Improvement of Input Current Waveforms
for a Matrix Converter Using a Novel HybridCommutation Method
Koji Kato*, Jun-ichi Itoh** Nagaoka University of Technology, Niigata, Japan

Abstract-- This paper proposes a novel hybrid
commutation method and a compensation method for the
output voltage error and input current error of a matrix
converter in order to improve the input current. The
proposed commutation method combines input voltage
commutation and load current commutation. There are twoconventional commutation methods; one that depends on
the polarity of the input line voltage and is called voltage
commutation, and one that depends on the polarity of theoutput current and is called current commutation. However,a problem with voltage commutation is that commutation
failure occurs at around an input line voltage of zero. It isdifficult to detect the voltage polarity due to dependence on
the offset and delay of the sensor. Similarly, current
commutation failure occurs at around a load current of zero.
The cause of these detection errors are detection delay andthe offset of the sensor.
However, the proposed
commutation method can decrease the commutation failure
without the need for a high accuracy sensor, because thecurrent commutation is compensated by the voltage
commutation. In addition, a new commutation error
compensation method is proposed for the proposed
commutation. The output voltage and input current error
are compensated at the same time, because the duty ratio of
each switch is directly compensated. The proposed method
is validated based on the experimental results with a 750 W
induction motor and a R-L load. The total harmonic
distortion (THD) of the input current and the output
current with the proposed hybrid commutation are 3.9%
and 2.1%, respectively, and are obtained for an induction
motor load with vector control.
Index Terms—Commutation, Matrix converter,
Error compensation method by commutation

I. INTRODUCTION
Recently, since a reverse-blocking insulated gate
bipolar transistor (IGBT) was developed, there have been
many studies for a matrix converter [1-5]. The matrix
converter has a lot of advantages for a conventional pulse
width modulation (PWM) rectifier and inverter system.
For example, high efficiency, compact size, long life timeand low input current harmonics can be realized, becauseof low conduction losses and a controllable input current,
and large electrolytic capacitors are not required.
One of the problems of the matrix converter is acommutation method which is the turn-on and turn-off

1-4244-0844-X/07/$20.00 ©2007 IEEE.

763

sequence of an AC switch with two IGBT. The
switching sequence is controlled to avoid a short circuitof the power supply and an open circuit of the reactive
load. If failure of the commutation causes a short circuit,then a large input current flows, and if the commutation
failure causes the open circuit of the reactive load, then alarge surge voltage occurs in the switching device. In
other words, failure of the commutation causes a large
snubber circuit, large current devices and waveform
distortion.
The commutation sequence has four steps in theconventional method. The sequence is determined by the
direction (polarity) of the input voltage (the voltage
commutation method), or the direction (polarity) of theload current (the current commutation method). The
voltage commutation method or the current commutation
method uses a voltage sensor or current sensor anddetection circuits for its direction.
To avoid the commutation failure, a high accuracy
detection circuit is required. However, a high accuracy
detection circuit results in high costs. Some studies havepresented methods to avoid commutation failure [6-15].
One of the methods does not pass through the medium
voltage of the power supply in the case of switching
between the maximum and minimum voltages [15].
However, this method increases the switching losses dueto the use of a large voltage difference for switching.
On the other hand, the commutation causes output
voltage error and input current error, such as the output
voltage error caused by the dead-time in conventional
inverters. Compensation methods for the output voltage
have been proposed in [13].
However, althoughconventional method can compensate the output voltage
error, there has been no discussion regarding theinfluence of the input current. Thus, the input current
still has waveform distortion.
The input current distortion caused by thecommutation failure and the conventional voltage error
compensation causes vibration of the input current.
Therefore, the loss of a large dumping resistor is required
to suppress the vibration of the input current.
This paper proposes a novel hybrid commutation
method and a compensation method for the output
voltage error including the input current error for thematrix converter. In addition, the influence of the input
current by commutation is compensated in order toimprove the input current waveforms without the need fora dumping resistor.
Although the novel hybrid

commutation method uses the direction of the input
voltage and load current, the proposed commutation
method can drastically suppresses commutation failure
without the need for high accuracy sensors. Moreover,since the pulse width is directly compensated by the duty
ratio in the proposed error compensation method, themethod is very simple, although two types ofcommutation are used. As a result, the influence of thecommutation for the input current can be decreased by
the proposed commutation method. This paper shows thevalidity of the proposed commutation method and error
compensation method through the experimental results.

S1a

Fig. 1 shows a basic model of the commutation
method with AC switches. The commutation has tosimultaneously avoid the short circuit of the power
supply and the open circuit of the load. We consider afour step commutation from the voltage souse v1 tovoltage souse v2 based on Fig. 1.

S1a

S1b

v2

S2b

S2a

Fig. 1. Commutation model.
㪦㪥
㪦㪝㪝
S1a

㪦㪥

II. HYBRID COMMUTATION METHOD

v1

S1b

S1b

S2a

S2a

S2b

S2b

Td
(a) Voltage commutation, (v1>v2).

Td(b) Voltage commutation, (v1<v2).

㪦㪥

㪦㪥
㪦㪝㪝

S1a

A. Voltage commutation method
Figs. 2(a) and (b) show the switching sequence using
voltage commutation. The switching sequence depends
on the direction of the voltage at the switching leg. In
this case, the switching operation can be distinguished as
IGBT mode (forward bias mode) and diode mode
(reverse bias mode). To prevent the short circuit, thevoltage commutation must prepare the dead-time between
the turn-on and turn-off of the IGBT mode switches. For
example, if we assume a switch from S1 to S2 in the caseof v1>v2, then the commutation sequence of the voltage
commutation is obtained as follows;
Initial condition ON: S1a, S1b OFF: S2a, S2b
Step 1 S2a ON
Step 2 S1a OFF
Step 4 S1b OFF
Step 3 S2b ON
The commutation failure which creates the shortcircuit is caused by the changing point of the voltage
direction. It should be noted that voltage commutation
failure causes not only a distortion of the input current,
but also, in the worst case, destroys the switching device
by the large input current.

㪦㪝㪝

㪦㪝㪝

S1a

S1b

S1b

S2a

S2a

S2b

S2b
Td
Td
(c) Current commutation, (iload>0). (d) Current commutation, (iload<0).
Fig. 2. Commutation pattern of Fig.1.
Input voltage

vr

vs

vt

Load current

Thresholdlevel
Voltage commutation

B. Current commutation method
Figs. 2(c) and (d) show the switching sequence using
current commutation. The switching sequence depends
on the load current direction. The open circuit generates
a large surge voltage since the reactive energy of the load
is changed to the voltage. To prevent an open circuit, thecurrent commutation must prepare the overlap-time
between turn-on and turn-off of the forward current
switches.
For example, if we assume a switch from S1 to S2 inthe case of iload>0, then the commutation sequence of thecurrent commutation is obtained as follows;
Initial condition ON: S1a, S1b OFF: S2a, S2b
Step 1 S1b OFF Step 2 S2a ON
Step 3 S1a OFF Step 4 S2b ON
The commutation failure, which makes the open
circuit, is caused at around the zero crossing point of theCurrent commutation

Fig. 3. Proposed commutation method.

load current. It should be noted that current commutation
failure causes not only a vibration of the output voltage,
but also, in the worst case, destroys the switching device
by a large surge voltage. In particular, failure of thecurrent commutation continually occurs, because thewrong load current due to the commutation failure cannot
flow in the right direction. In addition, the current
commutation requires a reverse hysteresis characteristic
to that of the current polarity signal.
C. Hybrid commutation method
Fig. 3 shows the principle of the proposed hybrid
commutation method. As previously discussed, thevoltage commutation is in danger of failing at around a
voltage difference of zero, and the current commutation is764

Tmax*
Gate pulse
Tmid*commandTmin*
Commutation
time
Load
current㪂

Tmax**

㪂㪂

Tmin**

Commutation
pattern
generator

6㪄

iu > 0 : 1
iu < 0 :-1㬍㬍

sign(iu)

Thresholdcurrentlevel(a) Configuration of a matrix converter.

Commutation
select

Kcomm
Voltage commutation : 1
Current commutation : -1

Commutation command

Fig. 5. Proposed commutation error compensation.

commutation methods can be considered, one that
actively uses the voltage commutation, and one that
actively uses the current commutation. However, thecurrent preference of a hybrid commutation is better thanthe others for a decrease in commutation failure when the
output frequency is lower than the input frequency,
because the number of commutation method changes
decreases.
III. ERROR COMPENSATION METHOD BY
COMMUTATION
A. Voltage error by commutation
Fig. 4(a) shows an equivalent circuit for one phase of
the matrix converter. The symbols, vmax, vmid, and vmin in
Fig. 4(a), indicate the maximum, medium, and minimum
voltage of the power supply, respectively. Figs. 4(b) and(c) show the relation between the output voltage and gate
pulses of the matrix converter. The output voltage error
occurs as shown by the shadowed part in Figs. 4(b) and(c). In the case of voltage commutation in the dead-time
period, which means that both IGBT mode switching
devices are turned-off, the output voltage determines the
direction of the load current.
The pulse width using the voltage commutation of thematrix converter can be expressed by Eq. (1).

(b) Voltage error in the case of voltage commutation.

Tmax*

㪦㪥

Td

㪦㪝㪝

Gate pulse Tmid*
command
Tmin*
S1a
S1b
Commutation S2aS2bpattern
S3a
S3b
Outputvoltage(Iload>0)
Outputvoltage(Iload<0)­T
Tmax *  Td
° max
°
*
®Tmid Tmid°
T
Tmin *  Td¯° min

vmax
vmid
vmin
vmax
vmid
vmin

iload ! 0
Output voltage error

Output voltage command
Output voltage(c) Voltage error in case of current commutation.
Fig. 4. Voltage error by commutation.

in danger of failing at around a load current of zero. Thus,
the proposed method combines both the voltage
commutation and the current commutation as follows.
- Zero crossing point of the load current: voltage
commutation- Others: current commutation
Therefore, the proposed hybrid commutation method
can decrease the commutation failure without the needfor a high accuracy detection circuit. Two type hybrid

765

­T
° max
°
®Tmid
°
T
¯° minTmax *  Td
Tmid *
Tmin *  Td

(1),

iload  0where Tmax represents the turned-on time of the switch
connecting with the maximum voltage, Tmid represents theturned-on time of the switch connecting with the medium
voltage, Tmin represents the turned-on time of the switch
connecting with the minimum voltage, Td represents thecommutation time of one step, the suffix ’*’ represents
the command, and iload is the load current.
From Eq. (1), the voltage error can be determined by
Eq. (2).
vVcommv*  (vmax  vmin )Td f s sign (iload )(2),

Fig. 5 shows the control block of the proposedcompensation method for commutation error. Although
the proposed commutation method uses two types ofcommutation (voltage commutation and current
commutation), the compensation block is almost the sameas the conventional dead-time compensation in the
inverter. That is, the proposed compensation method isvery simple. The commutation selection is achieved by
the magnitude of the load current.

where, y=sign(x) means
y=1 when x>0, y=-1 when x<0.
Similarly, in the case of current commutation, thevoltage error during the overlap-time of the forward
IGBT depends on the load current direction. In this case,the pulse width of the matrix converter can be expressedby Eq. (3).
­T
° max
°
®Tmid
°
°¯TminTmax *  Td
Tmid *
Tmin *  Td

iload ! 0

­T
° max
°
®Tmid
°
°¯TminTmax *  Td
Tmid *
Tmin *  Td

IV. EXPERIMENTAL RESULTS(3)

Table 1 shows the experimental conditions of the
proposed commutation and the compensation method. A
control method for the matrix converter applies thevirtual indirect control method used in [3]. This method

iload  0From Eq. (3), the voltage error can be determined by
Eq. (4)v*  (vmax  vmin )Td f s sign (iload )vIcommTABLE1 EXPERIMENTAL PARAMETERS.
Input voltage
200[V]
LC filter
Input frequency
50[Hz]
Cut-off frequency
1.3[kHz]
Commutation time
V/f
R-L load
750[W] Motor
control
Output frequency
20[Hz]
Motor speed
Threshold current levelr1.1 [A](4)

The input current distortion is generated by theconventional error voltage compensation method since
the output voltage is compensated by Eqs. (2) or (4).
Specifically, the voltage error adds to the voltage
command. However, this method only compensates theoutput voltage without consideration for the input current.
In this case, the voltage error compensation causes
vibration of the input current. Consequently, a large
dumping resistor loss is required to suppress the vibrationof the input current.
B. Proposed compensation method
In this paper, the voltage error is directly compensatedby the duty ratio according to Eqs. (1) and (3). In
particular, the commutation method is changed by themagnitude of the load current for the proposed
commutation. Therefore, the compensation duty ratio is
obtained by Eq. (5).
­°T ** T *  T sign( Idload ) K comm
max
max
®
**
*
°̄TminTmin  Td sign( I load ) K comm(a) Voltage commutation(c) Current commutation.
(d) Proposed commutation.
Fig.6. Experimental results for voltage commutation, current commutationand the proposed commutation (R-L load).
10
Output current THD [%]108㸣Voltage commutation4

㸣Proposed commutation2

㸡Current commutation(b) Proposed commutation.

(5),

where Kcomm represents a commutation method flag, if
the voltage commutation is used, then Kcomm = 1, if thecurrent commutation is used, then Kcomm=-1.

62 [mH]
6.6 [ǴF]2.5[Ǵs]Vectorcontrol
600[rpm]

86㸣Current commutation4
㸣Proposed commutation2
㸡Voltage commutation

0

100

200
300
400
500
0
100
200
300
400
500
Output Power [W]Output Power [W](a) Comparison of the input current THD.
(b) Comparison of the output current THD.
Fig.7. THD for the input and output current (R-L load).

766

can clearly separate the input current control strategy andthe output voltage control strategy. The change level
between the voltage commutation and the current
commutation was set to 20% of the rated current for a
750 W induction motor. The changing level is dependent
on the accuracy of the load current sensor.
Fig. 6 shows a comparison of the voltage commutation,
the current commutation and the proposed hybrid
commutation. The large rush current caused by thecommutation failure occurs at a point where themaximum voltage changes to the medium voltage as
circled of Fig. 6(a). On the other hands, the proposed
hybrid commutation changes smoothly without the rushcurrent at the voltage change point. A surge voltage andzero crossing distortion occurs during current
commutation as shown in the circled area of Fig. 6(c). In
contrast, there is no surge voltage or current distortion forthe proposed hybrid commutation.
Therefore, theproposed commutation method is valid for suppression of
the commutation failure.
Fig. 7 shows the comparison of the total harmonic
distortion (THD) for the input and the output current
using a R-L load. The voltage commutation deteriorates
the THD of the input current, because the commutation
failure of the voltage commutation triggers the current
vibration in an input L-C filter, which is connected to the
input side of the matrix converter. In contrast, the current
commutation increases the THD of the output current,
because the commutation failure leads to the distortion of(a) Waveform for voltage commutation.

FFT of input current [%](b) Waveform for the proposed hybrid commutation.

(c) Frequency spectrum of the input current.
Fig. 9. Experimental results under the motor load without a dumping
resistor in the input filter.

(a) Waveform for the proposed hybrid commutation(vector control).
20

35
30

㸣Input current without compensation

㸣Voltage commutation without Rf ( )15
THD [%]

25

10㸣Input current
with compensation20
㸣Voltage commutation
with Rf ( )15
2.6 point

105㸣 Output current without compensation
㸡 Output current with conpensation

0

5

0.9
point

㸡Proposed commutation with Rf( )㸡Proposed commutation without Rf( )

0

100
50
Output Power[%]Fig. 10. Comparison of the THD of the input current for the voltage andhybrid commutation under a motor load.
0

25

50
75
100
Output Power[%](b) THD for the input and output current (vector control).
Fig. 8. Experimental results using a motor load with vector control.

767the output voltage. In the proposed hybrid commutation,
low THD is obtained for the input and output currents.
These results confirm that the proposed method has bothadvantages of voltage and current commutation.
Fig. 8(a) shows the waveforms for the input and output
current, using vector control with an induction motor of
750 W. THD are obtained for the input current and theoutput current, using the proposed hybrid commutation,
and are 3.9% and 2.1% at the rated load, respectively.
Fig. 8(b) shows the comparison between the THD of
the hybrid commutation with or without the proposed
commutation error compensation methods. The THD for
input current is improved by 2.6 point by application of
the proposed commutation error compensation method.
Therefore, the proposed commutation error compensation
method is valid for decreasing the distortion of the input
current.
Fig. 9 shows the waveforms of the input and output
current and frequency spectrum of the input current
without a dumping resistor in the input filter, and for a
motor load controlling V/f control. A dumping resistor
with large volume is required, because the commutation
failure of the voltage commutation causes the vibration of
the input current. By applying the proposed commutation,
the vibration can be suppressed without the need for a
dumping resistor.
Fig. 10 shows the comparison between the THD of thevoltage commutation and the hybrid commutation with orwithout a dumping resistor. This result also uses a motor
load with V/f control. The experimental results given in
Fig. 10 indicate that the proposed hybrid commutation
method without a dumping resistor is better than theconventional voltage commutation with a dumping
resistor.
These experimental results confirm the validity of the
proposed commutation method and commutation error
compensation method.
V. CONCLUSIONSThis paper proposes a novel hybrid commutation
method that combines voltage commutation and current
commutation and a compensation method based on the
duty ratio. The advantages of the proposed commutationare;x
realization of low THD for the input current andoutput current at the same time,xcompensation of the input current error by thecommutation using the voltage error from thecommutation.
x
suppression of the vibration of the input current
without the need for a dumping resistor.
The THD of the input current and the output current
using the proposed hybrid commutation was 3.9% and2.1%, respectively, obtained with an induction motor loadusing vector control. The snubber capacity can be
decreased and the reliability of the switching device canbe improved using the proposed commutation method.

768

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