Improvement of Output Voltage with SVM in
Three-phase AC to DC Isolated Matrix Converter
Koji Orikawa

Yoshiya Ohnuma

Jun-ichi Itoh

Nagaoka University ofTechnology
Nagaoka, Japan

Nagaoka University ofTechnology
Nagaoka, Japan

Nagaoka University ofTechnology
Nagaoka, Japantcgoh@vos.nagaokaut.ac.jp

orikawa@vos.nagaokaut.ac.jp

ohnuma@stn.nagaokaut.ac.jp

itoh@vos.nagaokaut.ac.jp

Isolatedtransformer
Diode bridge
rectifierFig. 1. AC-DC converter with diode bridge rectifier and buck converter.

INTRODUCTION

Three-phase AC-DC power converters have received
significant attentions in community. In particular, heavy
industrials apply these converters in order to supply sufficient
DC power to specific equipment, such as the communicationequipment, from a three-phase AC power grid or generators. In
these applications, for the protection purpose and noise
elimination, an isolated transformer is typically being used in
the converter. However, the isolated transformer that generally
connects to the power grid is consuming large amount of space.
Figure 1 shows the conventional AC-DC converter which istypically applied in the spoken applications [1-2]. In order toisolate the converter from the grid supply, a large transformer
is generally connected between the grid and the AC-DC
converter. Then, the structure of AC-DC converter is composedfrom a three-phase diode bridge rectifier and a buck converter.
However, the diode bridge rectifier has poor harmoniccomponents in the input current and also the electrolytic
capacitors are required at the rear end of the rectifier to reduce
the DC ripple waveforms. On the other hand, the buckconverter is used to regulate the DC output voltage that meetsthe application requirements. In a high power system, the sizeof the transformer is generally large to ensure that current
density is sufficient, which becomes a significant drawback forthis converter.
In order to reduce the size of the transformer and also to
improve the harmonic components, Figure 2 shows a better
option of the AC-DC converter. The circuit consists of a PWM
rectifier and a high frequency resonant converter with a small

Srp

Ssp

Stp

Sap Sbp

Srn

Ssn

Stn

San Sbn

PWM rectifier

Inverter

Input filter

Keywords—Matrix converter; three-phase to single phase; ACDC; Space vector modulation

I.

Buck
converter

Load

Abstract—This paper discusses and evaluates theperformance of a 50-kVA three-phase AC to DC matrix
converter. Comparing to the conventional converter, which
consists of a PWM rectifier and an inverter, the matrix converter
does not require a large reactor at the three-phase input side, andrequire no DC smoothing capacitor at the DC link part. A space
vector modulation based on the virtual AC-DC-AC conversion
with four-step commutation patterns is proposed for theconverter. From the experimental results, the converter canobtain 2.49% THD on the input current and achieves
approximately 91.4% efficiency at 40kW.

Load

Goh Teck Chiang
Nagaoka University ofTechnology
Nagaoka, Japan

Diode rectifierFig. 2. AC-DC converter with PWM rectifier and inverter.

size isolation transformer [3-4]. The PWM rectifier is
employed in order to improve the harmonic components of the
input current. Then, high switching frequency resonant
converter is employed in order to reduce the size of thetransformer. Even the harmonic component issue in the input
current can be greatly improved; the drawback is a sufficientvalue of reactor is required at the front end of the PWM
rectifier.
Moreover, this converter produces higher losses due to theswitching intervals in the PWM rectifier. Similar to theprevious converter, a smoothing DC capacitor is required toconnect between the PWM rectifier and a half bridge converterin order to reduce the DC ripple components. On the other
hand, the full bridge converter which is connected to theisolated transformer, is employed with a high switchingfrequency and eventually produces a large amount of switchinglosses. Then, the rear end of the converter is connected to thefull bridge diode rectifier in order to transform the AC voltage
into the DC voltage.
In this paper, the authors discuss an AC-DC directconversion circuit based on the concept of matrix converterwith a space vector modulation (SVM) [5-6]. The matrix

The high frequency link isolation matrix converter withresonance converter has been discussed [7]. In Ref. [7], theauthors discussed a safe commutation in the matrix converter
during the zero voltage switching (ZVS) operation. In order toachieve ZVS, additional switches are employed in the dioderectifier so that the diode rectifier can become a structure ofresonance converter. Furthermore, additional inductor andcapacitor are included at the output of matrix converter toensure ZVS is achieved at low current. However, the control toachieve ZVS becomes complicated, thus, not all the switching
period can achieve ZVS operation which result the efficiency is
dropping.
In this paper, a simple matrix converter structure as shownin Fig. 3 is implemented with SVM to reduce the number of theswitching. Also, a 4-step commutation method is included tocompensate the pulse error during the switching intervals. The
proposed control enables low THD components on input
current and also achieves high efficiency. First of all, thecircuit structure is explained in the second chapter. Then, thecontrol strategies are illustrated and detailed in the chapter 3. In
particular, the beneficial of SVM with the 4-step commutationis shown to improve the output voltage error during theswitching intervals. Simulation and experimental results areprovided in the late chapters to demonstrate the circuit
performance. Finally, the validity of the proposed method is
evaluated in subjects to the harmonic components andefficiency.
II.

CIRCUIT TOPOLOGY

Figure 3 shows the circuit structure of the matrix converter.
A small LC filter is employed at the front end of the converter
to reduce switching ripples. Then, a three-phase AC to single
phase AC matrix converter is employed between the grid
supply and the isolated transformer. The isolated transformer isdesigned based on a general-purpose method. Each of theswitching modules in the matrix converter is composed from a
two anti-series connected IGBT, where 6 modules are
employed in the matrix converter. Then, the secondary side of
the transformer is devoted by a standard diode bridge rectifier
to obtain DC waveform. As shown in the Fig. 3, the 50-Hz gridvoltage is directly converted to the input voltage of thetransformer by the matrix converter without any passive
components.

Srp’ Ssp’

Stp’

Load

Input filter

converter is possible to directly convert three-phase AC
waveforms into three-phase AC waveforms and enables acontrollable frequency and output voltage amplitude, which
requires no passive components at the DC bus. In this paper,the matrix converter is composed from 12 unit of switching
devices only because of the three phase input single output
structure, as shown in Fig. 3. Comparing to the conventional
circuit, the matrix converter can achieve two stages conversion
and improve the efficiency. Furthermore, the matrix converter
can control the input current and output current at one time toensure low harmonic components of sinusoidal waveforms canbe achieved. On the other hand, a small size isolatedtransformer can be used because the high switching frequency
is possible.

Diode rectifier
Srn’ Ssn’ Stn’
3f-1f Matrix converter

Fig. 3. Circuit strucutre with matrix converter.

The size and weight of the AC-DC isolated matrix
converter can be greatly reduced because the passive
components that are used in the conventional converter (asshown in Fig.2); the boost-up reactor in the front end and thesmoothing capacitor at the DC bus, are not required.
Furthermore, due to the reason of the high switchingfrequency is possible in the matrix converter, the size of theisolated transformer can be reduced, comparing to thecommercial frequency isolated transformer.
However, the converter has two issues in the control thatneeds to be addressed. Due to direct conversion, the input
current and output current are required to control
simultaneously, which results the control technique becomescomplicated. Furthermore, commutation patterns are requiredin the switching intervals to ensure switching errors are notoccurring. To simplify the complexity of the control strategies,
a virtual AC-DC-AC conversion technique is proposed.
III.

PROPOSED CONTROL STRATEGIESThis chapter discusses the control techniques of the matrix
converter. In order to simplify the control techniques, a virtual
AC-DC-AC conversion technique which has been discussed in
Ref [8] is referred.
In Figs. 2 and 3, the input voltage is represented as t[vr,vs,vt]
and the output voltage (transformer input voltage) isrepresented as t[va,vb]. Sxy represents the switching function of
the switches, when Sxy is turned on, Sxy=1 and when Sxy isturned off, Sxy=0. The switching intervals for Fig. 2 can be
expressed as (1), where the left block is the full bridge inverter(Sap, San, Sbp, Sbn) and the right block is the PWM rectifier (Srp,
Ssp, Stp, Srn, Ssn, Stn).

va   sap
v    s
 b   bp

san   srp
sbn   srn

va   srp 'v    ' b   srn

ssp
'
ssn

 srp ' ' srn

ssp

'

ssn

'

'

ssp
ssn

vr 
stp   vs .
stn   
 vt v
'  r
stp   vs .
'stn   
 vt 'stp   sap'
stn   sbp

san   srp
sbn   srn

(1)

(2)

ssp
ssn

stp 
.
stn 

(3)

In the matrix converter, the relationship between the output
voltage t[va,vb] and input voltage t[vr,vs,vt] can be expressed in(2), where Sxy’ represents the switching intervals for the matrix

Figure 5 illustrates the input current command i* in thevoltage vector diagram which is based on the space vector
modulation. According to the position of i*, then thecorresponding voltage vector will be selected. (For example, inFig. 5, the input current command i* is located in the area
where V1 and V2 will be selected.) Then, the a and 
fundamental components of the input current commands arederived into voltage components Va and V. In subjects to theduty periods, T1, T2 and zero vectors Tz, the voltage vectors thatare responding to the fundamental voltage components can bederived into V1a, V1b, V2a and V2b, which can be expressed in (4).
T1 

1 va
A v

v 2a
.
v2 

T2 

1 v1a
A v1

va
v

v2 

010
V
100 3

q

Switching signals

4 step commutation
function(Refer. (10))

Switching Table(Table 1)

Compensationof deat-time. E.q.(12)

TZ’

iout
PLL vrt,vsr,vts
Detection values

vb

V2

010
001

i*

T2
V7
V8 V9

001 V4
100

001
V
010 5

T1

V6

100
100
010
V1 100 V8 =010
va 001
001
V9 =
001
V7 =

100
010

(4)
TABLE I.

.

1s an  0
sbn  0
1

TZ

T2’

Fig. 5. Fundamental voltage vector.

.

SWITCHING TABLE FOR THE MATRIX CONVERTER

Area1 Area2 Area3 Area4 Area5 Area6

From (4), switching patterns can be formed in according to
the desired voltage vectors and duty periods. However, theoutput voltage of the matrix converter is a square waveformthat has voltage polarity which can be expressed in (5). Note
that, the switching duty is considered as 50% which is the sameas in the conventional full bridge converter.
 s aps bp

T2

Fig. 4. Control block diagram.

0
1
.
1
0

(5)

Therefore, when (5) is substituted into (3), two patterns ofswitching intervals are happening in the virtual PWM inverter.
When the virtual PWM inverter is equaled t[1 0 0 1], no
particular changes are required. However, when the virtual
PWM inverter becomes t[0 1 1 0], an inverse form of switchingintervals are required.
SVM shows the advantages in considering the complicatedswitching intervals which is subjected to the condition of (5),because SVM provides flexibility in determining the duty
period. Table 1 shows the complete switching table for the

Positive

v1

Ib*

T1’

Carrier
f =10 kHz

Negative

A

v2a

PI

T1

※ The number of ”1”means switch is Turn on
100 Srp’=ON, Ssp’=OFF, Stp’=OFF
Example001 Srn’=OFF, Ssn’=OFF, Stn’=ON

Tz  1  (T1  T2 ).
v1a

-

Ia

*

Space vector
modulation. E.q.(4)Figure 4 shows the control block diagram. Here, a PI
regulator is used in order to regulate the input current
command i* and the output current iout. Then, the input current
commands are derived from the input voltages which aretransformed from a three-phase voltage into a two dimensional
vector in the stationary reference frame. The input current
command i* is taken into account in order to calculate therotation angle of the input current angles to ensure unity input
power factor, and also, it is used to determine the amplitude of
the input current.

i* +Fundamental vector

converter. Based on (1), the switching units in (2) can be
expressed into (3), that is, the switching units are themultiplication between the left block and the right block.

100
010
010
001
001
100
State1 V1 = 001 V2 = 001 V3 = 100 V4 = 100 V5 = 010 V6 = 010
010
010
001
001
100
100
State2 V2 = 001 V3 = 100 V4 = 100 V5 = 010 V6 = 010 V1 = 001
010
100
001
010
100
001
State3 V8 = 010 V7 = 100 V9 = 001 V8 = 010 V7 = 100 V9 = 001
001
100
100
010
010
001
State4 V5 = 010 V6 = 010 V1 = 001 V2 = 001 V3 = 100 V4 = 100
001
001
100
100
010
010
State5 V4 = 100 V5 = 010 V6 = 010 V1 = 001 V2 = 001 V3 = 100
100
001
010
100
001
010
State6 V7 = 100 V9 = 001 V8 = 010 V7 = 100 V9 = 001 V8 = 010

matrix converter based on the SVM. Positive and negative
show the polarity of the output voltage. States 1, 2 and 3
represent the T1, T2 and Tz for positive voltage and states 4, 5
and 6 represent the T1, T2 and Tz for negative voltage. In orderto output both positive and negative polarity of voltages in one
switching period, 6 kinds of voltage vector are required. From
Table 1, in each area for each of the state, upper switches are
represented as Srp’, Ssp’, and Stp’ and lower switches are
represented as Srn’, Ssn’and Stn’.
Due to the reason of direct conversion, in order to avoid
short circuit in term of voltage and open circuits in term of

v1

S1a

iload

S1b

NegativeorPositiveS2bv2(i) (ii) (iii) (iv)

Vout

S2a

v1

S1a
S1b

v2

S2b
S2a

v1

S1a
S1b

v2

S2b
S2a

On
On

v1

On
(i)

v2
Vout

Off
On

On
(iii)
On

S1b

iload

Off

S1a

S2b
S2a

v1

S1a
S1b

iload

v2
Vout

S2b
S2a

S1a

S1b

S1b

S2a

S2a

S2b

S2b

Vout

Fig. 8. Commutation model.
Off
(ii)
On

iload

v1

Vout

iload

On
On

Vout

v1
v2

Error

Error

(a) Current direction from positive toto negative.

(b) Current direction from negative
to positive.

Fig. 6. Detail of commutation patterns.
(i) (ii) (iii) (iv)(i) (ii) (iii) (iv)

Off
Off
(iv)

Vout

v2

Off
On

(i) (ii) (iii) (iv)

S1a

S1a

S1a

S1b

S1b

S2a

S2a

S2b

S2b

v1
Vout 0-v2

v1
Vout 0
-v2

Error

Error
(a) Current direction from positive toto negative.

(b) Current direction from negative
to positive.

(a) Current is positive.
Fig. 7. During the commutation sequence.

v1

S1a
S1b

v2

v1

S2b

On

On
(i)

S1a

Off

S2b
S2a

v1

On

On
(iii)
On

S1a
S1b

iload

v2

Off

S2a

S1b

v2

On

Vout

v1

S2b

v2
Vout

On

On

S1a

Off

S2b
S2a

iload

Off

S2a

S1b

iload

Off
(ii)

Off
(iv)

Vout

iload

On
On

Vout

(b) Current is negative.
Fig. 9. Sequence of the 4-step commutation.

current, a continuous 4-step commutation pattern is required ineach switching intervals. In the matrix converter, thecommutation is decided by input absolute voltage (therelationship between maximum, medium and minimum phase).
Figure 6 shows a simplify model of the matrix converter todemonstrate the 4-step commutation patterns. Note that since
the output voltage is formed directly depending on the input
voltage, v1 and v2 represent the input voltage which can be themaximum voltage, medium voltage or the minimum voltage.
The 4-step commutation is based on a voltage-dependentcommutation in a classical matrix converter [9]. In the voltagedependent commutation, output voltage errors occur
subsequently depending on the current direction. Figures 7(a)and (b) show the sequence of the 4-step commutation when the
output current is positive and negative, respectively. Note thatthe switching intervals in Fig. 7 demonstrate the switchingwhen S2a and S2b are turning on and S1a and S1b are turning off.
In Fig. 7(a), even the S2a is turned off at the first step, the flowof the output current remains at the same pathway. Then, theoutput current changes the pathway (flow into S2a and S2b) at
the second step of the commutation pattern. In Fig. 7(b), in theevents of first and second steps, the output current remains at
the same pathway. Then, the output current changes thepathway at the third step of the commutation pattern.
Figures 8(a) and (b) summarizes that, under the same
sequence in commutation, when V1 > V2, there is one delay
occurring in the output voltage when the current direction ispositive, and however, there are two delays occurring in the
output voltage when then current direction is negative.
Furthermore, in the matrix converter, the current direction
might change during the commutation sequence as shown in
Figs. 9(a) and (b).
In Fig. 8 (a), when the current is positive, the polarity of theoutput voltage is changed in the step 2 during commutation,
there are two delays occurring in the output voltage. In Fig.
8(b), when the current is negative, in the case of Fig. 7(b), twodelays occurring in the output voltage but when the polarity ofthe output voltage changes during the commutation sequence,
only one delay occurring in the output voltage.

As a result, the voltage error which is caused by thecommutation needs to be compensated. In order to compensate
the voltage error, one period of dead time is added into the duty
cycle as expressed in (6). The dead time period is added tobalance the output voltage in each switching periods. Figure 10
illustrates the error occurring in the output voltage error due tothe commutation.
'T1  T1
' T2  T2  Td
,
 '
'
'
TZ  1  (T1  T2 )

(T1  T2 )IV.

 T1'  T1  Td
'T2  T2, '''TZ  1  (T1  T2 )

(T1  T2 )


Error

TZ
V7

(6)

SIMULATION RESULTS

Figure 11 shows simulation results without the 4-step
commutation. In Fig. 11, from the sinusoidal input voltage andcurrent waveforms, unity power factor is achieved. The DC
output voltage is 400 V, and the current step control is applied
on 72 ms. Note that the input current can response to the load
current effectively when the current step control isimplemented. Moreover, there is no fluctuation of the DC
output voltage. Figure 12 demonstrates an extended image of
the Fig. 11 during the transient period. A smooth transition can
be noticed in the output DC current. The 10-kHz square wave
transformer voltage is achieved even the input waveform is a
50-Hz voltage. Furthermore, no significant spike voltage
occurring in the transformer voltage and DC output voltage.

Table 2 shows the experimental parameters. Figure 13
shows the experimental results at 50 kW condition. From theresults, input voltage and current waveforms show that unity
power factor is achieved. The DC output voltage is 400 V andthe DC output current is 125 A.
Figure 14 demonstrates the input power factor andefficiency that are subjected to the output power. From theresults, it is confirmed that the input power factor achieves

200

TZ
V8

T2
V5

T1
V4

Input voltage [vr]

0

0
-200
Primary side of transformer voltage [vpri]
400
0
-400
Primary side of transformer current [ipri]
400
0
-400

Output DC voltage [vout]

400
0
100
50
0

Output DC current [iout]

20

40

60
80
Time [ms]

100

120

Fig. 11. Simulation results (without 4-step commutation).
Input voltage [vr](V)

0
-200
200

Input current [ir](A)

0
-200
400
0
-400
400

Primary side of transformer voltage [vpri](V)Primary side of transformer current [ipri](A)Output DC voltage [vout](V)

400
Items

Value

Input voltage

100 V

Input frequency

50 Hz

Output frequency

30 Hz

Output R-load

1~20 W

Output L-load

1 mH

Carrier frequency

10 kHzItems
PI controller

Value

Kp

0.8 p.u.

Ti

0.7 msCommutation time
L

Input filter

3 ms
0.75 mH

C

15.4 mF

Cut-off
frequency

1.5 kHz

TZ
V7

-200
Input current [ir]
200

0
-400

EXPERIMENTAL PARAMETERS

T2
V2

T1
V1

Fig. 10. Output voltage error due to the commutation.

200

EXPERIMENTAL EVALUATIONSTABLE II.

0
V4
V5The simulation parameters are follows, the input voltage is
200 V, the input frequency is 50 Hz, the switching frequency is
10 kHz, cut-off frequency of LC filter is 1 kHz and thetransformer ratio is 1:2.6. Note that the simulation is running ina RL load condition without the 4-step commutation.
Furthermore, a current step control is included in the result todemonstrate that the matrix converter can response effectively
to a load change.

V.

V2
V1

0
100
50
0

Output DC current [iout](A)

72.5

73.0
73.5
Time [ms]Fig. 12. Extended results during the transition period.

74.0

140

Figure 15 shows the difference between two results, wherein Fig. 15(a) the voltage error compensation is not included andin Fig. 15(b) the voltage error compensation is included. From
Fig. 15(a) it can be noticed that the DC output current contains
frequency components due to the imbalance output voltage. Fig.
15(b) demonstrates that the frequency components can besuppressed after implementing the voltage error compensation.
Furthermore, the input current THD can be improved from
4.15% to 2.49% at 40 kW.
VI.

CONCLUSION

This paper discussed and evaluated a direct type of energy
conversion three-phase AC-DC converter. The matrix
converter can achieve unity power factor and high efficiency.
Moreover, the converter is small in size because (i) no passive
components are required such as the boost reactors andelectrolytic capacitors, and (ii) high frequency isolatedtransformer can be used. The authors utilize the simplicity of avirtual AC-DC-AC concept and propose a SVM control
techniques. Furthermore, a compensation method for the output
voltage, where the output voltage error is caused by the 4-step
commutation pattern, is considered and proposed. From thesimulation and experimental results, the matrix converter
shows that it can achieve 99% unity power factor and 91.4 %efficiency at a 50 kW condition. Moreover, the matrix
converter also enables low harmonic components in the input
current; the experimental results shows that the input current
THD is 2.49 % at a 40 kW condition.
REFERENCES
[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

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Hengchun Mao, Lee, F. C. Y., Boroyevich, D. and Hiti, S., “Review ofhigh-performance three phase power-factor correction circuits”, IEEE
Trans. on Industrial Electronics, Vol. 44, Issue. 4, pp. 437-446, Aug
1997
Kikuchi, J. and Lipo, T.A. “Three-phase PWM boost-buck rectifierswith power- regenerating capability”, IEEE Trans. on Industry
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Zhonghui Bing, Xiong Du and Jian Sun, “Control of Three-phase PWM
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Input
voltage vuv 0[500V/div]
Input
current iu 0[500A/div]
Outputvoltage vout
[500V/div]0
Outputcurrent iout 0[200A/div][5ms/div]

Fig. 13. Experimental waveforms at 50kW condition.

Efficiency and input power factor [%]99%. Also, the matrix converter can achieve efficiency 91.4%.
Note that the efficiency can be further improved by employing
the reverse-blocking IGBT in the matrix converter.

100

Input power factor

90

Efficiency
80

70

10

20
30
40
Output power [kW]50

Fig. 14. Efficiency and power factor.
Input
current iu[250A/div]0
Input
voltage vuv[250V/div]
Outputcurrent iout100[10A/div][5ms/div](a) Without the voltage error compensation.
Input
current iu[250A/div]
Input
0
voltage vuv[250V/div]
Outputcurrent iout100[10A/div][5ms/div](b) With the voltage error compensation
Fig. 15. Experimental results of the output current.