Input Current Stabilization Control of aMatrix Converter with Boost-up
Functionality
Jun-ichi Itoh* , Kazuhiro Koiwa *, and Koji Kato** Nagaoka University of Technology, 1603-1 Kamitomioka-cho Nagaoka City Niigata 940-2188, Japan
Abstract-- This paper proposes a circuit topology of amatrix converter that adding a boost up function in the
input side. The proposed circuit combines the matrix
converter with a V-connection AC chopper. A conventional
control method can be applied in this matrix converter, so
called the virtual indirect method. In order to suppress the
input filter resonance, this paper discusses about the input
filter design with a damping resistor. In addition, this paper
also proposed a stabilization control for the input current
that is using a V-connection chopper. The basic operationand validity of the proposed method is confirmed by thesimulation and experimental results. The total loss of the
proposed circuit is 20 % less than that the loss of theconventional back to back system.
Index Terms—Matrix converter, Damping
V-connection AC chopper

control,

I. INTRODUCTION
A matrix converter that is well known to convert an
AC power supply voltage directly into an AC voltage ofvariable amplitude and frequency without large energy
storages, such as electrolytic capacitors, have been
actively studied recently [1-12]. Practically applying ofmatrix converters into industrial, the following
advantages are found as compared with a back to backconverter (PWM rectifier and PWM inverter); (i) lightweight and long-life due to no passive components in thecircuit (ii) high efficiency power supplies because of lessswitching devices. The matrix converter is expected toapply in the hybrid electric vehicle system and the wind
power generator system in the future.
However, one disadvantage of the matrix converter isthe voltage transfer ratio, which defines the ratio between
the output voltage and input voltage, is being constrained
to 0.866. As a consequence, the output current of thematrix converter is higher than the back-to-back (BTB)
type converter, under the same output power.
Consequently, the motor loss and the converter loss will
be increased. Besides, the low voltage transfer ratio also
limits the applications of the matrix converters.
There are some discussions to improve the voltage
transfer ratio for the matrix converters. One of the easysolutions is to improve the voltage transfer ratio byconnecting a transformer between the power supply andthe matrix converter. However, the commercial
transformer applied in the power grid frequency is bulky.
In the Ref. [8], the matrix converter is proposed tooperate in over modulation range. The voltage transfer
ratio successfully improved to 0.94. However, the input

current and the output current contain of large distortions.
Additionally, the over modulation method can not boost
up the input voltage. Therefore, the use of a matrix
converter instead of the BTB system in the future, theboost up functionality is necessary for the specificapplication, which allows changes in the input voltage.
On the other hand, a Matrix-Reactance Frequency
Converter (MRFC), which consists of a matrix converter
and an AC chopper, has been studied [9]. In the Ref. [9],the output voltage of the MRFC can set higher than the
input voltage. However it seems that the MRFC requires
many components due to the insertion of the boost up
reactor and capacitor. In addition, it is difficult to control
the MRFC because the matrix converter and the chopper
need to synchronize with each other.
This paper proposes a circuit topology which connects
a V-connection AC chopper in the input side of thematrix converter that comes with a boost up functionality.
The only additional component of this proposed circuit isbidirectional switches because the input filter reactor isused as a boost reactor in this proposed method. One of
the features in this proposed circuit is that an automatic
voltage controller for the chopper is not required. As aresult, the capacitor in the boost-stage can become
smaller than the DC capacitor in the BTB system.
Moreover, this proposed circuit keeps the advantages of amatrix converter such as small size, light-weight andlong-life time. In order to suppress the input filter
resonance, a stabilization control is proposed in this paper.
In addition, this paper also discusses about the input filter
design method for the proposed converter. The
fundamental operation and validity of the proposed
method is confirmed by the simulation, experimental
results and loss analysis.
II. CIRCUIT TOPOLOGY AND CONTROL STRATEGY
Figure 1 shows the circuit diagram of a back to back
(BTB) converter, which consists of a PWM rectifier andan inverter. This system requires a large electrolytic
capacitor in the DC link part in order to smooth the DC
link voltage. The PWM rectifier requires an automaticcurrent 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 isconstrained by the control response of the DC link
voltage and the input current according to the AVR and
ACR.

The resonance between the input reactor and the input
capacitor occurs in the input side. In particular, when theresonant frequency is higher than the power gridfrequency, the variation by the resonance is appeared on
the input current and the capacitor voltage. In a
conventional matrix converter, the damping resistor,
which is connected in parallel to an input reactor, is used
to suppress the input current resonance. In addition, astabilization control method of the input current has beenstudied in Ref. [10-11].
On the other hand, the proposed converter connects aV-connection chopper in front of the matrix converter.
Furthermore, the current waveform of the filter capacitor
is a PWM waveform and the terminal voltage of the input
reactor is also a PWM waveform. Therefore, the damping
resistor will cause large loss because of many harmonics
are included in the voltage or current. In the next section,
the location of the damping resistor will be discussed tosolve the large loss due to the damping resistor
connection.
A. Location of a Damping Resistor
Figure 3 shows single phase equivalent circuits of the
AC chopper and high frequency equivalent circuits. In
equivalent circuit, a matrix converter is represented as acurrent source of Im because the input control

Electrolytic
capacitor

PWM inverter

Fig. 1 Back to Back converter.

Load

III. STABILIZATION METHOD OF INPUT CURRENT

PWM rectifier

LoadThis system is very flexible in term of voltage
condition between the input and the output side sinceboth converters are voltage type converters. However, theelectrolytic capacitor in DC link part gives known
problems such as large volume, high cost and short
lifetime in high temperature.
Figure 2 shows the proposed circuit diagram. The
proposed circuit connects a V-connection AC chopper in
the input side of the matrix converter. The additional
components are based on 4 reverse blocking IGBTs (RBIGBT) that is mainly constructed by silicon and diodes.
Additionally, the proposed circuit uses a minimum
amount of switching devices for this approach. The
proposed circuit does not require voltage control in the
input capacitor since both the input side and thr output
side of the V-connection chopper are AC voltage; i.e. thevoltage control of the V-connection chopper is an open
loop control. Therefore, the capacitor value does not
dominant by the voltage control response and the current
response. As a result, the proposed circuit does not affectthe size and the weight of the origin structure of a matrix
converter.
The maximum output voltage of the matrix converter
is decided by the duty ratio of the V-connection chopper.
It should be noted that the switches in the V-connection
chopper do not switch when the output voltage command
is lower than 0.866 of the input voltage. That is, in the
low voltage transfer ratio, the proposed circuit is able toobtain high efficiency obviously as same as original
matrix converter.

Fig. 2 Proposed circuit.

characteristic of the matrix converter is same as thecurrent source type converter.
Four various connection patterns for the damping
resistor are shown in Fig.3 (a)-(d). The loss of thedamping resistor can be separated into the fundamental
frequency component and the switching frequency
component of the input current.
At fist, the power loss of the damping resistor in Fig.3(a) is discussed. In high frequency equivalent circuit, achopper part and a current source representing a matrix
converter is concluded as a voltage source of vs. Then,the voltage source of vs is obtained by Fourier transforms.
The fundamental frequency of the switching function for
S1 is calculated by
2
1
vs = vo S1 = vo (1 + ∑ cos nπ sin nπD cos nωs t )(1),
π n=1 nwhere, ωs is the switching angular frequency and D is aduty ratio of the switch S1. n is the order of the switchingfrequency. In this paper, n=1 and vo is the capacitor
voltage in output side of the chopper. Therefore, the RMS
value of Vs is given byV
Vs = 0 sin πD(2),π

where Vo is RMS value of the output voltage. From theequivalent circuit, the damping resistor is determined by
R = 2Z 0ξ
(3),where Z0 is the characteristic impedance of the input filter
and from the damping factor ξ. Next, the reactor current
Is of high frequency component is obtained by the circuit
equation based on Fig. 3(a)-(ii). It should be noted thatthe input current is expressed by Z0 and ξ instead of thedamping resistor. The input current Iin for thefundamental frequency component can be calculated
from the output power of the AC chopper that is divided
by the input voltage. Consequently, the damping resistor

loss Ploss_Lseries is obtained by
2

2

Ploss _ Lseries = RI in + RI s =Vs2ξ 2 2ξ
I in +Zo
Z o 4ξ 2 + ( ω ) 2
2

(4),

ωc

TABLE IPARAMETERS
200 [V]LC filter
50 [Hz]
10 [kHz]
Output power
50 [Hz]Boost ratio

Input voltage
Input frequency
Carrier frequency
Output frequency

2 [mH]
40 [µF]
1.5 [kW]
1.23

where ωC is the cut off angular frequency of the input
filter, which is determined by
1
ωC =
(5),
LC
The characteristics impedance Z0 is determined by
L
Z0 =
(6),
C
(i) Single phase equivalent circuit(ii) High frequency equivalent circuit
Similarly, the loss of the damping resistor, which is(a) Resistor connected to reactor in series.
connected in parallel to the reactor as shown in Fig. 3(b),is calculated by the same formula.
Secondly, the power loss of the damping resistor in
Fig.3(c) is discussed. From the super position principle,
the high frequency equivalent circuit can be separated tothe power loss by the chopper and the matrix converter.
Additionally, the reactor L’ transforms a reactor value to (i) Single phase equivalent circuit (ii) High frequency equivalent circuit(b) Resistor connected to reactor in parallel.
the output side from the input side. It is determined by
L
L' =
(7),
(1 − D) 2
where D is the duty ratio of the switch S1.
In this case, the chopper can not be expressed by a
voltage source as previously discussed because thevoltage fluctuation of the capacitor can not be neglected.
For the voltage source, the chopper is represented by acurrent source of icp, which is the current of input reactor. (i) Single phase equivalent circuit (ii) High frequency equivalent circuit(c) Resistor connected to capacitor in parallel.
Then, the reactor current icp is obtained by
2
1
icp
icp = iin S1 = vo (1 + ∑ cos nπ sin nπD cos nω s t )(8),
π n=1 nCim
im icpFrom Fig.3(c)-(ii), the power loss Ploss_Cpara is the current
L
L
C
C
S1
flowing into the resistor for each circuit which is given by v
in
2ζZ 0
R
(9),
R
Ploss _ Cpara =(icp − im ) 2
R4ζ 2 (

ω 2
) +1
ωC

Similarly, the loss of the damping resistor, which isconnected in parallel to the reactor as shown in Fig.3 (d),is calculated by the same formula in Fig. 3(c).
Finally, the optimization of the location of the damping
resistor is decided by the power loss of the damping
resistor.
Figure 4 shows the relations between the damping
resistor loss and the damping factor. Table 1 shows thecalculation parameter for Fig.4. Firstly, when thedamping resistor is connected in parallel to the reactor,
the damping resistor loss becomes larger because thereactor voltage contains the switching ripple caused by
the chopper PWM operation. Secondly, the damping
resistor loss is also increased in the following twoconnections; when the damping resistor connects to thecapacitor in parallel and the reactor in series, because thedamping resistor loss includes the fundamental
component. As a result, the minimum loss is only
achieved when the damping resistor is connected to thecapacitor in series. However, the loss in the damping
register is still large when the damping factor is set toS2(i) Single phase equivalent circuit(ii) High frequency equivalent circuit(d) Resistor connected to capacitor in series.
Fig. 3 Equivalent circuits of the AC chopper.
connection in parallel to capacitor
connection in parallel to reactor

0.2
0.18
0.16

connection in series
to reactor

0.14
0.12
0.1
0.08
0.06

connection in series
to capacitor

0.04
0.02
0

0.2

0.4
0.6
0.8
1
Damping factor
Fig. 4 Relation between the damping resistor loss and damping factor.

more than 0.3 as shown in Fig.5. Since the damping
resistor loss can not be neglected, a damping control isrequired in the chopper control.
B. Design of the LC Filter
The damping resistor is used to suppress a resonancein the LC filter. The main components in the input
current and voltage ripple are around the switchingfrequency. In order to determine the filter design, theripple component of the switching frequency is evaluatedin this paper.
The amplitude of the ripple current and ripple voltage
on the input filter are calculated by the equivalent circuit
shown in Fig.3 where the damping resistor is notconnected. The maximum value of the current ripple andthe voltage ripple is expressed by the following
respectively,
2Vo
I rip =
sin nπD(10),
πωs L
2 I in(11).
sin nπDπωs C
It is confirmed that the voltage ripple and the current
ripple is decreased by increasing the input reactance andthe filter capacitance.
Figure 5 shows the voltage and current ripple
characteristics for the capacitance. Fig. 5 was calculated
according to the conditions in Table 2. It is noted that theinductance of the reactor is changed according to thecapacitance because the cutoff frequency of the input
filter is set to 1 kHz constantly. The capacitance is not
only normalized by the input impedance, but also thevoltage and current ripple are normalized by the rated
output voltage and the rated input current. There is a trade
off relationship between the voltage ripple and current
ripple against the capacitance. It is important to choose
the balance point to optimize the performance of the
input filter. Thus, the author suggests capacitor of 3.35 %is the most suitable parameter.

that is caused by the resonance in the input filter, astabilization control for the matrix converter has been
proposed in [10]-[11]. In these papers, the distortion
component of the terminal voltage is removed by using aband pass filter (BPF). After that, the distortion
components are subtracted by the input current command.
Since the proposed circuit uses the V-connection chopper,
the stabilization control should be applied to the chopper
control instead of the matrix converter.
Figure 6 shows the control block diagram for the
proposed circuit. The applied control method for thematrix converter is the virtual indirect control method
which can be referred in [7]. The matrix converter and theV-connection chopper can be easily controlled
independently. The proposed stability control isimplemented 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, theTABLE IIPARAMETERS
Input voltage
200 [V]
Input frequency
50 [Hz]Carrier frequency
10 [kHz]
Boost ratio
1.23
Output power
1.5 [kW]
Cut-off frequency
1 [kHz]Output voltage
246 [V]
Input current
4.3 [A]

Vrip =

C. Damping Control of the Input Current
In order to suppress the oscillation in the input current

0.4

Voltage ripple
Current ripple

Ripple (p.u.)

0.3
0.2
0.1
0
0.001

0.1
Capacitor (p.u.)
Fig. 5 The voltage and current ripple characteristics.

Fig. 6 Control block diagram of the proposed circuit.

0.01

1

harmonics components are appeared as ripple
components. The distortion component of the input
current is extracted by using a high pass filter (HPF).
After that, the distortion component is added to the
chopper command Dc*. It should be noted that the
proposed control does not require a high speed feedback
regulator. It means that the capacitor and the boost-up
reactor are not dominated by the control response of the
input current and the capacitor voltage.

Input voltage
Input frequency
Carrier frequency
Output frequency

TABLE IIISIMULATION PARAMETER.
200 [V]LC filter
50 [Hz]
10 [kHz]
Output power
50 [Hz]Load

2 [mH]
40 [µF]
1.5 [kW]R-L

IV. SIMULATION AND EXPERIMENT RESULTS
A. Simulation results
The operation of the proposed circuit is demonstrated
by the simulation results. Table 3 provides the parameters
and the conditions for the simulation circuit. The cut-off
frequency of the input filter was set to 1/10 of theswitching frequency. Note that the damping resistor is not
used in the simulation.
Figure 7 shows the waveforms of the proposed circuit.
In the Fig. 7(a), the damping control is not applied.
Therefore the input current has large oscillation based on
the LC resonance. The input current of THD (Total
harmonic distortion) is 7.6 %. On the other hand, in Fig.
7(b), the large oscillation components are suppressed incomparison with Fig. 7(a). As a result in Fig. 7 (b), it isconfirmed that the input current and output voltage THD
are 6.6 %, 1.2 % respectively.
Figure 8 shows the simulation results when the output
voltage ratio changes to 1.2 from 0.8. The output voltage
starts to change from 40 ms, gradually. The output
voltage is reached 1.2 time of input voltage. The input
current of THD is 11.1 %. The chopper is not switching
until the 40 ms. Thus, the switching loss is not occurred.
Figure 9 shows the loss analysis of the proposed circuitwith damping resistor connected to the reactor in series
by using a circuit simulator (PSIM, Powersim
Technologies Inc) and a DLL file (Dynamic Link
Library) [12]. The reverse blocking IGBT (RB-IBGT) is
used for the proposed system in this simulation. The input
current oscillation is suppressed by the damping resistor
only. In this case, the damping resistor loss becomeslarger as shown in Fig.9. Therefore the input current
oscillation cannot be suppressed by using the damping
resistor only, this will affect the features of matrix
converter.
Figure 10 shows the loss analysis between the BTB
system and the proposed circuit. The damping control isapplied for proposed circuit. The damping resistor loss
decrease drastically. In addition, the proposed circuit
could decrease the switching loss by about 2/3 incompared with the BTB system. In one switching cycle,
the number of switching for the proposed circuit is 8
times; however the number of switching is 12 times in the
BTB system. Therefore, the loss in the proposed circuit islower than the BTB system. These simulation results
confirmed the validity and fundamental operations of the
proposed circuit.

(a) Input and output waveforms without damping resistor and damping
control.

(b) Input and output waveforms with damping resistor and damping
control.
Fig. 7 Simulation results of the proposed circuit.

Input voltage
Input frequency
Carrier frequency
Output frequency

TABLE IVSIMULATION PARAMETER.
200 [V]LC filter
50 [Hz]
10 [kHz]
Output power
50 [Hz]Load

2 [mH]
13.2 [µF]1.5 [kW]
R-L

Input voltage waveform vr

100 V/div

Input current waveform ir

5 A/div

Output voltage waveform vuv

200 V/div

Output current waveform iu

5 A/div

00

00
Switching pattern of switch S1
1
0
Output voltage ratio
1.2
0.8
50
100
20
Time ms
Fig. 8 Simulation results of the proposed circuit.

150

loss [W]B. Experimental results
Figure 11 shows the experimental result of the
proposed circuit. Table 5 shows the parameters of theexperiment. The input voltage is increased to 1.25 times
by the AC chopper in proposed circuit.
However, the input current ir has distortion which isdue to the commutation failure is occurring when crosspoint of the filter capacitor voltage magnitude. Although,the commutation failure will be decreased by thecommutation method which is combined the voltage
commutation and the current commutation [13].
Additionally, the input current and the output voltage
waveforms will be improved by the damping control.
It should be noted that the output line voltage vuv
is observed by using a low-pass filter of 1.2-kHz
cut-off frequency to observe the low frequency
component distortion.

Fig. 9 Loss analysis of proposed circuit with damping resistor.

V. CONCLUSIONSThis paper proposed a circuit topology for the matrix
converter with boost up functionality and the stabilization
method in the input current control. The proposed circuit
combines a matrix converter with a V-connection AC
chopper. The advantages of the proposed circuit are
following;•
The proposed circuit has advantages of the matrix
converter such as small size, light-weight and longlife time, even added a chopper in the input side.
•
The matrix converter and the V-connection chopper
can be controlled independently.
•
The loss of the proposed circuit is lower than the
BTB system.
In addition, this paper discusses about the input filter
design method for the proposed circuit. First, in order tosuppress the resonance between the reactor and thecapacitor in the input filter, the damping resistors areinserted. When the damping resistors are connected to thecapacitor in series, it is suitable in terms of highefficiency. Secondary, the design method of the LC filter
is discussed. The LC filter is designed from the voltage
and current ripple characteristics. As a result, thecapacitor of 3.35 % is the most suitable parameters.
In future works, the commutation failure will bedecreased by the commutation method which is
combined the voltage commutation and the current
commutation. Furthermore, the input current and theoutput voltage waveforms will be improved by thedamping control.
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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Fig.10. Loss analysis of proposed circuit and BTB system.
TABLE V
Circuit parameter.
Input voltage
90 [V]
2 [mH]
LC filter
Input frequency
50 [Hz]19 [µF]
Carrier frequency
10 [kHz]
Boost ratio of chopper
1.25
Output frequency
50 [Hz]Transfer ratio of MC
0.75
Damping resistor
Load
R-L
26 [Ω]
Input voltage vr[V]

250[V/div]

Input current ir[A]2[A/div]

000
Output voltage vuv[V]（LPF）
0

[3]

[4]

[5]
[6]

250[V/div]

Output current iu[A]5[A/div]
10[ms/div]
Fig. 11 Experimental results of the proposed circuit.

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