10, the error of output voltage is decided. The
relationship of duty reference of T1 and T2 is changed by each
30° of the grid voltage. Therefore, the amplitude of the output
vector against each duty reference is changed. Therefore, theerror compensation is changing by the amplitude relationshipbetween T1 and T2. The output voltage compensation due thevoltage commutation is expressed as follows:
T1 ' = T1 − Td
T2 ' = T2
T ' = 1 − (T '+T ' )
1
2
 Z
,

1

S1a

(b) T1 < T2
Fig. 11. Relation among space vectors and output voltage error with voltage
commutation(a) iload > 0. v1 > v2(b) iload > 0. v1 < v2

Fig. 12. Output voltage error by current commutation.

T1 ' = T1 + Td
T2 ' = T2
T ' = 1 − (T '+T ' )
1
2
 Z
,

T1 ' = T1
T2 ' = T2 + Td
T ' = 1 − (T '+T ' )
1
2
 Z
,

(T1 > T 2 )(T1 < T2 )(5)

The error compensation for the proposed hybrid
commutation is expressed as equation (6) in combination withequation (4) and equation (5).
T1 ' = T1 − K comm TdT2 ' = T2
T ' = 1 − (T '+T ' )
1
2
 Z
,

(T1 > T 2 )T1 ' = T1
T2 ' = T2 − K comm Td
T ' = 1 − (T '+T ' )
1
2
 Z
,

(T1 < T2 )(6)(a) T1 > T2(b) T1 < T2
Fig. 13. Relation among space vectors and output voltage error with current
commutation.

In case of the voltage commutation, Kcomm =1. In case of
the current commutation, Kcomm =-1. The error compensationfor each commutation can be achieved.
V.

TABLE I.

EXPERIMENTAL CONDITIONS.

EXPERIMENTAL RESULTS

Table I shows the experimental conditions for 10kW. The
switching devices at the three-phase to single-phase matrix
converter are IGBT (CM400C1Y-24S). The commutation
time td is decided by switching characteristics of IGBT. The
sum of the raise time and turn on delay time of this IGBT isshorter than 1.0 μs. Therefore, the commutation time set 1.0
μs.
Figures 14–15(a) show the experimental waveforms of thesingle-phase-to-three-phase matrix converter at 10kW with thecurrent commutation method and with the voltage
commutation method, respectively. The commutation failureswith the current commutation method occur at the zerocrossing points in the matrix converter output current. The
matrix converter output current is abruptly blocked and thesurge voltage occurs which increases the snubber capacitor
voltage. Meanwhile, the commutation failures with the voltage
commutation method occur when the relationship of the gridvoltages changes due to the delay or detection error of thevoltage sensor. Therefore, the input side of the matrix
converter is shorted and the input current distortion increases.
Figures 14–15(b) show the collector current of Srp. The
Grid voltage 250 V/div[V]Grid current 50A/div
Flag : Current commutation
Maximum peak current is lower than 200 A

Collector current of Srp’ 200A/div(a)

Operation waveforms at 10kW

4 ms/div(b) Collector current

Fig. 14. Current commutation method. The large current due to short-circuit is nothing by the current commutation. Therefore, the low gird current THD isachieved.
Grid voltage 250 V/div[V]Grid current 50A/div
Flag : Voltage commutation

Maximum peakcurrent 320 A

Collector current of Srp’ 200A/div(a)

Operation waveforms at 10kW

4 ms/div(b) Collector current

Fig. 15. Voltage commutation method. In the critical area, the grid current is distorted. Because, short-circuit of the voltage source occur by the commutation
failure. The maximum peak current at Srp is 320 A.

(a)Operation waveforms at 10kW(b) Extended waveforms of Fig. 15(a) (c) Commutation flag

Fig. 16. Proposed hybrid commutation method.

8

Proposedcommutation

6

4.9%
4

Current commutation

2

1p.u. = 10 kW
0360

Voltage commutation

0

0.2

0.4
0.6
0.8
Output power [p.u.]1(a) Grid current THD against load

Snubber capacitor voltage [V]Input current THD[%]

10

340

50V

320

Current
commutation

Proposedcommutation

300
1p.u. = 10 kW
2800Voltage commutation

0.2

0.4
0.6
0.8
1
Output power [p.u.](b) Snubber capacitor voltage against load

Fig. 17. Comparison of grid current THD and snubber capacitor voltage with each commutation method. By the application of the proposed commutation, thelow grid current THD and suppression of the snubber capacitor voltage can be achieved.

collector current at the critical region of the grid voltage isabruptly increased with the voltage commutation. It is causedby the commutation failure based on delay of the voltage
detection. Consequently, the input current is distorted. The
switching devices can be broken by the large current due toshort-circuit. In contrast, in current commutation, the collector
current of Srp is lower than 200 A. the current commutation
works reliably when the relationship of the input voltages are
not accurately obtained.
Figure 16(a)-(c) show the experimental waveforms withthe proposed hybrid commutation method, the extended
waveforms, and the regions where the current commutation
method and the voltage commutation method are alternated,
respectively. The current commutation method is applied at
the regions where the relationship of the grid voltages changes,
whereas the voltage commutation method is applied at theother regions. Therefore, the proposed hybrid commutation
method effectively suppresses the commutation failures
without any additional fast-response-time current sensors.
Figure 17(a) shows the distortion characteristics of each
commutation methods. The input current THD of the current
commutation method is the lowest with the value of 2.7% at
10 kW because the commutation failures with the current
commutation method do not affect the input current distortionof the matrix converter. On the other hand, the input current
THD with the voltage commutation method is the highest withthe value of 7.6% at 10kW. It is confirmed that the input
current THD with the proposed hybrid commutation method is
reduced by 64% compared to the voltage commutation method.
Figure 17(b) shows the snubber capacitor voltage
characteristics of each commutation methods. The snubber
capacitor voltage with the current commutation method
becomes the highest because the commutation failures withthe current commutation method abruptly block the matrix
converter output current. In contrast, the snubber capacitor
voltage is decreased by 13% by applying the proposed hybrid
commutation method. The proposed hybrid commutation
method contributes to not only the reduction of the voltage
stress on the snubber capacitor but also reduce the additionalswitching loss caused by the commutation failure.
Figure 18(a) shows the efficiency characteristics of each
commutation methods. The maximum efficiency among threecommutation method is 93.6% with the current commutation
at 10kW. However, the efficiency of other commutation
methods is over than 93.5%. Therefore, the efficiency
characteristics over the wide load range is not affected by thecommutation method.

CONCLUSIONSIn this paper, the hybrid commutation method with thecurrent estimation for the single-phase-to-three-phase matrix
converter in isolated AC-DC converter was proposed. The
proposed commutation is alternated between the voltage
commutation and the current commutation to reduce thenumber of the commutation failure. The experiment confirmedthat with the proposed hybrid commutation method, a low
input current THD of 2.9% and a low snubber capacitor
voltage of 13% in comparison with the current commutation at
rated power were achieved. The short-circuit of gird is
suppressed by the current commutation with the current
direction estimation method.
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Efficiency[%]VI.

(a) Efficiency against load

Input power factor[-]Figure 18(b) shows the input power factor of each
commutation methods. Input power factor is almost same
between the proposed hybrid and current commutation. In the
proposed hybrid commutation method, the low grid current
THD and suppression of the snubber capacitor voltage isachieved to keep the efficiency and high input power factor.

(b) Input power factor against load
Fig. 18. Comparison of efficiency and Input power factor with each
commutation method. These characteristics among three commutaion
methods is almost same.
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