Damping Control Combined to Output Stage for a
Multi-Modular Matrix Converter
Hiroki Takahashi

Jun-ichi Itoh

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

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

Abstract— This paper discusses a damping control that is
applied for multi-modular matrix converters to suppress theoscillation by the LC resonance caused from the input filter. The
multi-modular matrix converter connects a multiple windingtransformer with several modules, which each module isconsisting of a three-phase to single-phase matrix converter. It isfound that the multi-modular matrix converter has theresonance problem between the leakage inductance of thetransformer and filter capacitors. In this paper, the damping
control that is combined to the output current control of themulti-modular matrix converter is implemented to suppress theresonance and to achieve better input current quality. The
proposed damping control can divert the output current sensors
for ACR (Auto Current Regulator), which is generally used inadjustable speed drive system of a motor, and additional sensors
are not required. From the experimental results, the proposed
damping control improves the input current THD by 72.1 %.

I.

INTRODUCTION

Recently, matrix converters have attracted a lot of
attentions among the researchers because this converter has no
DC energy buffer such as bulky electrolytic capacitors [1]-[7].
Matrix converters promise to achieve higher efficiency,
smaller size and longer life-time compared to the conventional
BTB (Back to Back) system which consists of a PWM (Pulse
Width Modulation) rectifier and a PWM inverter. In addition,
matrix converters achieve bidirectional power flow, unity
input power factor, and sinusoidal input and output waveforms.
In order to utilize these advantages of matrix converters
for high power applications, such as the wind turbines, pumps
and blowers, the multi-modular matrix converters that consistof several modules of three-phase to single-phase matrix
converter and a multiple winding transformer are investigated[8]-[10]. The multiple winding transformer is placed between
a power grid and matrix converter modules, and output
terminals of each module are connected in series or parallel inorder to provide high voltage or high power. The advantagesof this modular structure with the multiple windingtransformer are following: 1) the circuit structure, especiallyplacement of devices in the modules are simple; 2) special

modulation schemes to prevent the interference between theconnected modules are not required because the transformer
can isolate each module. Consequently, high power
conversion systems employing matrix converter topologies
can be designed and composed easily with the conventional
modulation schemes.
The multi-modular matrix converter requires LC filters in
the input side to eliminate the harmonic current due to theswitching operation and to assist in commutation similarly to
the general matrix converters. Besides, the multi-modular
matrix converter uses the filter capacitors only because theleakage inductance of the transformer can be treated as thefilter reactors. That is, filter reactors are not required.
Nevertheless, if the LC resonance occurs between the leakage
inductance and the input filter capacitors in the matrix
converter modules, the resonance can result in substantial
distortions in the input current. A general solution to the
problem of resonance in a standard matrix converter is toconnect damping resistors in parallel with the input filter
reactors [11]. However, in the multi-modular matrix converter,
the damping resistors cannot be connected in parallel with theleakage inductance of the transformer, practically.
One of other solution to suppress the resonance is toconnect the damping resistors in series with the input filter
capacitors in the modules. However, this method results inmore losses in the damping resistors due to harmonic current
caused by switching operation in comparison with the former
method. Hence, the solution using a special control tosuppress the resonance is necessary.
In the controls to suppress the filter resonance, active
damping controls for current source converters and generalmatrix converters have been proposed [12]-[16]. Thesemethods suppress the resonance with virtual damping resistors
in parallel with filter capacitors based on the input current
control. On the other hand, the damping control combinedwith the output current control of a standard matrix converter
was suggested [17]. This method can achieve the resonant
suppression and output current control at a same time, andalso control input current with open-loop. However, thedamping control suitable for multi-modular matrix converters
and its validity have not been clarified. In addition, thedamping controls which have been discussed in [12]-[16]generally require high accuracy and high speed response
voltage sensors connected to the filter capacitors of every
matrix converter module.

: 20deg leadwindingr Module ps
3 t U2 n: 20deg lag
winding

In this paper, the damping control that is implemented into
the output stage of the multi-modular matrix converter is
proposed. The proposed damping control can suppress thefilter resonance and also divert the output current sensors forACR (Auto Current Regulator), which is generally used inadjustable speed drive system of a motor, instead of using
high speed response voltage sensors on the input stage. Firstly,
the mechanism of the filter resonance is clarified in this paper.
Second, the proposed damping control is discussed with thecontrol block diagram. Finally, the validity of the proposed
damping control for the multi-modular matrix converter isconfirmed by simulation and experimental results.
II.

r Module ps
3 t U1 n

r Module ps
3 t U3 nr Module ps
3 t V1 n
r Module ps
3 t V2 n

3r Module ps
3 t V3 nr Module ps
3 t W1 n
r Module ps
3 t W2 n

MULTI-MODULAR MATRIX CONVERTERA.

System Configuration
Fig. 1 shows the system configuration of a series multimodular matrix converter with nine modules as shown in [8][10]. The series topology can output 7-level high voltage
which results in low harmonic components. A multiple
winding transformer is located between the power source andmatrix converter modules. The transformer cancels the loworder harmonics in the primary current of the transformer andreduces the ripples in the output voltage due to phase shift ofthe secondary windings by 20 degrees. In addition, this system
can set the voltage transfer ratio freely because the transformer
is employed, although conventional matrix converters have
limitation of the voltage transfer ratio.

r Module ps
3 t W3 nMultiple
Matrix converter
windingLoadmodulestransformer
Fig. 1. System configuration of a series multi-modular matrix converter withnine matrix converter modules. A series multi-modular matrix converter
provides high output voltage and multilevel waveform similar to sinusoidal.
Power
grid

Fig. 2 shows a simple model of a multi-modular matrix
converter with single module per output phase for analysis andconsideration. In Fig. 2, each module consists of a three-phaseto single-phase matrix converter which controls output phasevoltage and secondary current of the transformer. The
bidirectional switch in the three-phase to single-phase matrix
converter modules uses 2 series-connected IGBT-diode. Filter
capacitors are connected closely with the bidirectionalswitches to mitigate surge voltage to the switches. An output
terminal p is connected to load and another terminal n forms
the neutral point with other modules.
B. Mechanism of Filter ResonanceFig. 3 shows the single-phase equivalent circuit of input
filters of the multi-modular matrix converter as illustrated inFig. 2. In Fig. 3, Ll is the leakage inductance of thetransformer, Cf is the filter capacitor and Rmcs is the load
resistance which consumes the steady power. Then, the input
power factor is assumed to unity. Note that Ll, Cf and Rmcs areconverted to the primary side of the transformer. In addition,
the exciting reactance of the transformer is assumed to bemuch larger than the leakage inductance for the simplicity.
The filter resonance occurs because of an equivalent
negative resistance which is virtually generated at a constantM

20deg leadwindingr Module p
s
U n
3 t

3

r Module p
s
V n
3 t

20deg lagwindingr Module ps
3 t W n

M

(a)
p
r
s
t
n
Filter capacitors

Three-phase to single-phasematrix converter(b)Fig. 2. Simple model of a multi-modular matrix converter with single
module per output phase for analysis and consideration. (a) System
configuration of a multi-modular matrix converter with three modules; (b)configuration of matrix converter modules which controls output phasevoltage and secondary current of the transformer.

power load. The mechanism to generate the negative
resistance will be described as follows.
First of all, the filter capacitor voltage vc, the input currentof multi-modular matrix converter imc and the output powerpmc are defined as follows.


vc  vcs  vc 





imc  imcs  imc 





pmc  pmcs  pmc where, suffix s represents steady components based on thevoltage source angular frequency in whereas suffix  means
differential components caused by transient state. Then, thesteady components are expressed from (4) to (7).

vcs  2Vc cos int 



iL

imc
Ll

vp

vc

imcs  2 I mc cos int 



Vp(s)

1
sLl

IL(s)

Ic(s)

pmcs  vcsimcs  Vc I mc 1 cos 2int  

Rmcs 



vcs
V
 c 
imcs I mc



1



Then, from (1) to (3), imc is represented by (8).

imc 

p mc

vc



Equation (8) is applied with the linear approximation method
around the steady state operating point because (8) is anonlinear equation. The input current imc is separated into
steady and differential components and they are expressed as(9) and (10), respectively.



imcs 

p mcs
1

vcs 
vcs
Rmcs

Vc(s)
H1(s)

1
H2(s)
Rmc Vc(s) Fig. 4. Block diagram of a single-phase equivalent circuit of the input filters

where, Vc and Imc are the RMS values of the filter capacitor
voltage and input current of the multi-modular matrix
converter. Note that the output power of the single-phasemodel oscillates with the frequency by twice of in though theoutput power of three phase model is constant.



1
sCf

Imcs(s) Rmc Vcs(s)Imc(s)

Rmcs

Fig. 3. Single-phase equivalent circuit of the input filters in the multimodular matrix converter. The mechanism of the filter resonance is clarified
using this equivalent circuit.

Imc(s)



ic

Cf



in the multi-modular matrix converter at constant load. H1(s) and H2(s) are
the LPF and HPF respectively. This diagram has a positive feedback loop
due to the equivalent negative resistance gain and becomes unstable with LC
resonance.

Equation (11) indicates the fluctuation of the input current of
the multi-modular matrix converter against the fluctuation of
the filter capacitor voltage. In addition, an equivalent negative
resistance is generated at a constant power control, which is
obvious because the coefficient of vc is a negative value.
Fig. 4 shows the block diagram of the single-phaseequivalent circuit of input filters in the multi-modular matrix
converter at constant load. In order to separate the steady anddifferential components, filters named H1(s) and H2(s) areintroduced. H1(s) and H2(s) are the LPF (Low Pass Filter) andHPF (High Pass Filter) respectively, and defined by (12).

H1 s   H 2 s   1 





Then, Fig. 4 has a positive feedback loop because of thenegative resistance gain -1/Rmc. As a result, this system
becomes unstable with LC resonance. Therefore, the multimodular matrix converter must cancel the negative resistancegain with its control strategy at a constant load.
III.

CONTROL STRATEGY TO SUPPRESS FILTER RESONANCE

Fig. 5 shows the control block diagram of the multimodular matrix converter employing the conventional active
damping control. The basic concept of this technique is top  vc imcs
imc  mc insert a virtual harmonic damping resistor connected invcs
parallel with the filter capacitor Cf owing to the input current
control block in Fig. 5. As a result, the virtual harmonic
For a constant load, pmc becomes zero and (11) is derived.
damping resistor cancels the negative resistor with noinfluence on the fundamental component. However, the active
damping control requires high speed response and highimcs
1
imc  vc  vc  accurate voltage sensors in order to detect high frequency
vcs
Rmcs
harmonic components. Besides, if the conventional active
damping control is applied to the multi-modular matrix
converter as illustrated in Fig. 5, the required voltage sensors

are increased with the number of modules, which is not costeffective. For example, the multi-modular matrix converterwith nine modules as shown in Fig. 1 needs 18 voltage sensors
at least for the active damping control. Therefore, the damping
control for the multi-modular matrix converter which is
independent from the voltage sensor is preferred.
In addition, as mentioned above, the conventional active
damping control may be introduced to the input stage of themodules. On the other hand, for adjustable speed drive systemof a motor, the current control is requited to the output stage ofthe multi-modular matrix converter when a vector control
which composes ASR (Auto Speed Regulator) and ACR is
implemented. Then, design of these controllers becomescomplex because matrix converters have no energy buffers.
Hence, the damping control which is combined with theoutput current control for a motor is preferred.
In order to overcome these issues, in this paper, thedamping control combined to the output current control of themulti-modular matrix converter is proposed. The proposed
method can divert the current sensors for ACR and does not
require the voltage sensors at filter capacitors. Thus, therequired sensors for the proposed damping control are
independent from the number of modules. Furthermore, thedesign of controllers for ACR and damping control aresimpler than the damping control in the input current control
because the information of the controllers is collected to the
output stage.
Fig. 6 shows the system block diagram of the multimodular matrix converter with the proposed damping control.
The matrix converter modules control the output voltage andthe secondary current of the transformer at a same time. The
output voltage control block includes a damping control tosuppress the input filter resonance, and a vector control whichis composed by ACR and ASR. On the other hand, thesecondary current of the transformer is fed by open loop
control. Then, the secondary voltage phase angles of thetransformer q2U, q2V and q2W are calculated from (13) to (15)with the primary voltage phase angle of the transformer q1.


q 2U  q1   9 [rad ] 





q 2V  q1 





q 2W  q1   9 [rad ] Next, this paragraph explains the output voltage control
block. First of all, HPF which has a time constant Thpf
separates the harmonic components caused by the filter
resonance from the output current, Idout and Iqout. This is basedon the principle that the resonant distortion appears in the
output current since the matrix converters has no energy buffer.
Then, the cut-off frequency of the HPF is set lower than theresonant frequency because the fundamental frequency
component in the output current is converted to a constantvalue by a synchronous reference frame. Besides, theharmonic components are converted to ripples. Second, theextracted ripples are multiplied by the damping gain Kd, andsubtracted from the output current. The above shows thetheory of the damping control in order to suppress the resonant
distortion. On the other hand, the output current is controlled
by ACRs for the deviation obtained from the output current
commands Idout* and Iqout*, and feedback values from thedamping control. Then, the damping control path becomes
positive feedback eventually.
Fig. 7 shows the block diagram of a single-phaseequivalent circuit of the input filters with the proposed
damping control, where  is the modulation index of theditto below (U-phase module)*Mditto below (V-phase module)

3

3f – 1f
MatrixConverter

v2cr v2ct
2

Tan-1

3f
sThpf
/
Kd
dq 2 1+sThpf 2
3f
/
ab 2

i2d* = 1i2q* = 0

q2

1
s

2

Damping
12
control i2r*i2s*2
dq i2t* Switching
Signals/
2 3f 3
Cal.

q

ASR
Iqout*
Idout*=0

iU
iW

3f
/
dq

Idout
Iqout

vU*
dq Vdout*vV*/
3f V *
*
qout
vW

ACR

W-phase module
Fig. 5. Control block diagram of the multi-modular matrix converter employing the conventional active damping control. The active damping control tosuppress the filter resonance is installed to input current control block. On the other hand, the output voltage control block has ACR for the output current and
ASR for the motor speed. The damping control gain Kd behaves a virtual harmonic damping admittance in parallel with filter capacitors and suppress the filter
resonance. However, the required voltage sensors for the conventional damping control increase with the number of modules.

ditto below (U-phase module)*Mditto below (V-phase module)

3
vR
vT

2

1
s

3f – 1f
MatrixConverter

3f/ab
2
Tan-1

Cf

q1

12

Secondary
Voltage
Angle
Cal. (13)-(15)

q2U
q2V

i2d* = 1i2q* = 0 2

i2r*
i2s*
dq i2t* Switching/
Signals3
3f
Cal. [3]q2W

Damping control
3f Idout/
dq Iqout

iU
iW

dq
/
3f

vU*
vV*
vW*

sThpf
1+sThpf

KdsThpf
1+sThpf

Kd

ASR
Iqout*

q

Idout*=0

ACR

Vdout*

Vqout*
W-phase module
Fig. 6. Control block diagram of the multi-modular matrix converter with the proposed damping control. The output voltage control block includes a damping
control to suppress the filter resonance, ACR and ASR for a vector control. In contrast, the secondary current control of the transformer is fed by open loop.

multi-modular matrix converter at steady state, Iout(s) is theoutput current, Ioutd(s) is the output of the damping control
which subjects the ripples due to the resonance in Fig. 6,
Voutd(s) is the output of the PI controller regarding theresonant components, and Imcd(s) is the compensation value
owing to the damping control. It is confirmed that thedamping control loop is added in the filter block diagram.
Then, the gain due to the damping control loop cancels thenegative resistance gain which is the cause of the resonancebecause the damping control path is positive feedback in Fig.
6. Consequently, the system becomes stable and the filter
resonance can be suppressed.
IV.

SIMULATION RESULTS

Table I presents simulation conditions for the multimodular matrix converter with three modules drawn in Fig. 2.
The simulation is tested with a vector control which iscomposed by the ASR and the ACR to control rotation speedof the IPM (Interior Permanent Magnetic) motor. The negative
resistance appears because the ACR keeps constant output
power in the motor load. In addition, note that the filter
reactors are added instead of the large leakage inductance of atransformer. On the other hand, Table II shows the IPM motor
parameters as the load in the simulation.
Fig. 8 shows the input and output waveforms of the multimodular matrix converter at steady state in simulations. Notethat these results are obtained when the IPM motor operates at
rated speed and rated torque output. Fig. 8 (a) shows the result
without damping controls and (b) shows the result with theproposed damping control. It can be confirmed that the
primary current of the transformer contains large distortion
caused by the filter resonance from Fig. 8 (a), and the primary
current THD (Total Harmonic Distortion) is 62.9 %. Moreover,
the output line voltage and the output current have large
distortion too because matrix converter modules have noenergy buffers. Then, the output current THD is 15.4 % from
Fig. 8 (a). On the other hand, in Fig. 8 (b), the resonant
distortion in the output current is mitigated by the proposed

Vp(s)

1
sLl

IL(s)

Ic(s)

Imc(s)1sCf

Imcs(s)Imc(s)

1

1+sTi
Kp

1
Rmc

Vcs(s)1
Rmc

Vc(s)

Vc(s)

H1(s)
H2(s)

sThpf
1
1+sThpf Rmc
Iout(s)Damping Control LoopKd

sTi
Imcd(s) Rmc
Voutd(s) Ioutd(s)Fig. 7. Block diagram of the single-phase equivalent circuit of the input
filters in the multi-modular matrix converter with the proposed damping
control. This figure indicates a damping mechanism why the proposed
damping control suppresses the filter resonance.
TABLE I. SIMULATION CONDITIONS.
Input line voltage

200 Vrms

ASR natural frequency 63.7 Hz

Input frequency

50 Hz

ACR natural frequency 650 Hz

Rated power

3 kW

Carrier frequency

10 kHzTrans. turn ratio

1

Damping gain

0.6 p.u.

Leakage inductance

9.42 %

Input filter C

8.55 %

Damping HPF
cut off frequency

30 Hz

TABLE II. IPM MOTOR PARAMETERS.
Rated speed

1800 rpm (1 p.u.)

Rated line voltage

180 Vrms

Rated power

1.5 kW

Rated current

6.1 Arms (1 p.u.)d-axis inductance

11.5 mH

q-axis inductance

23.0 mH

Stator resistance

0.783 W

Inertia moment

0.00255 kgm2

damping control. As a result, the input current contains lessdistortion compared to Fig. 8 (a). Both the primary current of
the transformer and the output current THDs are under 1 % in
Fig. 8 (b). In addition, the output line voltage obtains 5 levels
waveform.
Fig. 9 shows the transient waveforms regarding the IPM
motor. Fig. 9 (a) shows the result without damping controlsand (b) shows the result with the proposed damping control. In
Fig. 9 (a), the dq-axis currents and output torque oscillate
during acceleration period and at rated speed and rated torqueoutput due to the filter resonance. However, in Fig. 9 (b), thecurrent and torque oscillations are suppressed by the proposed
damping control. Then, the overshoot of the d-axis current by
1.2 p.u. occurs when the rated torque is provided although thed-axis current command is set to zero. This problem will beovercome by the optimal design of the controllers in future
works. Therefore, it is confirmed from the simulation resultsthat the proposed damping control suppresses the filter
resonance and achieves stable operation with the IPM motor
load.
V.

EXPERIMENTAL RESULTS

Table III presents experimental conditions for the multimodular matrix converter with three modules drawn in Fig. 2.
Note that the experiments are tested with a constant power
load composed by a R-L load and the ACR, not a vector
control. Then, the negative resistance appears even if the R-L
load is used instead of the motor because the ACR keeps
constant output power. In addition, the filter reactors are added
instead of the large leakage inductance of a transformer incommon with the simulation condition. Also, the voltage
sensors in the filter capacitors are used because thecommutation sequence based on the input voltage of thematrix converter are applied. However, the commutation
sequence can be changed to a current type control using theoutput current, and the voltage sensors are not needed.
Fig. 10 shows the input and output waveforms of themulti-modular matrix converter obtained by the experiments.
Fig. 10 (a) shows the result without damping controls and (b)shows the result with the proposed damping control. In Fig. 10(a), the filter resonance is excited, and the primary current of
the transformer and the output current have resonant
distortions. In addition, the output line voltage is synthesizedin over modulation region because the filter capacitor voltage
is fluctuated by the filter resonance. Then, the primary currentof the transformer and the output current THDs are obtained
as follows, 20.1 % and 7.13 %. The reason that the current
THDs measured from experiments are lower than thesimulation results is that loss of the transformer and modules
behave damping resistors. In contrast, the filter resonance issuppressed by the proposed damping control in Fig. 10 (b).
Consequently, the input and output currents obtain lower
distortion compared to Fig. 10 (a). Then, the primary currentof the transformer and the output current THDs are 5.61 %and 2.62 %, respectively. Thus, the proposed damping control
mitigates the resonance distortions by 72.1 %. Furthermore,
the output line voltage obtains 5 levels waveform without theover modulation. Therefore, it is confirmed that the proposed

200 Input phase voltage [V]0-200 Primary current of the transformer [A]200-20
Output line voltage [V]
1000
0
-1000
20 Output current [A]0-200.24

0.25

0.26

0.27
(a)

0.28

0.29

0.3s

200 Input phase voltage [V]0-200 Primary current of the transformer [A]200-20
Output line voltage [V]
1000
0
-1000
20 Output current [A]0-200.24

0.26

0.27
0.28
0.29
0.3s
(b)
Fig. 8. Input and output waveforms of the multi-modular matrix converter as
drawn in Fig. 2 at steady state in simulations. (a) Without damping controls
which results in the primary current and the output current THDs by 62.9 %and 15.4 % respectively; (b) With the proposed damping control which
results in the primary current and the output current THDs are under 1 %.
0.25

Motor speed [p.u.]
1 Speed command
Actual speed0Output torque [p.u.]2
10d-axis current [p.u.]
Current command Idout* = 0
10Actual current Idout-1
q-axis current [p.u.]2
Current command Iqout*
1
Actual current Iqout
0
0.15
0.2
0.25
0.3s
0.1

(a)
Motor speed [p.u.]
1 Speed command
Actual speed0Output torque [p.u.]2
10d-axis current [p.u.]
Current command Idout* = 010-1
q-axis current [p.u.]2
Current command Iqout*
1
0
0.15
0.2
0.1

Actual current Idout

Actual current Iqout
0.25
0.3s

(b)
Fig. 9. Transient waveforms regarding the IPM motor. (a) Without damping
controls which results in steady perturbation in the output torque and dq-axis
currents due to the filter resonance; (b) With the proposed damping control
which results in suppression of the steady fluctuation.

damping control suppresses the filter resonance and achieves
stable operation.
Fig. 11 shows the harmonic components analysis of the
primary current of the transformer. Fig. 11 (a) shows the result
without the proposed damping control and (b) shows the resultwith the proposed control. In Fig. 11 (a), the primary currentof the transformer includes the 340-Hz and 440-Hz
components of approximately 10 % caused by the filter
resonance. In contrast, in Fig. 11 (b), the resonant components
are mitigated by the proposed damping control. In addition,
the harmonic components within a range from 100-Hz to 1.25kHz are suppressed by the proposed damping control since thecontrol has low cut-off HPF (30-Hz). Then, the upper limit ofsuppressible harmonics is decided by the control bandwidth
due to the carrier frequency.
Fig. 12 shows the THD characteristics obtained from theprimary current of the transformer subjected to the load
power. Note that the output line voltage is kept to 240-Vrms
constantly. Without any damping controls, the primary
current THD of the transformer is increased to approximately
20 % over 60 % load due to the resonance. On the other hand,the proposed damping control suppresses the THD under 7 %in the region more than 30 % load. Then, in the light load
region especially under 20 % load, the proposed damping
control cannot reduce the current THD because the main
reason of increasing THD is caused by the small amplitude of
the fundamental component of the primary current although
the distortion components is almost constant unrelated to theload. Besides the distortion is caused by the commutation
failure, is not caused by the filter resonance. Thus, theproposed damping control suppresses the resonant distortionin larger range of the output power.
Fig. 13 shows the THD characteristics of the primary
current of the transformer subjected to the leakage inductanceof the transformer. Without any damping controls, the primary
current THD of the transformer increases with the leakage
inductance. In particular, the data in the region over 10 % of
the leakage inductance of the transformer could not be taken
because the primary current of the transformer diverges due tothe destabilization. However, the proposed damping control
suppresses the primary current THD. Then, if the allowable
THD is set to under 10 %, the proposed damping control canbe applied to the condition which the leakage inductance ofthe transformer is under 14.1 %. Hence, the validity of the
proposed damping control is confirmed in experiments.
VI.

CONCLUSION

This paper discusses the damping control to suppress the
LC resonance caused from the input filter of the multimodular matrix converter. Past works related to the damping
control for current source converters and general matrix
converters have not clarified the validity for the multimodular matrix converter.
In this paper, a damping control suitable for the multimodular matrix converter is proposed. The proposed damping
control is combined to the output current control of the multi-

TABLE III. EXPERIMENTAL CONDITIONS.
Input line voltage

200 Vrms

Input frequency
Rated power

Output frequency

30 Hz

50 Hz

Load resistance

83.7 %

3 kW

Load inductance

1.88 %

Trans. turn ratio

1

ACR natural frequency

650 HzLeakage inductance

9.42 %

Load current command 0.95 p.u.

Input filter C

8.55 %

Damping gain

0.6 p.u.

Carrier frequency

10 kHzCommutation time

2.5 msDamping HPF
cut off frequency

30 Hz

Primary phase voltageof transformer 250 V/div

Primary currentof transformer 10 A/div

Output current 10 A/div

Output line voltage 500 V/div
10 ms/div

0

0

0

0

(a)
Primary phase voltageof transformer 250 V/div

Primary currentof transformer 10 A/div

Output current 10 A/div

Output line voltage 500 V/div
10 ms/div

0

0

0
0

(b)
Fig. 10. Input and output voltage waveforms of the multi-modular matrix
converter with three modules in experiments. (a) Without damping controls
which results in the primary current THD and the output current THD by
20.1 % and 7.13 % respectively; (b) With the proposed damping control
which results in the primary current THD and the output current THD by
5.61 % and 2.62 % respectively.

modular matrix converter. Therefore, the proposed damping
control suppresses the filter resonance and also diverts theoutput current sensors for ACR, which is generally used inadjustable speed drive system of a motor, instead of using
high speed response voltage sensors on the input stage.
From simulation and experimental results, the multimodular matrix converter without damping controls has large
resonant distortion in the primary current of the transformer
and the output current. However, the proposed damping
control can mitigate the distortion by 72.1 % at steady state. In
addition, from the THD characteristic of the primary currentof the transformer which subjects to the load power, theproposed control suppresses the THD under 7 % over 30 %load region. Moreover, the proposed damping control
mitigates the resonant distortion under 7 % in conditions of
the leakage inductance from 4.71 % to 14.1 %. Thus, theproposed damping control suppresses the filter resonant andthe validity of the proposed control is confirmed inexperiments.

100%
10%
1%

REFERENCES

0

[1]

100%

500

1k
1.5k
Frequency [Hz](a)2kfundamental
340Hz
440Hz

10%
1%

0

500

1k
1.5k
2k
Frequency [Hz](b)
Fig. 11 Spectrum of the primary current of transformer with experiments. (a)Without damping controls; (b) With the proposed damping control. In (a),340-Hz and 440-Hz components caused by the filter resonance are included.
However, these components can be reduced in (b) by the proposed control.

25

Primary current THDof transformer [%]No damping controls
20
15
Proposed
damping control

10
5
0

40
60
80
100
Output power [%]Fig. 12. THD characteristics obtained from the primary current of thetransformer subjected to the load power. The proposed damping control
reduces the resonant distortion under 7 % over 30 % load region.

0

20

25
No damping controls
20

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fundamental
340Hz
440Hz

15
Proposed
damping control

10
5
0

0

5
10
Leakage inductance of transformer %XL [%]15

Fig. 13. THD characteristics of the primary current of the transformer
subjected to the leakage inductance of the transformer. The proposed
damping control mitigates the resonant distortion under 7% in entire rangeof the leakage inductance of the transformer.