Experimental Verification for a Matrix Converter with a V-connection AC
Chopper
Kazuhiro Koiwa and Jun-ichi Itoh
Nagaoka University of Technology
1603-1 Kamitomioka-cho
Nagaoka city Niigata, Japan
Tel. / Fax: +81/ (258) – 47.9533.
E-Mail: itoh@vos.nagaokaut.ac.jp
URL: http://itohserver01.nagaokaut.ac.jp/itohlab/index.html

Keywords«Matrix converter», «Converter control», «current/voltage control»

Abstract
This paper proposes a circuit topology for a matrix converter with a boost up function in the input
side. The proposed circuit uses a V-connection AC chopper to achieve the boost-up function. The
matrix converter and the V-connection AC chopper are independently controlled, where a virtual
indirect control method is applied to the matrix converter, and the control of the V-connection AC
chopper is an open-loop control with a damping. One problem of this system is the resonance happens
between the input reactor and the filter capacitor. In order to suppress the resonance, the damping
control is implemented in the AC chopper. In this paper, the operation of the proposed circuit alongwith the loss analysis is discussed in details. For the simulation and experiment results, the proposed
circuit is confirmed obtaining the maximum efficiency of 95.1 %, which is higher efficiency than thatof a conventional back-to-back converter.

I. Introduction
A matrix converter (MC) which can convert an AC power supply voltage directly into an AC
output voltage of variable amplitude and frequency without the large energy storages, such as
electrolytic capacitors, have been actively studied recently [1-4]. The following advantages are foundas compared with a back-to-back converter, which consist of a PWM rectifier and a PWM inverter; (i)light-weight and long-life due to no large passive components in the main circuit (ii) high efficiency
because of less switching devices in the current path. The MC is expected to apply in the renewableenergy field such as hybrid electric vehicle systems, the wind power generator systems and others.
However, one disadvantage of the MC is the voltage transfer ratio, which defines as the ratio
between the output voltage and the input voltage, is being constrained to 0.866. Consequently, theoutput current of the MC is higher than that of the back-to-back (BTB) type converter, under the same
output power. Even the motor can drive at rated frequency as the field-weakening control is applied.
However, the output current is increased and the efficiency of the system is reduced. Further, themotor loss increases due to the high input motor current. Besides, the restricted voltage transfer ratio
also limits the applications of the MCs.
There are many discussion topics on improving the voltage transfer ratio of the MCs. One of theeasy solutions is to connect a transformer between the power supply and the MC. However, thecommercial frequency transformer applied in the power grid frequency is bulky.
On the other hand, a Matrix-Reactance Frequency Converter (MRFC), which consists of a MC andan AC chopper, has been studied in [2]. Reference [2] shows that, the amplitude of the output voltage
can control to extend which is higher than that of the input voltage. However the MRFC requires many
components due to the insertion of the boost up reactor and capacitor. In addition, the control becomescomplicated due to the regular synchronizing between the MC and the chopper is required.

In the Ref. [4], the MC has been proposed to operate in an over modulation range. The voltage
transfer ratio is successfully improved to 0.94. However, the input current and the output voltage
contain large harmonic components. Additionally, the output voltage amplitude by the overmodulation method cannot get over the amplitude of the input voltage. In other word, the MC cannot
apply for the higher voltage application than the input voltage. Therefore, in considering of applying
the MC in the near future of power electronics field, the boost-up functionality is important.
This paper evaluates a matrix converter circuit topology which connects a V-connection AC
chopper at the input side of the MC that comes with a boost up functionality. The additional
component of this circuit is consists of the bidirectional switches only because the reactors in the input
filter are being used as boost reactors in this method. One of the features in this system is that an
automatic voltage controller (AVR) for the chopper is not required. As a result, the capacitor in the
boost-stage is smaller than that of the DC capacitor in the BTB system. Moreover, the origin
advantages of the MC remain in the proposed circuit because the V-connection AC chopper does notwork when the output voltage is lower than the limitation of the voltage transfer ratio for the MC.
In this paper, the proposed circuit is demonstrated by using a 1.4 kW prototype. The fundamental
operation and the validity of the proposed method are confirmed by the experimental results, where
the maximum efficiency of 95.1 % and the input power factor of 0.996 are obtained respectively.

II. Circuit topology
2.1 BTB system
Figure 1 shows the circuit diagram of a back-to-back (BTB) converter, which consists of a PWM
rectifier and an inverter. This system requires a large electrolytic capacitor in the DC link part to
reduce the ripple voltage formed by the rectifier. The PWM rectifier requires an automatic current
regulator (ACR) to control the input current. Besides that, an automatic voltage regulator (AVR) for
the DC link voltage is also required to obtain the input current command. Then, the minimum
capacitor value is constrained by the control response of the DC link voltage and the input current
according to the AVR and ACR.

Load
Fig. 1. Circuit configuration of the BTB system.

2.2 Proposed circuit
Figure 2 shows the proposed circuit diagram. The proposed circuit connects a V-connection AC
chopper in the input side of the MC. The additional components are based on four reverse blocking
IGBTs (RB-IGBT) that is mainly constructed by silicon and diodes. The relationships between the
input voltage vin and the output voltage vout is expressed byvout   chop  mc  vin(1)
where, mc is the modulation index of the MC, chop is the boost-up ratio of the chopper and vin is
the input voltage. The proposed circuit does not require a voltage control for the input capacitor sinceboth the input side and the output side of the V-connection chopper are AC voltage; i.e. the voltage
control of the V-connection chopper uses an open loop control. Therefore, the capacitor value does not
dominant by the voltage control response and the current response for the input side. As a result, theV-connection AC chopper and its components do not dominate the size and the weight in comparison
to the origin structure of a MC.
The maximum output voltage of the proposed circuit is decided by the duty ratio of the Vconnection chopper. It should be noted that the switches in the V-connection chopper do not operatewhen the voltage transfer ratio is lower than 0.866 of the input voltage. That is, at the range of low
output voltage, the proposed circuit is able to obtain high efficiency similarly to the original MC.
Besides, since the MC uses bi-directional switches, are required to apply with commutation pattern
to prevent the source and load from open circuit and short circuit. In this paper, the 4-step
commutation method is applied in the proposed circuit [8]. And also, the voltage of the filter
capacitors is used in this commutation.
Figure 3 shows the control block diagram of the proposed circuit. The pulse pattern of the MC isgenerated by the virtual indirect control method [4]. The MC and the V-connection chopper can becontrolled independently. The proposed stability control is implemented on the d-q frame of the AC
chopper control. It should be noted that the proposed control does not require a high speed feedback
regulator. It means that the filter capacitor and the filter reactor are not dominated by the control
response of the input current and the capacitor voltage.
Matrix converter
V-connection
AC chopper
vr
Sc1
vu
vcr
Sc2
vs
vcs
vv
vct
vw
Sc3
vt
Sc4
L
C
Fig. 2. Circuit configuration of the proposed circuit.

Load

1

mc

1
Vin

Fig. 3. Control block diagram of the proposed circuit.

III. Controller design
3.1 BTB system
Figure 4 shows the control block diagram of BTB system. iin and Edc are the input current and theDC link voltage in the BTB system, respectively. And also, ic is the capacitor current in the smooth
capacitor. Figure 4-(a) and 4-(b) show the control block diagram of ACR and AVR, respectively. The
ACR is necessary for the control of the input current in the AC-DC conversion. In addition, the AVR
is inserted into the ACR to control the DC link voltage along with the input current command. The
transfer function of the ACR and the AVR are expressed by (2) and (3), respectively.
KI
LTi
G ACR (2)KK
s2  I s  ILLTiKV K DCTV
G AVR (3)
K K
K K
s2  V D s  V D
C
CTV
where, the transient response of the ACR is faster than the AVR and the equation (3) is calculated
by equaling the gain of the ACR to 1. Also, Kv and Tv are the proportional gain and the integrated timeof the AVR, respectively. KI and TI are the proportional gain and the integrated time of ACR,
respectively.
iin*

1
1  sTiKI

1  sTi
sTi

1
sL

iin

Edc*

(a) ACR

iin* ACR
1  sTv
1  sTi
KV
KI
sTi
sTv

1
sL

iin

KD

ic 1 Edc
sC(b) AVR
Fig. 4. Control block diagram of BTB system.

3.2 Proposed circuit
Figure 5 shows the response block diagram of the V-connection AC chopper. Kv is the converter
gain, which is defined as a half of the maximum output voltage in the V-connection AC chopper. THPF
is the time constant of high pass filter (HPF). Then, the transfer function is expressed by (4).
1
1
s
Vout
LC
LCTHPF
Gdamp (4)
Kv Kd 2
1
1
1
Vin
3

s (
s 2
)s  2THPF
L LC
 LCTHPF
The damping resistor R is calculated as resonance suppressed by the damping control. The
transient response of the transfer function for the AC chopper with the damping resistor R is expressedby (5).
1
R
s
V
 L
  LC
Gresist  in 
(5),
R
1
Vout
s2  2s 2
 L
  LCWhen the gain of the equation (4) is equal to (5) at resonance frequency, the damping resistor R isexpressed by (6).

 4  LCK v 2 K d 2THPF 2

R

2
(6),
THPF
2
2
2
) L2 C 2   2 C 2 K v K d THPF ]LC
where, the resonance frequency of the proposed circuit is changed by the V-connection AC
chopper.
sTHPF
Kv Kd
im
1  sTHPF
vin
1
1 vout
1
iin
i2
iC sC

sL
1
vconv

[(  2 Fig. 5. Block diagrams for the input filter with a damping control.

3.3 Relationships between the control response and the capacitance
Figure 6 shows the gain characteristics of a board diagram comparison between the BTB systemand the proposed circuit. Table I shows the calculation condition for the gain characteristics. The
resonance frequency of the proposed circuit is set to 1/10 of the switching frequency. Note that theequivalent resonance frequency of the proposed circuit is decreasing with the boost-up ratio of the AC
chopper. In this paper, in order to integrate the guide of the filter design, the capacitor C is picked up
as the boost-up ratio of the chopper, which is equal to 1.
The design of the damping gain Kd is explained as following. In this paper, the damping gain in thedamping control is designed to obtain the same characteristics when the damping resistor is used in the
input filter. In other words, the gain of the equation (4) and the equation (5) are equally at theresonance angular frequency. Consequently, the damping gain Kd is calculated by (7).
2T
2 L   HPF

LC 
Kd 
K vTHPF
4 2   2
2(7)

where,  is the damping factor and is expressed by (8).
R C
(8)
 
2 L
The damping gain Kd became 0.018 in the condition of Table 1 and equation (7).
It is a requirement that the response of the ACR is faster than the AVR. However, the transient
response of the ACR is limited by the switching frequency. Therefore, the transient response of the
AVR is also limited by the ACR.
On the other hand, the proposed circuit is unstable without applying the input current stabilization
methods control (damping control in the filter) due to the resonance between the input reactor L andthe filter capacitor C. Then, the maximum gain is equaled to 45 dB in the view of the input filter loss
which is become the damping factor. On the other hand, the maximum gain of the proposed circuitwith the damping control is 17.8 dB. Thus, the resonance between the input reactor and filter capacitor
is suppressed by the damping control. In addition, it is confirmed that the damping control can
suppress the resonance of the input filter without degrading the voltage transient response. Therefore,
the filter capacitor depends on the response of the input filter. For this reason, the cut-off frequency of
the filter is higher than the transient response frequency of the ACR. As a result, if the capacitance ofthe filter capacitor is decided by the voltage response, then the filter capacitor of the proposed circuitis smaller than the smooth capacitor of a BTB system.
20 Without the stability methods
10
0
-10
-20

(proposed circuit)

ACR(BTB system)

With the damping control(proposed circuit)
-3dB

AVR
(BTB system)

-30
-40
100

10000
1000001000
Angular frequency (rad/s)
Fig. 6. Gain characteristics comparison between BTB system and the proposed circuit.

Table I : Calculation parameters

BTB system

Proposed circuit

Input reactor L
Smooth capacitor C

7 mH

Input reactor L

2 mH

470 F

Filter capacitor C

13.2 F

DC voltage Edc

283 V

Boost-up ratio

1.15

Converter gain KD

0.866

Converter gain Kv

164

Response angular ACR
frequency
AVR
ACR
Dampingfactor
AVR

5000 rad/sResonance angular
5300 rad/s
500 rad/s
frequency c
0.7*1
Damping gain Kd
0.018
0.7
*1
0.41
KI
Integrated time
Proportional
3.18 msof HPF THPF
KV
gain
49 *1
TI
0.28 ms
Integrated
Switching frequency fs
10 kHztime
2.8 msTV*1 This gain is standardization value.

IV. Simulation and experimental results
4.1 Basic operations
4.1.1 Simulation results
Figure 7 shows the operation waveforms of the proposed circuit. Table 2 provides the parameters
and the conditions for the simulation circuit. Figure 7(a) shows the operation waveform without
applying the input current stability control method. Then, the total harmonic distortion (THD) of the
input current and output voltage THD are 63.2 % and, 15.4 % respectively. It is confirmed that theresonance distortion occur in the input current waveform. On the other hand, Figure 7(b) shows theoperation waveform, where the damping controls is applied in the AC chopper for the suppression on
the resonant distortion. For these results, it is confirmed that the output voltage can increase to 27 V.
Furthermore, the input current THD and output voltage THD can be improved to 6.6 % and, 1.2 %respectively.
Figure 8 shows the simulation results when the output voltage ratio changes from 0.8 to 1.2. The
output voltage ratio is the ratio between the output voltage and the input voltage in the proposed
circuit. The output voltage starts to change from 40 ms. Gradually, the output voltage is reached 1.2
time of the input voltage. The input current of THD is 11.1 %. The AC chopper is not switching before
the 40 ms, that is before the voltage transfer ratio reaches the limit 0.866, the AC chopper remains at
off-state. Therefore, the switch Sc1 in Fig.8 shows no switching, and the switching loss is not occurred.
100 (V/div)
Input phase voltage vr
100 (V/div)
Input phase voltage vr
00
Input current ir

5 (A/div)0

Input current ir

2.5 (A/div)0
Output line voltage with LPF vuv 100 (V/div)0

Output line voltage with LPF vuv 100 (V/div)0

Output current iu
020

2.5 (A/div)

Output current iu

5 (A/div)

0
60
80
100 20406080Time (ms)Time (ms)(a) Without the input current stability methods.
(b) With the damping control.
Fig. 7. Operation waveforms by simulation.
40

100

4.1.2 Experimental results
Figure 9(a) shows the experiment operation waveforms of the proposed circuit. Table 3 provides
the parameters and the conditions for the experimental circuit. Note that the damping control is appliedin this experimental set-up. As a result, it is confirmed that the voltage transfer ratio can be improved
and the power factor is nearly to 1.
Figure 9(b) shows the harmonic analysis by Fast Fourier Transformation. Furthermore, the input
current THD and output voltage THD are 7.6 % and, 1.58 % respectively.
The reasons why the input current THD of the experiment degraded in comparison with thesimulation are following. The proposed circuit in the simulation uses an ideal switching pattern andideal components. For this reason, the open circuit and the short circuit between the power source andthe load are not considered. However, it is necessary to commutate the switching pattern to prevent thesource and the load from short circuit or open circuit in the experiment. As a result, the input current
has distortion due to the voltage error which is caused the switching commutation. Besides, there arecommutation failures in the switching pattern because of the error on the voltage detection.
Figure 10 shows the transient response of the AC chopper at the starting operation. The AC
chopper has not operated while the output line voltage command equals to 115 V. When the output
line voltage command changed 200 V from 115 V, it is confirmed that the transient response of the
input and output current are stable. Thus, the proposed circuit can stably operate during the transient
response.
Figure 11 shows current THD characteristics based on the output power. Note that the damping
control is applied in the V-connection AC chopper. It is confirmed that the output current THD is lessthan 2 %. On the other hand, the input current THD is less than 10 %. The input current THD becomes
Input phase voltage vr 300 (V/div)
200
Input current ir 5 (A/div)

850 Hz

0

-20
-40

0
Output line voltage vuv 500 (V/div)0

Input current (dB)

0

-60

1000
1500
2000
Frequency (Hz)(a) Input and output waveforms.
(b) Harmonic analysis results of the input current.
Fig. 9. Operation waveforms of the proposed circuit.

Output current iu 10 (A/div)

10 (ms/div)0500

Table III : Experimental parameters
Input phase
2 mH
115 V
voltage(2.36 %)
LC filter
Input
13.2 F
50 Hz
frequency(11.1 %)
Boost ratio
Carrier
10 kHz1.15
of chopper
frequency
VoltageTime
0.865
constant of 3.18 ms transfer
ratio of MC
HPF THPF
OutputOutput line
40 Hz
200 V frequency
voltage
Damping
Load
R-L
0.018
gain Kd

Output line voltage command
116 V
200 V
Input phase voltage vr 250 (V/div)0
Input current ir
0
5 (A/div)0
Output line voltage vuv 250 (V/div)0
Output current iu 10 (A/div)

10 (ms/div)

THD (%)

Efficiency (p.u.)
Power factor

Fig. 10. Transient response of the chopper
starting operation.
poor as the output power decrease. This is because once the output power reduces, although theharmonic distortion of the input current amplitude is constant, the fundamental amplitude of the input
current becomes smaller. Besides that, the validity of the damping control is confirmed in all range ofthe output power.
Figure 12 shows the efficiency and power factor characteristics of the proposed circuit. As a result,
it is confirmed that the maximum efficiency and power factor are 95.1 % and 0.996 respectively. In
addition, the efficiency is over 95 % and the power factor is over 0.99 when the output power is higher
than 1.2 kW.
Figure 13 shows the converter efficiency on a condition the output power is controlled to 1.4 kW
constantly and the output line voltage is gradually increase proportional to the output frequency. Whenthe output line voltage is less than 170 V, the proposed circuit could achieve high efficiency point of
95.7 %. As the output line voltage is larger than 170 V, the switching loss in the AC chopper occurs
and the efficiency of the proposed circuit starts to reduce. Since, the switching loss increased due tothe boost ratio in the AC chopper.

Efficiency (%)

Boost-up
Operation
Stoppedchopper
96
95.5
95
94.5
94
93.5
93
140 160 180 200 220 240 260
Output line voltage (V)Fig. 13. Efficiency characteristics of the output
voltage at constant output power of 1.4-kW.

4.2 Loss analysis
Figure 14 shows the loss analysis of the converter at 1.4 kW. The loss ratio of the AC chopper isequal to 25.2 % (15.8 W). On the other hand, the loss ratio of the matrix converter is equal to 52.6 %(33 W). In addition, the total loss of the input reactor and the filter capacitor is 22.2 % (14 W). The bidirectional switches are composed by using two IGBTs in this experimental circuit. For this reason,
the efficiency is reduced due to the conduction loss from the free-wheeling-diode (FWD). If RB-IGBT
can be applied as the bi-directional switches, the efficiency of the system can be improved. According
to Figure 14, it is expected that the loss which is equal to 19.2 W (conduction loss of FWD) can be
decreased. Thus, efficiency is expected to improve by 1.3 %.
Figure 15 shows the loss comparison between the BTB system and the proposed circuit. Note that
the IGBTs of the same switching characteristics are using in the proposed circuit and the BTB system
in order to compare the loss equally. In addition, the switching devices in the proposed circuit use RBIGBT. In other word, the conduction loss of FWD in the proposed circuit is not considered. According
to the loss analysis, the converter loss of the proposed circuit is similar to the inverter or the rectifier in
BTB system. On the other hand, the total loss of the chopper in the proposed circuit is less than therectifier or even the inverter due to the low conduction. The chopper circuit is composed by the type of
V-connection. For this reason, the number of devices in the chopper where the current passes throughis 2/3 less than the rectifier. Therefore, it is confirmed that the proposed circuit which inserted in Vconnection AC chopper can achieve a higher efficiency than the BTB system.

35
Loss (W)30
25
20Copper loss of
input reactor
No-load loss

15
10

16

Conduction
loss of IGBT

6

14
12
10
8
4
2

5
0

18

Recoveryloss
Switchingloss
Conduction
loss of FWD

Loss (W)40

Input and output line voltage : 200V
Output power : 1.4kW
Output current : 4.04A

Matrixconverter
Fig. 14. Property of the loss.

Filter

Chopper0

15 W 15.5 W 10.9 W 15.9 W Recovery
loss
Switchingloss
Conduction
loss of
FWD
Conduction
loss of
IGBT
Rectifier Inverter Chopper MC
Boost-up
BTB system
matrix converter
Fig. 15. Loss analysis of BTB system andproposed circuit.

V. Conclusions
This paper proposed a circuit topology for the MC with boost up functionality by using a Vconnection AC chopper. The advantages of the proposed circuit are following; The proposed circuit has the advantages of the origin MC such as small size, light-weight andlong life-time, even an AC chopper is added into the input side.
 The MC and the V-connection chopper can be controlled independently.
 High speed feedback controller such as AVR is not necessary for the proposed circuit.
Consequently, the filter of the proposed circuit can be designed with a small filter capacitor.
In order to stabilize the input current, the damping control is applied in the chopper. The proposed
circuit remains high efficiency even damping control is applied in the filter because the resistance lossof damping resistor is low.
The proposed circuit is experimented by using a 1.4 kW prototype. A unity input power factor is
obtained. Besides, the voltage transfer ratio could be improved by the boost-up operation. The input
current THD and output current THD are 7.6 % and 1.58 % respectively. The experimental resultsconfirmed that the proposed circuit could achieve a maximum efficiency and power factor of 95.1 %and 0.996. Therefore, the fundamental operation of the proposed circuit is confirmed by theexperimental results. It is confirmed that the loss of the proposed circuit is less than that of the BTB
system.
In future works, the damping gain and the input filter will be optimized.

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