A Damping Control Method for a Matrix Converterwith a Boost-up AC Chopper
Kazuhiro Koiwa

Jun-ichi Itoh

Major of Energy and Environmental Science
Nagaoka University of Technology
Nagaoka, Niigata, Japan
newkoiwa@stn.nagoakaut.ac.jp

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

Abstract— This paper proposes a circuit topology for a matrix
converter with a boost-up AC chopper in the input stage. In
order to suppress the input filter resonance, the authors havedeveloped a stabilization control for the input current using a Vconnection AC chopper. However, the input current is requiredas the signal for the damping control. In this paper, the damping
control using the existing filter capacitor voltage is proposed. Inorder to verify effectiveness of the proposed damping control, theproposed circuit is demonstrated by a 1.8-kW prototype. As aresult, it was confirmed that the input current THD can besuppressed approximately 72.5% improved by applying the input
current-type or the filter capacitor voltage-type damping controls.

In order to solve this problem, a Matrix-ReactanceFrequency Converter (MRFC), which consists of a MC and an
AC chopper, has been studied in [2-3]. Reference [2] and [3]shows that, the amplitude of the output voltage can control toan extension which is higher than that of the input voltage.
However the MRFC requires many components including theboost-up reactor and capacitor. In addition, the control
becomes complicated because the regular synchronizing
between the MC and the chopper is required.

Keywords- Matrix converter; V-connection AC chopper;
damping control; Capacitor voltage

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 [1-8]. The following advantages are found ascompared with a back-to-back converter, which consist of a
PWM rectifier and a PWM inverter; (i) light-weight and longlife time due to no large electrolytic capacitor in the main
circuit (ii) high efficiency because of less switching devices inthe turn-on current path. The MC is expected to apply in the
future renewable energy field such as hybrid electric vehicle
systems, the wind power generator systems and others.
However, one of the disadvantages 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, the output current of the MC is higher than thatof 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, the motor loss increases due to the higher motor
current. Besides, the restricted voltage transfer ratio also limits
the applications of the MCs. Therefore, in considering of
applying the MC in the near future of power electronics field,
the boost-up functionality is important.

On the other hand, another MC which can boost-up thevoltage is connected in the previous stage of the MC. In otherwords, conventional circuit is composed as back-to-backaround the filter capacitor. If MC operated by direction of theboost-up voltage is selected, high efficiency is obtained.
However, the number of this circuit is twice of MC. Thus, thecosts become higher.
This paper proposes a circuit topology which connects a Vconnection AC chopper [4] in the input stage of the MC thatenables boost-up functionality. However, the input filter
resonance occurs in the proposed circuit. In order to suppress
the input filter resonance, the current-type damping control has
been proposed in [5]. In this case, the current sensors arenecessary for the damping control, which results the cost of thesystem becomes higher.
In this paper, the capacitor voltage-type damping control
which uses the existing filter capacitor voltage as the input
signal is proposed. The voltage sensors have already been usedin the control of the MC and the commutations. Thus, the input
filter resonance can be suppressed without the current sensors.
The constitutions in this paper are following. At first, thedamping gains are designed using the extent input current andcapacitor voltage. Then, the two damping controls arecompared in term of performances by the bode diagram. The
proposed circuit is demonstrated by a 1.8-kW prototype.
Additionally, the efficiency, input power factor and input
current THD characteristics are measured. As these results, it isconfirmed that the effectiveness of the proposed damping
control is verified by experiment.

II.

CIRCUIT TOPOLOGY

Fig.1-(a) shows the proposed circuit which connects a Vconnection AC chopper in the input stage of the MC. The
power device in the AC chopper uses eight IGBTs. The
relationships between the input voltage vin and the output
voltage vout is expressed byv out     mc  v in







where, mc is the modulation index of the MC,  is the boost-up
ratio of the chopper and vin is the input voltage. Basically, thefunction of the AC chopper is simply boost-up the input
voltage. Then it does not uses a feedback control for the filter
capacitor since both the input side and the output side of the
AC chopper are AC voltage. Therefore, the capacitor value
does not dominate by the voltage control response and thecurrent response for the input side in contrast with a BTB
system. As a result, the V-connection AC chopper and its
components do not dominate the size and the weight incomparison to the origin structure of a MC. In addition, themaximum output voltage of the proposed circuit is decided by
the duty ratio of the AC chopper. It should be noted that theswitches in the AC 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.

(a) Main circuit.



s2 

1
2
  LC1(b) Block diagram of input filter without input current
stability methods.

Figure 1. Circuit configuration of proposed circuit.




III.

1

  LC

Thus, it is confirmed that the input filter resonance occurs
as the angular frequency is (3).

1

 LC





DAMPING CONTROL STRATEGY

A. Matrix Converter Control
Fig.2 shows the control block diagram of the proposed
circuit. In this paper, the pulse pattern of the MC is generated
by the virtual indirect control method [6-7]. The virtual indirectcontrol method can separate into input current control andoutput voltage control. Thus, the conventional control method
can be applied into each of the control. The input current
command icd* and icq* are generated from the capacitor voltage
in order to keep constant output power [8]. Thus, they are
expressed by (4) and (5), respectively.

V-connection AC chopper

L

1
sC



Fig.1-(b) shows the block diagram of input filter without
the input current stability methods. According to this block
diagram, the transfer function between the input voltage andthe capacitor voltage is expressed by (2).

v
G BMC  c 
vin

1

1
sL

Matrix converter

Load

ir

it

Sc1
Sc4

PLL
vcr
vcs
vct

3

vu
vv *
vw *

1

mc

1
Vin

Output-line voltage
commands

1/X

vcr
vcs
vct

C

9

2
2

Effective
value cal.

*

Input current
stability control(by iin or vc)

Sc2
Sc3

DC

*

+

+

+

Carrier

V-connection AC
chopper control

3
Input current ir*,is*,it* Virtual
rectifiercommand cal.
Input control
Eq. (4), (5) current
commandsvu*
Virtualvv *inverter*vw
control
Output voltage
commands

Figure 2 Control block diagram of proposed circuit.

PWM
composition

*

icd 



*

icq 


p  vcd  q  vcq
2

vcd  vcq

2





p  vcq  q  vcd
2

vcd  vcq





(a) Control diagram of AC chopper.

where, p is the active instantaneous power command, q is
the reactive instantaneous power command. Note that p isequal to 1, and q is equal to 0 in this paper.

sTHPF
1  sTHPF

Beside, in order to simulate constant power sources,automatic current regulation (ACR) has been introduced in thecontrol of the MC.

1(b) Block diagram of input filter.
Figure 3. Input current-type damping control.

1

 mc



1
Vin

(a) Control diagram of AC chopper.

1
sL

1

1
sC


1


sK c
1  sTLPF(b) Block diagram of the input filter.
Figure 4. Capacitor voltage-type damping control.

Fig.3-(b) shows the transfer function block diagram of the
input current type damping control. Kv is the converter gain,
which is defined as a maximum input voltage in the AC
chopper. THPF is the time constant of HPF. Then, the transfer
function from the input side of the AC chopper to the output
side of the AC chopper is expressed by (6).

1
1
s
 LC
 LCT HPF

K
K
1
1
1
v
d_I
s3  (s 2
)s 2  2
THPF
L
 LC
 LCT HPF

1
sC




Fig.3-(a) shows the control diagram of the damping control
with the input current. The input currents are detected as
signals to use damping control. Additionally, high pass filter(HPF) is used to decouple the oscillation component into the
input current. The damping control is implemented on the d-q
frame of the AC chopper control. The fundamental frequency
component on the d-q frame becomes a constant value, i.e. DC
signal. In addition, the harmonics components are appeared as
ripple components. The distortion component of the input
current is extracted by the HPF. After that, the distortion
component is added to the chopper command Dc*.



Vc
Vin

1

1
sL

B. Input Current Type Damping Control
The resonance between the input reactor and the filter
capacitor occurs in the input stage. In general, in order tosuppress the input filter resonance, the damping resistor isconnected at the input filter. However, the efficiency isdegraded because of the damping resistor loss. In contrast, thedamping control can suppress the input filter resonance without
degrading of the efficiency [9]. In case of the proposed circuit,we confirmed that the input filter resonance could not be
suppressed by the damping control. There, the input currenttype damping control is applied to the AC chopper.

G damp _ I 

1
Vin

1

 mc

2

R
1
s
V
 L
  LC
Gresist  in 
Vout s 2  R s  1
2 L
 2  LC When the transfer function of the equation (6) is equaled to(7) at resonance frequency, the damping gain Kd_I is expressedby (8).
2L  2 Assume that the damping control suppresses the oscillation
component as same as connecting the damping resistor R. The
transient response of the transfer function for the AC chopperwith the damping resistor R is expressed by (7).

Kd _ I 



THPF
LC

K vTHPF2

4 2   2

where,  is the damping factor which expresses by (9).





R
2

C
L 



Note that the input reactor of the proposed circuit isvirtually changed due to the AC chopper [10].
C. Capacitor Voltage Type Damping Control
In the input current-type damping control, the effect ofsuppression of resonance distortion can be confirmed. However,in this damping control method, the current sensors arenecessary to apply in the damping control. As a result, the costof the proposed system is higher due to increasing amounts ofthe current sensor. In one hand, the damping control method
using the existing filter capacitor voltage is proposed.
Fig.4-(a) shows the control diagram of the filter capacitor
voltage. The operation of the proposed block damping control
is as following. At first, the capacitor current ic is estimated bydifferentiation from the capacitor voltage vc. After that, d-axis
current is obtained on d-q frame. In addition, switching ripple
included in d-axis current is extracted by using a low-pass filter(LPF). It is multiplied to the damping gain Kd. Finally, thedistortion component is added to the chopper command Dc*.
However, the differentiation cannot use due to the noise. In thispaper, instead of the differentiation, a HPF is used as pseudo
differentiation. The proposed damping control is operating forthe distortion component as the feedback regulator. On theother hand, the fundamental component is not affected. For thisreason, the chopper control does not require the high speed
response. It means that the filter capacitor and the boost-up
reactor are not dominated by the control response of the input
current and the capacitor voltage. Then, the transfer function
from the input side of the AC chopper to the output side of the
AC chopper is expressed by (10).
1

LCTLPF

Gdamp _ V 



s3 

s

1

LC

1 2 K v K d _V1T
 2LPF ) s  2
s (
TLPF
L
 LC
 LC

 

Similar to the design by the input current-type damping
control, when the transfer function of the equation (10) is
equaled to (7) at resonance frequency, the damping gain Kd_V isexpressed by (11).



K d _V 2 2 LC  TLPF

K v K c4 2  1

2





Accordingly, the damping gain can be designed fromrequired damping factor by (11).
Fig.5 shows the gain characteristics comparison between
without the damping control and with two damping control.
Note that each frequency response is calculated by (2), (6) and(10). In addition, Table 1 shows the calculation parameters. As
a result, the proposed circuit without the damping control isunstable due to input filter resonance. In addition, the voltage

Gain (dB) 

Figure 5. Gain characteristics.
Table 1. Calculation parameters.
Input phase voltage

115 V

Output line voltage

200 V

Input current-type damping control
Damping gain Kd_I

0.014

Output power Po

1.8 kW

Time constantof HPF THPF

3.18msBoost-up ratioof AC chopper

1.15

Input reactor

10.5 mH

Damping gain Kd_V

0.02

13.2 FTime constantof HPF THPF

13.2 sConverter gain Kv

282 V

Filter capacitor

Resonance angular 2340 rad/s
frequency c

Capacitor voltage-type damping control

gain without the damping control is approximately 145dB. On
the other hand, the maximum voltage gain with the input
current-type damping control or the capacitor voltage-type
damping control is 17.5dB and 15dB. Thus, it can be
confirmed that the voltage gain between the input side andoutput side of the AC chopper is approximately improved by
130dB. Moreover, the input filter resonance can be suppressed
without degrading the voltage response. In additionally, it canbe confirmed that the suppression effects of the input filter
resonance of the capacitor voltage-type damping control is
obtained as same as the input current-type damping control.
Thus, the resonance distortion on the input current can besuppressed without the current sensors.
IV.

SIMULATION RESULTS

Fig.6 shows the operation waveform of the proposed circuitwith the input current type damping control. Table 2 shows thesimulation conditions. In the simulation, in order to simulate
constant power sources, the current resources are used in the
output load. Note that the damping control is applied after
0.1ms on simulation. Accordingly, the distortion of theresonance frequency components occurs in the input current
waveform while the damping control is not applied. The input
current total harmonic distortion (THD) is 38.2%.
Fig.7 shows the operation waveforms with the filter
capacitor voltage-type damping control. Table 2 shows thesimulation conditions. As a result, the resonance distortion in
the input current is suppressed in steady state. Moreover, it isconfirmed that the output power Po is constant. The input
current THD is 3.3%. Thus, the input current THD can be 35%
decreased with the damping control.

V.

EXPERIMENTAL RESULTS

Table 2. Simulation and experimental conditions.

Fig.8 shows the photo of experimental platform. As IGBT,
1MBH50D-060 (Fuji electric corp.) and SK-80-GM-063(SEMIKRON Inc.) are used in the prototype. In order toprotect the switching devices from the surge voltage, dynamic
clamp circuit (No.1 in this photo) and snubber circuit (No.2 isthis photo) are used as the protect circuit.
Fig.9 shows the experimental result without the damping
control. Table 2 shows the experimental conditions. In the
proposed circuit, the input filter resonance does not occur
because of the chopper loss becomes a role of the damping
resistor. There, it considered that a generator was connected in
the input stage of the proposed circuit. Thus, the input reactor
is connected 10.5mH (16.5%). Moreover, the PI-control gains
in ACR were calculated from the standard transfer function.
Additionally, the output line voltage vuv was observed by using
LPF which the cut-off frequency is equal to 1.5 kHz. Besides,
since the MC uses bi-directional switches, are required to apply
with commutation pattern to prevent the source and load fromopen circuit and short circuit. In this paper, the 4-step
commutation method is applied in the proposed circuit [11].
And also, the voltage information of the filter capacitors is usedin this commutation. According to this result, the input current
THD and the output line voltage are 23.5% and 7.48%,
respectively. Thus, the waveforms are distorted by the input
filter resonance.
Fig.10 shows the experimental results with the input current
type damping control. Accordingly, the resonance distortion in
the input current is suppressed by applying the damping control.
It is accomplished that the input current THD and the output
line voltage THD are 10.3% and 3.52%, respectively. Fromthese results, it is confirmed that the input current THD and theoutput line voltage THD can be improved 56.2% and 47% in
contrast with the damping control is not applied. Incidentally,
the damping factor  is obtained by (12) from (8).
 



1
2

K v K d _ I THPF
 2 L2 

2L  THPF222
  2 K v K d _ I THPF
C




According to equation (10), the damping factor by the input
current-type damping control is 0.73 calculated in thisSimulation

Experiment

Input phase voltage Vin

115 V

Input frequency fin

50 Hz

Carrier frequency fs

Chopper

10 kHzMC

Input reactor L

2 mH

Filter capacitor C

13.2 F

Boost-up ratio of the chopper
Damping gain Kd_V
Load

10.5 mH
13.2 F
1.155

c

0.5
Constant
current source

4.0
R-L load(12.5 , 5mH)

No.2
Matrix converter
Boost-up AC chopper

No.1

Figure 8. Experimental platforms.

experimental result. Note that calculated the damping factor isonly by the damping control. However, the distortion can besuppressed by the damping control as well as the chopper loss.
Therefore, the input current waveform is distorted because of
the input filter resonance is excessively compensated by thedamping control in the experiment.
Fig.11 shows the experimental results with the filter
capacitor voltage-type damping control. The resonancedistortion can be suppressed as well as the input current type
damping control. The input current THD and the output line
voltage THD are 6.47% and 5.36%, respectively. From theseresults, it is confirmed that the input current THD and theoutput line voltage THD can be improved by 72.5% and 28.3%
in contrast with the case damping control is not applied.
Similar to the input current type damping control, the damping
factor is expressed from (11) by (13).

 



1
2

K v K d _ V K c
 LC  TLPF 2   2 K v 2 K d _ V 2 K c 2
2





According to equation (13), the damping factor by the filter
capacitor voltage-type damping control is 0.012 calculated inthis experimental result. The damping factor is lesser incontrast with the input current-type damping control. Therefore,
the input current waveform is sinusoidal because the input filter
resonance is not excessively compensated.
Fig.12 shows harmonic components of the input current
without the damping control and with two damping controls.
At first, in comparison between the results with/without thedamping control, almost of the harmonic components in theboth results with the damping control is reduced than the
results without the damping control. Therefore, theeffectiveness of damping control is confirmed to control thestabilization of the input current. Next, the filter capacitor
voltage-type damping control is compared with the input
current-type. As a result, it is confirmed that the suppression
effect of the resonance distortion is similar to the input current
type damping control. However, the even order components of
the input current type damping control is larger than that of the
proposed damping control. This is because the input filter
resonance is excessively compensated by the input current type
damping control and the chopper loss.

Fi
gure 9. Experimental result without damping control.
THD : 10.3%
Input
current
ir 0
5 (A/div)

Output line
voltagevuv 0
100 (V/div)

THD : 3.52%

10 (ms/div)

Figure 10. Experimental result with input current-type damping
control.

Fig.13 shows the efficiency characteristics. Note that theoutput line voltage is 170V constantly. In addition, in order tochange the output power, the load resistance is changed.
According to this result, the efficiency is improved by applying
the damping control. This is because the harmonic loss isdegraded due to suppression of the resonance distortion. Then,the maximum efficiency of the proposed circuit is 93.83% at
1.0-kW load.
Fig.14 shows the input power factor characteristics.
According to the result, the input power factor by applying
each damping control is higher. This is because the leading
current becomes larger due to harmonic component in the input
current. Then, it can be achieved that the maximum input
power factor is 0.988 as the output power is 1.0 kW.
Fig.15 shows the input current THD characteristics. Notethat the gains of ACR were designed from the standard transfer
function. In this experiment, the damping gain of the input
current-type damping control Kd_I is 0.5. As a result, it can beachieved that the input current by the input current-type
damping control is sinusoidal in comparison with Fig.10.
According to the result, the input current THD isapproximately 30% and 55% improved by applying eachdamping control. However, effect of the resonance suppression
is decreased, with increasing the output power. This is because
the AC chopper loss which rolls in effect of the damping isincreased with increasing the output power. Furthermore, theinput current THD with the input current-type damping control
is lower than that of the capacitor voltage-type damping control.
Thus, it is confirmed that the effect of the resonancesuppression by the input current-type damping control is higher
in comparison with the capacitor voltage-type damping control.
However, the harmonic distortion can be suppressed by the

Figure 11. Experimental result with capacitor voltage-type
damping control.

Figure 12. Harmonic components of input current.

capacitor voltage-type damping control without the current
sensor. Therefore, it is not necessary to add extra current

sensors and detection circuit in the proposed circuit, which as aresult can reduce the cost of the system.
Efficiency (%)

VI.

93.8

CONCLUSION

In this paper, the input current stability control was
proposed without the detection of the input current and theoutput line voltage. The damping control can suppress the input
filter resonance without degrading the efficiency. There, thedamping control was applied in the AC chopper by thecapacitor voltage.

[4]

[5]
[6]

Capacitor voltage-type
damping control
800

1000

1200

1400

Output power (W)1600

Input current-type
damping control

Input power factor (p.u.)

0.99
0.98

Capacitor voltage-type
damping control

0.97
0.96

Without damping control

0.95
0.94
0.93
600

800

1000

1200

1400

1600

Output power (W)Figure 14. Power factor characteristics.
20
Without damping control
18
16
Capacitor voltage-type
14
damping control
12
10
8
6
Input current-type4
damping control
2
0
600
800
1000
1200
1400
1600

Output power (W)REFERENCES

[3]

93.2

1

In future works, the damping gain will be optimized.
Besides, effectiveness of the damping controls will be verified
in the motor load.

[2]Without damping control

93.4

Figure 13. Efficiency characteristics.

The proposed circuit with the damping control wasdemonstrated by a 1.8-kW prototype. As a result, it confirmedthat the input current THD and the output line voltage THD
could be reduced by 72.5% and 28.3%, respectively. Then, thedamping factor is 0.012. Moreover, it could be revealed that theefficiency and the input power factor were improved by thedamping control. Then, it could be accomplished that the
maximum efficiency and the input power factor are 93.83%
and 0.988, respectively. Additionally, it could be confirmedthat the effect of the resonance suppression by the input
current-type damping control is higher in comparison with theproposed damping control. However, the harmonic distortion
can be suppressed by the capacitor voltage-type damping
control without the current sensor. From these results, theresonance distortion could be suppressed by the proposed
damping control without additional current sensors.

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93.6

93
600

The effect of resonance suppression of two damping
controls was compared without the damping control by thebode diagram. As a result, it could be confirmed that the effectof resonance suppression of the proposed damping control was
obtained as same as the conventional damping control.

[1]Input current-type
damping control

Figure 15. Input current THD characteristics.
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