Single-step commutation method
for three-phase to single-phase matrix converter
Shunsuke Takuma
Nagaoka University of Technology
Nagaoka, Niigata, Japan
takuma_s@stn.nagaokaut.ac.jp

Keisuke Kusaka
Nagaoka University of Technology
Nagaoka, Niigata, Japan
kusaka@vos.nagaokaut.ac.jp

Abstract— This paper proposes a single-step commutation
method based on an output current direction estimation for athree-phase-to-single-phase matrix converter. Conventional
four or two-step commutation causes a commutation failure
due to the detection error of grid voltages. In addition, an input
current is distorted due to an output voltage error in the low
modulation index on a three-phase to single-phase matrix
converter. A zero vector to decrease an output current up to
zero is proposed to achieve single-step commutation under all
region. In the proposed single-step commutation, by
modulating only one of two devices in a bi-directional switch
and utilizing a zero vector, the commutation failures are
avoided completely regardless of the voltage detection error.
As experimental results, the input current distortion is 2.3% at
10 kW with the proposed single-step commutation. The input
current THD in low modulation index is reduced by 34.9% incomparison with the conventional four-step commutation. The
proposed single-step commutation has a considerably simple
commutation algorithm.
Keywords—single-step commutation, three-phase to singlephase matrix converter,

I. INTRODUCTION
A lot of studies on electric vehicles (EVs) and plug-in
hybrid vehicles (PHEVs) have been accelerated over the past
decade. EVs or PHEVs still require the long battery charging
time. Therefore, high-power battery chargers with a widevoltage range are researched in order to solve this problem[1-4]. In [5-9], isolated AC-DC converters using a matrix
converter as a middle-frequency AC-AC converter connectedwith the transformer at the primary side have been proposed.
The matrix converter volume will be greatly reduced toremove a buffer capacitor compare with other topologies.
However, it is necessary to a complex commutation
sequence for a safety switching.
Generally, a commutation sequence at the switching
timing of the power devices are required for the matrix
converters in order to prevent a commutation failure such as
short-circuit at a voltage source and open-circuit at a current
source. This commutation sequence consists of four times ofswitching for two bi-directional switches. The conventional
commutation methods to utilize the input voltage polarity or
the output current direction are proposed [10]. The voltage
commutation with a safety operation is required to obtain therelationship of the input voltages clearly. However, the fourstep commutation with the voltage polarity or the current
direction is a complex commutation algorithm which greatly
restricts the applicable control hardware.
An isolated AC-DC converter with a wide voltage range
from 200 V to 500 V in CHAdeMO is required. The output
voltage of a three-phase to single-phase matrix converter is

Jun-ichi Itoh
Nagaoka University of Technology
Nagaoka, Niigata, Japan
itoh@vos.nagaokaut.ac.jp

adjusted by changing a modulation index. When a low
modulation index, switching pulses of the matrix converter
are narrow compared with a high modulation index. Then,the output voltage error occurs due to short-pulse, which isshorter than dead-time. It is necessary to reduce the numberof the commutation step in order to reduce the output voltage
error.
In [11-14], a two-step commutation is proposed in orderto solve a problem, which is a complex algorism. The twostep commutation is separated into two methods based on the
input voltage polarity of the output current direction. The
commutation failure still occurs with the two-step voltage
commutation at the critical area. On the other hands, the twostep current commutation is suppressed by the commutation
failure due to the voltage detection error. However, it isdifficult to apply the two-step current commutation for thethree-phase to single-phase matrix converter, because theoutput current direction is changed during one switching
period. The high accuracy current sensor or the estimation
method is required to obtain the output current direction. In
addition, the input current is distorted at the low modulationindex, because the conventional two-step commutation still
remain the commutation time of one step.
In this paper, the single-step commutation is proposed fora three-phase to single-phase matrix converter in order toimprove the input current total harmonics distortion (THD)
in the wide voltage range. The output voltage error by
several-step commutation is decreased by the proposed
single-step commutation. In addition, the commutation
failures do not occur regardless of the voltage detection error.
The original idea of this paper is to turning-on only one oftwo devices in the bi-directional switches based on thecurrent direction and to use a voltage vector which let theswitches naturally turn-off. Therefore, the proposed singlestep commutation is applied to the three-phase to singlephase matrix converter even in the critical area. The
effectiveness of the proposed single-step commutation is
confirmed with a 10-kW prototype.
II. CIRCUIT CONFIGULATION
Figure 1 shows the isolated AC-DC converter with thethree-phase to single-phase matrix converter. The matrix
converter does not employ a buffer capacitor and an initialcharging circuit The proposed circuit consists of a LC filter
to eliminate switching ripple, the three-phase to single-phasematrix converter, the middle frequency transformer, a dioderectifier, and a smoothing inductor. In particular, the threephase grid voltage is converted to a middle frequency singlephase voltage by the matrix converter. Consequently, thevolume of the transformer is significantly minimized because
this transformer is operated with this middle frequency

single-phase voltage. The output voltage is adjusted by themodulation index of the three-phase to single-phase matrix
converter.
III. PRINCIPLE OF SINGLE-STEP COMMUTATION

Snubber circuit
Srp

Ssp

Ll

vmc

Lm

Srn Ssn Stn
3f-1f Matrix converter

Diode rectifierFig. 1. Isolated AC-DC converter with three-phase-to-singlephase matrix converter. an several-step commutation isrequired for the operation of the three-phase to single-phasematrix converter.
Vmax

Vmax
Spl SprVmid

Circuit
model

I >0

Vmax
Spl SprVmid

Sml SmrI >0

Spl SprVmid

Sml Smr

Vmin

I >0

Sml SmrVmin
Snl Snr

Vmin
Snl Snr

Snl Snr

Vmax
Outputvoltage

Vmid
Vmin

Spl
Spr
Commutation Smlpattern
Smr
Snl
Snr

If the output current frequency is lower than theswitching frequency such as the three-phase to three-phasematrix converter, a single-step commutation based on theprinciple is achieved by keeping the same current direction
during the switching period. However, the output current
direction is changed during half cycle of the switchingfrequency in the three-phase to single-phase matrix converter.
Therefore, the single-step commutation is not used for thethree-phase to single-phase matrix converter with theconventional modulation scheme. The zero vector is changed
to apply the single-step commutation.

(a) I >0
Vmax

Vmax
Spl SprCircuit
model

Vmid

I <0

B. Zero vector for single-step commtation
Figure 3 shows the space vector modulation (SVM) tocontrol the input current of the three-phase to single-phasematrix converter. SVM is based on the detection of six 60
deg. intervals (Sector I, II, III, IV, V, and VI) of the input
voltages. In addition, the magnitude relationship of the gridvoltage is changed at the center of each sector. Therefore,
area is defined by

Vmax
Spl SprVmid

Sml SmrI <0

Spl SprVmid

Sml SmrVmin

Vmin
Snl Snrn A : ( n  1) 3    2 3
Area 
 n  1, 2,3, 4,5, 6  B : n     n 
 2 3
3

imc

Stp

Load

vr
vs
vt

Input filter

A. Single-step commutation on equivarent model
Figure 2 shows the principle of the proposed single-step
commutation, which is divided into three modes. As shownin Fig. 2 (a), when the matrix converter starts to transit from
Vmax-phase to Vmid-phase with the positive output current, theswitch Spl, Sml and Snl turn-onat Vmax-phase, Vmid-phase and
Vmin-phase. At the first step, the switch Spl at Vmax-phaseturns-off and the current commutates from Vmax-phase to
Vmid-phase. At the second step, the switch Sml at Vmid-phaseturns-off and the current commutates from Vmid-phase to
Vmin-phase. The output voltage is also changed at single step
commutation completely. The switching signal of the one oftwo devices in the bi-directional switches, is decided bycurrent direction. In this commutation sequence, by applying
the modulation of only one of two devices in the bidirectional switches, the short circuit and the open circuit are
avoided regardless of the voltage detection error. Therefore,
the transition from an input phase to another input phasewithout any commutation failures is achieved. As shown in
Fig. 2 (b), the switching sequence are applied when the
output current direction is negative in the same manner.

I <0

Sml SmrVmin

Snl Snr

Snl Snr

Vmax
Outputvoltage

Vmid
Vmin

Spl
Spr
Commutation Smlpattern
Smr
Snl
Snr

(b) I <0Fig. 2. Switching mode each current direction on equivarent
commutation model.

 The output voltage of matrix converter at single-phase side
has a middle frequency as same as the carrier frequency.
Note that the zero vector Vz, which outputs the zero voltage,is decided by the sector. These duty reference T1, T2, and Tz
are calculated by (2–4).

where n is number of the sector, and  is the angle of the referenceof the input current vector i*.

Output vectors, which are close to the input voltage
vector are selected to reduce the input current distortion. In
sector I, the positive voltage at the output voltage is
outputted to select V1 and V2 during the first half of thecontrol period, whereas the negative voltage is outputted touse V4 and V5 during the second half of the control period.



T1 

1 v
A v

V2

V2 



T2 



1 V1
A V1

v

v



v

V3

V2

Sector II







TZ  1  (T1  T2 ) 

A

V1
V1

V2 

V2  



Sector III

V4

Vz





where Ll is the leakage inductance of the transformer, imc is
the output current at single-phase side, and vin is the input
voltage which is connected to output side.
Figure 5 shows the current estimation method to achieve
the single-step commutation. The output current is
synchronized with the switching carrier by SVM. The
switching signal for zero vector is selected to reduce theoutput current up to zero. The zero current at the output side
is necessary until end of the zero vector in order to achieve
the single-step commutation under all switching. Actually,
the current direction estimation results are synchronized with
the negative edge of the zero vector.
Figure 6 shows the transient state during one switching
period with proposed single-step commutation. These modes
during one switching period in sector I are explained to use
the equivalent circuit with the current source at single-phase
output side. The output current source is defined as theinstantons current of the leakage inductance at the middlefrequency transformer. U-phase, V-phase and W-phasevoltage are defined as maximum voltage-phase, middle
voltage-phase and minimum voltage-phase.


[t0 – t1] The switching signals of the upper side andthe lower side arms are selected to connect the
maximum voltage-phase and minimum voltagephase.
[t1 – t2] The switch Srp turns-off to change output
voltage from maximum voltage-phase to minimum
voltage-phase at the arm of the upper side.. The
current path is also changed by single-step only.
[t2 – t3] The switch Ssp and Snt turn-off and the switch
Snr turns-on. The current path is also changed from

Vz

Sector I

Area A

V1

Vz Zero vectors

V5

V6Space vector modulation.

Figure 4(b) shows the switching state of the proposed
zero vector for the single-step commutation. The proposed
switching state of the zero vector selects to connect the gridand the output side. Therefore, the output current isdecreased to zero. The proposed zero vector achieves a safe
commutation after zero vector without the change of thecurrent direction because the output current is changed fromzero to positive or negative only. Time tzero of reducing
current up to zero is expressed byit zero  Ll mc 
vmc

Area B

Sector VI

Sector V

Fig. 3.

V1 v


Sector IV

Figure 4(a) shows the switching state of the conventional
zero vector. The switches of one leg of three-phase to singlephase matrix converter are on to keep the output current pathand to output zero voltage. However, the output current
direction during zero vector and next vector are mismatched.
Therefore, a commutation failure occurs by the switchingbased on the principle of single-step commutation.

V2
Sector I
i*

Spr

Sps

Spt

Srp

Ssp

Stp

Vmax
Vmid
Vmin

imc

Srn

Ssn

Stn

Snr

Sns

Snt
vmc = zero(a) Conventional method
Spr

Sps

Spt

Spr

Sps

Spt

Srp

Ssp

Stp

Srp

Ssp

Stp

vmax
vmid
vmin

vmax
vmid
vmin

im

imc=zero

Srn

Ssn

Stn

Srn

Ssn

Stn

Snr

Sns

Snt

Snr

Sns

Snt

vmc = -(vmax-vmin)

vmc = zero(b) Proposed method
Fig. 4. Switching state during zero vector. Output current
Conventional zero vector
Duty reference
T1+T2+Tz
T2+Tz
T1+Tz
Tz

Carriervmax-vmin
vmid-vmin

Single-phase
output voltage vmc0-(vmid-vmin)-(vmax-vmin)

Vz
Tz

V1
T1

V2
T2

Vz
Tz

V4
T1

V5
T2

Vz
Tz

Single-phase0
output current imc
Positive

Current direction(Estimation result)

Negativet0

t1

t2 t3 t4

t5

t6 t7

Fig. 5. Estimation principle of current direction. The output
current is synchronized the switching carrier by SVM.
Therefore, the output current direction is also same
relationship.

Vmid-current source-Vmin to Vmin-current source-Vmax.
As a results, the output current is decreased to zero.
This period is calculated by (5).











[t3 – t4] The polarity of the applied voltage of theswitch Stn and Spt are reversed biased when the
output current is zero. Therefore, the output current
keep on zero during zero vector.

Spr

Sps

Spt

Spr

Sps

Spt

Srp

Ssp

Stp

Srp

Ssp

Stp

Vmax
Vmid
Vmin

[t4 – t5] The switches Stn and Spt turn-off, and theswitches Snt and Stp turn-on in same time. If theswitching timing has a deference due to the delay of
the gate driver and the variation of the switching
devices, the commutation failure such as surge
voltage by open-circuit and short-current by shortcircuit do not occur.

Vmax
Vmid
Vmin

Srn

Ssn

Stn

Srn

Ssn

Stn

Snr

Sns

Snt

Snr

Sns

Snt

(a) t0 - t1

[t5 – t6] The switch Srn turns-off to change output
voltage from maximum voltage-phase to minimum
voltage-phase at the arm of the lower side. The
current path is also changed by single-step only.
[t6 – t7] The switch Ssn and Stn turn-off and the switch
Spt turns-on. The current path is also changed from
Vmid-current source-Vmin to Vmin-current source-Vmax
in order to obtain the zero current at the output side.
The proposed single-step commutation is required toreduce the output current up to zero until next
switching.

Spr

Sps

Spt

Spr

Sps

Spt

Srp
Vmax
Vmid
Vmin

Ssp

Stp

Srp
Vmax
Vmid
Vmin

Ssp

Stp

Srn

Ssn

Stn

Srn

Ssn

Stn

Snr

Sns

Snt

Snr

Sns

Snt

(c) t2 – t3
Sps

Spt

Spr

Sps

Spt

Srp

Ssp

Stp

Srp

Ssp

Stp

Srn

[t7 – t0] The applied voltage of the switches Stn andSpr is the reversed biased when the output current iszero. Therefore, the output current keep on zero
during zero vector. The proposed single-step
commutation is achieved by the switching sequence.

Snr

Vmax
Vmid
Vmin
Ssn

Stn

Srn

Ssn

Stn

Sns

Snt

Snr

Sns

Snt

(e) t4 – t5
Sps

Spt

Spr

Sps

Spt

Srp

Ssp

Stp

Srp

Ssp

Stp

Vmax
Vmid
Vmin

imc
fc 
vmc

Fig. 6.

(f) t5 – t6

Spr

Vmax
Vmid
Vmin

Srn

Ssn

Stn

Srn

Ssn

Stn

Snr

Sns

Snt

Snr

Sns

Snt

(g) t6 – t7

Tz  Ll(d) t3 – t4

Spr
Vmax
Vmid
Vmin

C. Limitation of appling single-step commutation
The proposed single-step commutation is employed thezero current at the end of the zero vector. The requirement toachieve the proposed single-step commutation is expressedby(b) t1 – t2(g) t7 – t0

Switching state during one carrier frequency.

where fc is the carrier frequency of SVM to control the threephase to single-phase matrix converter. The duty of the zero
vector is longer than the time of reducing the output current
up to zero. The minimum voltage of the output voltage
excluded zero voltage is the half of the line to line voltage at
grid side.
D. Implementation for single-step commutation
Table I shows the switching table for the proposed
single-step commutation. The switching table depends on the
sector, area, and the selected output vector. The switchingpulse of the same vector is changed by the sector. In addition
the switching pulse is changed by area because maximumphase, medium voltage-phase and minimum voltage-phase
are also changed. According to the principle of the singlestep commutation as shown in Fig. 2, the gate signals are
decided for the six bidirectional switches. For example, theoutput vector V1 is selected in the sector I, Srp, Stp and Stn are
turned-on. Ssp, Srn and Ssn are turned-off.
Figure 7 shows the gate signal generation for the
proposed
single-step
commutation. The
complexcommutation algorism as the four-step commutation does not
required because only single-step commutation using aswitching table and the current direction estimation. The
three-phase current reference is converted by Clarketransformation for SVM. As shown in Fig. 3, the switching
signal is selected by the sector and the vector based on the current reference according to Table I. As shown in Fig.
5(a), the current direction estimation is updated at thenegative edge of the zero vector. The one of two devices Sxl
or Sxr in the bi-directional switches is operated by the gate
signals depending on the current direction. Another one ofthat is turned-off during half cycle of the switchingfrequency. The assignment of the gate signal depending on
the current direction is express byS xr  0
iload  0
 S xl  S x
 x=p,m,n S xr  S x iload  0
 S xl  0

where subscript x indicates p (Vmax-phase) or m (Vmid-phase)or n (Vmin-phase) depend on the output line to line voltage
vmc. Sx is the switching signal of the bi-directional switch
according to Table I. 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.

TABLE I.

SWITCHING TABLE FOR SINGLE-STEP COMMUTATION.

III
VI
I
II
IV
V
V1 V2 Vz V2 V3 Vz V3 V4 Vz V4 V5 Vz V5 V6 Vz V6 V1 Vz
111 011 001 010 010 001 111 101 100 001 001 100 111 110 010 100 100 010
Area A001 001 100 111 110 010 100 100 010 111 011 001 010 010 001 111 101 100
Switchingsignal101 111 001 010 010 100 110 111 100 001 001 010 011 111 010 100 100 001
Area B001 001 010 011 111 010 100 100 001 101 111 001 010 010 100 110 111 100
SectorVectoriu*,iv*,iw*
3i*,i*uvw⇒

Detection value
vu, vv, vw
3

Fig. 7.

uvw⇒

2vv
2

SectorSpace
vectormodulationarctan

VectorZero vector
10

Switching patterngenerator
using Table I.

Current
direction
estimation

Example) Sector: I Area: A Vector: V1
111001

Srp = ON Ssp= ON Stp= ON
Srn= OFF Ssn= OFF Stn= ON

Switchingsignals6

Current
direction

Sortingby eq.(7)6

Gatesignals

Short-pulse
masking

12

Vz

Signal generation for proposed single-step commutation.

Finally, the short-pulse in the gate signals is masked
because the short-pulse wide td more than the sum of theraise time and the turn-on delay time required between theswitching and next switching on the three-phase to singlephase matrix converter. However, the input current isdistorted by the output voltage error due to the masking of
the short-pulse. The output voltage error with the proposed
single-step commutation is minimum compared with othermulti-step commutation methods.

TABLE II.
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)
td

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

Input filter

IV. EXPERIMENTAL RESULT
Table II shows the experimental conditions for 10-kW
prototype. The output voltage range is from 200 V to 500 V.
The switching devices at the three-phase to single-phasematrix converter are IGBTs (MITSUBISHI ELECTRIC:
CM400C1Y-24S). The one-step time td is decided by theswitching characteristics of IGBT. The sum of the raise time
and the turn-on delay time of this IGBT is shorter than 1.0 s.
Therefore, the one-step time of the proposed single-step
commutation and the conventional four-step commutation is
1.0 s. The output voltage error compensation by severalstep commutation is applied to the three-phase to singlephase matrix converter with the conventional four-step
commutation.
Figure 8 show the gird voltage and current waveforms
and the current at the lower switching devices of the threephase to single-phase matrix converter at 10 kW with thedelay time 50 s of the voltage detection on FPGA. As
shown in Fig. 8 (a), the commutation failure with the fourstep voltage commutation occurs in the regions, where therelationship of the grid voltages changes. As a result, thesurge current at the lower switching devices is approximately
220 A. Consequently, the life time and the reliability of theswitching devices are decreased. In addition, the input
current is distorted by the commutation failure. As shown in
Fig. 8 (b), the proposed single-step commutation based on
the current direction estimation achieves to avoid shortcircuit. It confirms from this result that the proposed singlestep commutation method operates the matrix converter
without any commutation failures regardless of the input
voltage detection error. Consequently, the input current
distortion is 2.9%. In addition, the surge current at the lower

EXPERIMENTAL CONDITIONS.

Commutation time00

vu 250[V/div]

iu 50[A/div]
220 A
irp 100[A/div]0

4[ms/div](a) Conventional four-step voltage commutation.
00

vu 250[V/div]

iu 50[A/div]
irp 100[A/div]< 150 A0

4[ms/div](b) Proposed single-step commutation.
Fig. 8.

Operation waveforms at rated power of 10 kW.

Input voltage vr 250[V/div]

Input voltage vr 250[V/div]
0

0

0

0
Input current ir 50[A/div]
Output voltage vmc 500[V/div]

Input current ir 50[A/div]
Output voltage vmc 500[V/div]

THD = 4.2%

0

0

0

0
Output current imc 100A/div

Not zero

Output current imc 100A/div
Fig. 9(b)10[s/div]

10[ms/div](a) Conventional four-step voltage commutation(b) Extended Fig. 9(a)Input voltage vr 250[V/div]

Input voltage vr 250[V/div]

0

0

0

0

Input current ir 50[A/div]
Output voltage vmc 500[V/div]

Input current ir 50[A/div]
Output voltage vmc 500[V/div]

THD = 2.3%

0

0

0

0

Output current imc 100A/div

Output current imc 100A/div

Fig. 9(d)Reach to zero

10[ms/div](c) Proposed single-step commutation

10[s/div](d) Extended Fig. 9 (c)Fig. 9. Waveforms with conventional four-step voltage commutation and proposed single-step commutation undet high modulation index (MI = 0.85) at
rated power of 10 kW. The conventional four-step method results in a high current THD of 4.2% compared with the current THD of the proposed
single-step commutation. the output current with the proposed single-step commutation is decreased to zero quickly.

switching devices is always suppressed by the proposed
single-step commutation.
Figure 9(a)-(b) show the input and output waveforms ofthe matrix converter with the four-step voltage commutation,and the extended waveforms at the high modulation index,
respectively. The input current has low THD by 4.9% andhigh-power factor as 0.99. However, the output current does
not zero at the end of the zero vector.
Figure 9(c)-(d) show the input and output waveforms ofthe matrix converter with the proposed single-step
commutation, and the extended waveforms at the highmodulation index, respectively. It is clear that the output
current during the zero vector quickly decreases to zero.
Therefore, the output current direction is not changed at thecommutation after the zero vector. The proposed single-step
commutation is achieved under all switching without thechange of the current direction by switching.

Figure 10 shows the characteristics of the input current
distortion with each commutation method at the highmodulation index. The commutation step is greatly decreasedby the proposed single-step commutation to keep the
performance of the input current control. The input current
THD of the proposed single-step commutation is lower than
one of the conventional four-step commutation under entire
region. The output power range ,which is lower than THD
5.0% input current is extended by 33.3%.
Figure 11(a)-(b) show the input and output waveforms ofthe matrix converter with the conventional four-step voltage
commutation, and the extended waveforms at low
modulation index, respectively. The output voltage error
against the output voltage RMS is large compared to the highmodulation index. Therefore, the input current is distorted
due to the output voltage error by the masking of the shortpulse.

Input voltage vr 250[V/div]
0

0

0

0

Input current ir 50[A/div]
Output voltage vmc 500[V/div]

Input current ir 50[A/div]
Output voltage vmc 500[V/div]

THD = 10.6%

0

0

0

0

Output current imc 200A/div

Not zero

Output current imc 200A/div

10[ms/div]
Fig. 11(b)(a) Conventional four-step voltage commutation
Input voltage vr 250[V/div]

10[s/div](b) Extended Fig 11(a)Input voltage vr 250[V/div]

0

0

0

0
Input current ir 50[A/div]
Output voltage vmc 500[V/div]

Input current ir 50[A/div]
Output voltage vmc 500[V/div]

THD = 6.9%

0

0

0

0
Output current imc 200A/div

Reach to zero

Output current imc 200A/div

Fig. 11(b)(c) Proposed single-step commutation

10[s/div]

10[ms/div](d) Extended Fig12 (c)Fig. 11. Waveforms with conventional four-step voltage commutation and proposed single-step commutation undet low modulation index (MI = 0.35) at
rated power of 10 kW.

20.0
18.0
16.0
14.0
12.0
10.0
8.0
6.0
4.0
2.0
0.0

Conventional
current commutation

Modulation index : 0.85
Output voltage : 500 V
1p.u.=10 kW

Conventional
voltage commutation
Proposed commutation

35.0
Input current THD[%]

Input current THD[%]

Figure 11(c)-(d) show the input and output waveforms ofthe matrix converter with the proposed commutation, and the

30.0
25.0
20.0

0.0

0.2

0.4
0.6
Output power[p.u.]

0.8

1.0

Fig. 10. Comparison of grid current THD with each commutation
method at low modulation index. The output power range withlow THD is extended of 33.3% by the proposed single-step
commutation.

extended waveforms at low modulation index, respectively.
It confirms from this result that the proposed single-step
commutation method operates the matrix converter
regardless of the modulation index. The zero current during
the zero vector for the proposed commutation is achieved.
Figure 12 shows the distortion characteristics of each
commutation methods at the low modulation index. The
input current THD of the proposed single-step commutation

Conventional
voltage commutation

10.0

0.0
0.0

THD 5.0%

Conventional
current commutation

15.0

5.0

Extended by 33.3%

Modulation index : 0.35
Output voltage : 200 V
1p.u.=10 kW

Proposed commutation

0.2

0.4
0.6
Output power[p.u.]

0.8

1.0

Fig. 12. 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.

is 7.7% at 10 kW. In the low modulation index, the proposed
single-step commutation has the high performance incomparison with the conventional four-step commutation atentire loads.
Figure 13 shows the THD characteristics of each
commutation methods against the modulation index at a
rated power of 10 kW. The input current THD of the
proposed single-step commutation is the lowest with thevalue of 2.9% at 10 kW in the high modulation index. In the
low modulation index, the input current THD of theconventional four-step commutation is more than 11%. If the14.0
Input current THD[%]switching pulses are shorter than the dead-time, the output
voltage error occurs. As a results, the input current isdistorted. On the other hand, the proposed commutation iscompleted only single-step. Therefore, the input current
keeps low distortion under all modulation index. It is
confirmed that the input current THD with the proposed
single-step commutation method is improved by 34.9%
compared to the conventional four-step voltage commutation
method with the low modulation index. In addition, theoutput voltage range is also improved by 28.6% with the low
THD.

Output power 1p.u.
Conventional
voltage commutation

12.0
10.0
8.0

Proposed commutation

6.0
THD 5.0%

4.0
2.0

Extended by 28.6%

0.0
0V. CONCLUSION
In this paper, the single-step commutation was proposed
to improve the input current distortion in the three-phase to
single-phase matrix converter. Compared to the conventional
four-step commutation, the input current THD was reducedby 34.9% with the proposed single-step commutation at low
modulation index. the output voltage range was also
improved by 28.6% with the low THD, which is lower than
5.0%. In addition, the commutation algorithm of the
proposed single-step commutation was much simpler thanthe conventional several-step commutation. On the otherwords, the simple control hardware is employed for thematrix converter with the proposed single-step commutation.
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