Investigation of Switching Loss Reduction for the
Matrix Converter Based on Virtual AC/DC/AC
Conversion using Space Vector Modulation
Jun-ichi Itoh

Takumi Mura

Hiroki Takahashi

Dept. of Electrical, Electronics andInformation Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
itoh@vos.nagaokaut.ac.jp

Dept. of Electrical, Electronics andInformation Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan

Dept. of Electrical, Electronics andInformation Engineering
Nagaoka University of Technology
Nagaoka, Niigata, Japan
thiroki@stn.nagoakaut.ac.jp

Abstract—This paper proposes a space vector modulation
based on the virtual AC/DC/AC conversion method for amatrix converter to reduce the switching loss. The switchingloss of the matrix converter is not decided by only the numberof switching times but also depending on the voltage andcurrent in the selected switching devices based on themodulation. The proposed method can minimize the maximum
instantaneous switching loss which is caused by the selection ofswitching state with the absolute maximum values in the input
voltages and the output currents. This can be achieved bychanging over the zero-vectors of virtual inverter in the
proposed method. In this paper, the loss characteristics of thematrix converter using the proposed method are demonstrated
experimentally. From the experimental result, it was
confirmed that the proposed method can reduce the losses by
23.9 % in comparison with a conventional space vector
modulation method.
Keywords-matrix converter; switching loss;
AC/DC/AC conversion; space vector modulation;I.

virtualINTRODUCTION

Recently, the matrix converters which can convert an AC
power supply voltage into an AC output voltage that delivers
variable amplitude and frequency without the large energy
storages, such as electrolytic capacitors, have been actively
studied [1-11]. Matrix converters have advantages such as
light-weight and long life-time due to no large passive
components in the main circuit. In addition, matrix
converters can achieve high efficiency because of lessswitching devices in the current path, in comparison with a
Back-to-Back system, which consist of a PWM rectifier anda PWM inverter. Therefore, many control methods formatrix converters have been proposed and shown thefollowing benefits, low switching loss, low input current
harmonics, and low output voltage harmonics [6-11].
In order to reduce the harmonics components andswitching loss, many PWM strategies of matrix converters
have been studied [8-11]. Almost of the conventional method
decrease the switching times of matrix converters, whichaims at reducing the switching loss, similar to the otherconverter system.

However, the switching loss of the matrix converter is
not determined by only the number of the switching times
because the voltage and current of the switching devices arevariable at any time. Moreover, the voltage and current of thedevices are selected among the three-phase input voltage andoutput current. Thus, the instantaneous switching loss of adevice occurs with nine combinations of the input voltages
and the output currents. From these reasons, if the number ofswitching times is reduced, the total switching loss may not
be decreased because large turn-on or turn-off loss occurs
per switching. In other words, if the turn-on or turn-off loss
per switching can be smaller, the total switching loss can be
reduced in spite of the numbers of switching times.
This paper proposes a space vector modulation (SVM)
control method to reduce the switching loss of matrix
converters based on the virtual AC/DC/AC conversion
method. The proposed method can minimize the maximum
instantaneous switching loss which is generated at the device
synthesizing the input voltage and the output current with the
instantaneous absolute maximum value. The proposed
method changes over the zero-vectors of the virtual inverter
to avoid the switching of the device which connects between
the input phase with the instantaneous absolute maximum
voltage and the output phase with the instantaneous absolute
maximum current. That is, the switching states synthesized
by the proposed method do not have instantaneous maximum
switching loss.
At first, this paper describes the SVM based on thevirtual AC/DC/AC conversion. Second, the principle of theswitching loss reduction by the proposed method ispresented. Finally, the experiment using a 2-kW prototype isdemonstrated to confirm the validity of the proposed method
in term of loss characteristics. As these results, it isconfirmed that the proposed SVM method can reduce theswitching loss in the entire load power.
II.

VIRTUAL AC/DC/AC CONVERSION METHOD

Fig. 1 shows the circuit configuration of the matrix
converter. Matrix converter consists of a LC filter and ninebidirectional switches. The virtual AC/DC/AC control
method was proposed as a control technique for the matrix

converter [4]. Then, the output phase voltages t[vu vv vw] areshown as (1) using input phase voltage t[vr vs vt].

 vu   d ru
v   d v   rv
v w   d rw



d su
d sv
d sw

d tu  v r 
d tv  v s  
d tw   vt where dnm is duty ratio of the switch in the matrix converter(n: input phases, m: output phases) which is determined form
0 to 1.
Fig. 2 shows the virtual AC/DC/AC conversion system
which is constructed by a rectifier and an inverter. The
virtual AC/DC/AC control method considers the matrix
converter as a virtual rectifier and a virtual inverter to obtain
designated switching pulse commands. The rectifier iscontrolled as a current source type rectifier, and the inverter
is controlled as a voltage source type inverter. The switchingstates in Fig. 1 can be expressed by the switching states inFig. 2. Equation (2) expresses the formula for the duty
composition in a matrix converter.

 d rud
 rv
 d rw

d su
d sv
d sw

d tu   d up

d tv    d vp
d tw   d wp

d un  dd vn   rpdd wn   rn

d sp
d sn

d tp 
d tn 

Figure 1. Circuit configuration of the matrix converter.



where, dij is duty of the switch in the virtual AC/DC/AC
converter (i: r, s, t, u, v, w, j: p, n).

Figure 2. Virtual AC/DC/AC converter which generates same input andoutput waveforms with the matrix converter in Figure 1.

According to (2), the duty commands of the virtual
rectifier and the virtual inverter are multiplied by each upperarm (p side) and lower arm (n side), respectively. Then, theduty commands of the matrix converter are obtained fromthe multiplied duty commands.
A. Determination of the virtual rectifier vector
Fig. 3 shows the space vector diagram of the virtual
rectifier. I1 ~ I6 are the input phase current vectors. Index of
the input current vectors represents the switching states ofthe virtual rectifier switches. For example, (RT) indicatesthat Srp and Stn are in ON state and other switches are in OFF
state in Fig. 2.
It is assumed that the command vector of the virtual
rectifier is in sector 1 in Fig. 3. Then, -axis and -axis
components of the input current command vector Iin* areexpressed by -axis and -axis components of the input
phase current vectors I1 and I2, and its duties are obtained by(3).

 I in *   I 1
 * 
 I in    I1
 1  1

 

I 2
I 2
1

0   d in1 
0   d in 2  
1   d in 0 

Figure 3. Space vector diagram of the virtual rectifier.



where, dink is duty ratio of the input phase current vector in
the selected sector (k: 0 ~ 6).



B. Determination of the virtual inverter vector
Fig. 4 shows the space vector diagram of the virtual
inverter. V1 ~ V6 are the output phase voltage vectors. Indexof the output voltage vectors are the switching states for thevirtual inverter switches. For example, (110) indicates that
Sup, Svp and Swn are in ON state and other switches are in OFF
state in Fig. 2.
It is assumed that the command vector of the virtual
inverter is in sector 1 of Fig. 4. Then, -axis and -axis
components of the output voltage command vector Vout* areexpressed by -axis and -axis components of the output
phase voltage vectors V1 and V2, and its duties are obtainedby (4).

Vout *  V1*
Vout   V1
 1  1

 



V2
V2 
1

0   d out 1 
0   d out 2  
1   d out 0 

where, doutl is duty ratio of the output phase voltage vector in
the selected sector (l: 0 ~ 6).
C. Composition of the switching states
The switching state of the matrix converter based on thevirtual AC/DC/AC conversion method depends on theswitching states of the virtual rectifier and inverter.
Therefore, if the virtual inverter outputs zero-vector whichmeans that the output voltage is zero, the matrix converter
can outputs three zero-vectors due to the switching states ofthe virtual rectifier.
Table I shows the switching states of the matrix converter
focused on the zero-vector of the virtual inverter. Then, forexample, (RRR) of the matrix converter vector indicates that
all output phases connect to input R-phase. The inverter has
two zero-vectors which are expressed by (000) and (111). As
shown in Table I, the matrix converter outputs one of threezero-vectors when the inverter outputs zero-vector.
Therefore, the matrix converter based on the virtual
conversion method has redundancy to the zero-vectors. Any
zero-vectors in the virtual inverter can be selected because
the zero-vectors does not affect the input and output
waveforms.
As shown Table II, when switching state changes from
(TRT) to (TTT), v-phase is connected from R-phase to Tphase only. On the other hands, when switching statechanges from (TRT) to (RRR), u-phase and w-phase are inswitching. Therefore, switching states are difference due toselected inverter zero-vector. In addition, it is confirmed thatthe instantaneous switching loss depends on not only theswitching times but also the relationship between the input
and output phases due to the selected redundant zero-vectorof the virtual inverter [11].
III.

Figure 4. Space vector diagram of the virtual inverter.
TABLE I.

SWITCHING STATES OF THE MATRIX CONVERTER
FOCUSED ON THE ZERO-VECTORS OF THE VIRTUAL INVERTER.

Rectifier vector
RS
RT
TABLE II.

Inverter vector

Matrix converter vector

000

SSS

111

RRR

000

TTT

111

RRR

THE DIFFERENCE OF SWITCHING PHASE DUE TO THE
REDUNDANCY OF ZERO-VECTOR

Before

After

TRT

TTT

TRT

RRR

REDUCTION FOR SWITCHING LOSS BY ZEROVECTORS

It is assumed that the command vector of the virtual
rectifier is in sector 1 in Fig. 3 and the command vector of
the virtual inverter is in sector 1 in Fig. 4. Then, thecommand vector of the virtual rectifier is synthesized by the
input phase current vectors, (RS), (RT) and (RR). Then, it isconfirmed that Srp in the virtual rectifier is in on-state duringsector 1. In other words, the maximum phase in the input
voltages is r-phase during sector 1 in order to get the largest
voltage at the virtual DC-link part in Fig. 2. Thus, themaximum input voltage phase is distinguished from othertwo input phases by on-state switch during its sector.
Fig. 5 shows the decision method of the absolute
maximum voltage phase using the middle phase pole in thevirtual inverter. This is a method to distinguish the output
phase with the absolute maximum current value without
sensors. Note that this method can be used when the output
power factor is almost unity only. The output phase with the(a) Vmid* < 0.

(b) Vmid* > 0.
Figure 5. Decision method of the absolute maximum voltage phaseusing middle phase using the middle phase pole in the virtual inverter.

absolute maximum phase voltage command changes
according to pole of the middle phase voltage command(Vmid*) in Fig. 5. At sector 1 in Fig. 5, when the pole of the
middle phase voltage command is negative, it can be
confirmed that the maximum voltage command phase is uphase. On the other hand, when the pole of the middle phasevoltage command is positive, the maximum voltage
command phase is w-phase. When the output power factor isalmost unity, the output current phase corresponds to the
output voltage command. Hence, the maximum output
current phase is distinguished from other two output phasesby the method in Fig. 5.

TABLE III.

COMPOSITION OF THE SWITCHING STATES FOR MATRIXCONVERTER IN SECTOR 1 OF THE SPACE VECTOR DIAGRAM OF THE
VIRTUAL RECTIFIER AND IN SECTOR 1 OF THE SPACE VECTOR DIAGRAM OF
THE VIRTUAL INVERTER.

VirtualrectifierRS

Vmid*<0

Table III shows the composition of the switching states
for the matrix converter in sector 1 of the space vector
diagram of the virtual rectifier and in sector 1 of the space
vector diagram of the virtual inverter. As mentioned above,in these sectors, the input phase with the instantaneous
absolute maximum voltage is r-phase and the output phasewith the instantaneous absolute maximum current is u-phaseduring Vmid* < 0 or w-phase during Vmid* > 0. According toTable 3, in region of Vmid* < 0, u-phase is connected to rphase in on-state at any time when the zero-vector of thevirtual inverter is (111). Therefore, the maximum
instantaneous switching loss is not generated because Sru in
Fig. 1 is not in switching operation. If the zero-vector (000)is selected in this region, Sru is in switching operation and the
maximum instantaneous switching loss occurs. On the other
hand, in region of Vmid* > 0, w-phase is connected to r-phasewith the least switching times when the zero-vector of thevirtual inverter is (000). Thus, the maximum instantaneous
switching loss is minimized because Srw in Fig. 1 is inswitching operation with the least switching times. If thezero-vector (111) is selected in this region, the switchingtimes of Srw will increase and the maximum instantaneous
switching loss is generated more.

RT

RR

RS

Vmid*>0RT

RR

Virtualinverter
110
100
111
110
100
111
110
100
111
110
100
000
110
100
000
110
100
000

Matrixconverter
RRS
RSS
RRR
RRT
RTT
RRR
RRR
RRR
RRR
RRS
RSS
SSS
RRT
RTT
TTT
RRR
RRR
RRR

Fig. 6 shows flowchart for the proposed method togenerate the duties for matrix converter. Input command
vector Iin* is obtained by transforming input 3-phase current
commands ir*, is*, it* to -frame. Next, the input sector ischecked by the input current command vector. Then, thevirtual rectifier duties can be calculated by (3) anddistributed to the switches composing the input phase current
vector in the selected sector. The virtual inverter duties arealso calculated by (4) using the output 3-phase voltage
commands. Each vector duty is transformed to the duties of
the inverter switches by (5) and (6).

 d up   sup1
  
 d vp    svp1
 d wp   s wp1
  

sup 2
s vp 2s wp 2

sup 0   d out 1 
s vp 0   d out 2  s wp 0   d out 0 d un  1  d up
d vn  1  d vp d wn  1  d wp





Figure 6. Flowchart to generating duty for matrix converter.

Input phase voltage vr 250[V/div]
TABLE IV.

EXPERIMENTAL PARAMETERS.

Input voltage (line-to-line)

0

200V

Input frequency

50Hz

Output frequency

45Hz

Modulation index of MC

0.9

Load

R-L (1600W)

Carrier frequency

10kHz

LC filter fc

980Hz

Input current ir 10[A/div]0
Output line voltage vuv 250[V/div]00
Output current iu 10[A/div]

Time 10[ms/div]

Load(a) The convertional SVM method.

(b) The proposed SVM method.
Figure 8. Input and output waveforms in steady state. The proposed
SVM method can achieve the equal or higher performance in comparison
with the conventional SVM method.

Figure 7. Control block diagram of the proposed SVM method. The
block of “ zero-vector change over” is added to the control block diagramof the conventional SVM method

where, sxyz is switching function. Then, sxyz = 1 corresponds
to on-state and sxyz = 0 corresponds to off-state (x: u, v, w, y:p, n, z: 0~6).
At the block of “zero-vector change over” in the
flowchart, the inverter zero-vector is changed by pole of the
middle output voltage, as shown (7).
s up 0  1, s vp 0  1, s wp 0  1 v mid  0 s up 0  0, s vp 0  0, s wp 0  0 v mid  0 

IV. EXPERIMENTAL RESULTS
Table IV shows the experimental parameters. In addition,a conventional SVM that does not change over the virtual
inverter zero-vectors was experimented, too.
Fig. 7 shows the control block diagram of the proposed
SVM method. The proposed method adds the “Zero-vector
change over” block to the conventional control block
diagram.
Fig. 8 (a) and (b) shows the experimental waveforms ofthe conventional SVM and proposed SVM respectively.. The
input current and output current is controlled as sinusoidal

waveforms and unity input power factor is obtained in bothcontrol methods. The total harmonic distortion (THD) in the
input current and output current are 4.8% and 2.1 % in Fig. 8(a). On the other hand, the THD in the input current andoutput current are 4.4 % and 1.4% in Fig. 8 (b). Thus, theproposed SVM method can achieve the equal or higher
performance in comparison with the conventional SVM
method.
Fig. 9 shows a loss analysis between the proposed andconventional SVM methods. In Fig. 9, the proposed method
can reduce loss over the entire load power region, and theloss by approximately 23.9% can be reduced in comparison
with that of the conventional SVM method at 1.6-kW load.
Then, the efficiency of the proposed SVM method is 94.1 %.
Hence, the proposed SVM can reduce the switching loss ofmatrix converter because the zero-vectors of the virtual
inverter are changed.
Fig. 10 shows the switching states between theconventional and proposed SVM methods when the input
sector is 1 and the output sector is 1. The proposed SVM
method does not select the zero-vector (TTT) which is
selected by conventional SVM method. This is the evidence
that the proposed SVM method changes two zero-vectors
and uses only one zero-vector of the virtual inverter to avoid

the switching state to generate the instantaneous maximum
switching loss. In addition, the proposed SVM method
reduces switching times by two times because the selectedzero-vector can be combined at once. In the conventional
SVM method, the zero-vectors at the carrier peak and at thecarrier bottom are different and are distributed equally,
respectively. However, the proposed SVM method uses the
only vector. Thus, the proposed SVM method can distributethe zero-vector at the carrier bottom and reduce theswitching time. Therefore, the proposed SVM method could
reduce a loss as compared with conventional SVM method.
V. CONCLUSION
This paper proposes a space vector modulation (SVM)
control method in order to reduce the switching loss of amatrix converter based on the virtual AC/DC/AC conversion.
The proposed method focuses on the instantaneous
maximum switching loss which is generated at the device
synthesizing the input voltage and the output current with the
instantaneous absolute maximum value. In other word, theproposed method can reduce the switching loss by the
reduction of the switching states which generateinstantaneous maximum switching loss, not the reduction of
the switching times. The reduction of the instantaneous
maximum switching loss is realized by changing the zerovector of the virtual inverter. From the experimental results,
it is confirmed that the proposed method can control matrix
converter with input and output sinusoidal waveforms. In
addition, the proposed method can reduce loss over the entire
load power region, and the loss by approximately 23.9% canbe reduced in comparison with that of the conventional SVM
method at 1.6-kW load. Finally, from the transition ofswitching states in 1 carrier period, it is confirmed that the
proposed SVM method does not select the zero-vector which
generates the instantaneous maximum switching loss.
Therefore, the proposed SVM method is useful to reduce theswitching loss of matrix converters.
This study was supported by Industrial Technology Grant
Program in 2009 from New Energy and Industrial
Technology Development Organization (NEDO) of Japan.
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