Control Strategy for a Matrix Converter with a
Generator and a Motor
Junnosuke Haruna

Jun-ichi Itoh

Nagaoka University of Technology
Nagaoka, Japan
haruna@stn.nagoakaut.ac.jp

Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp

Abstract— This paper proposes the stability control method forthe input current of the matrix converter considering thesynchronous reactance of a generator and a motor drive. Whenthe stability control uses the input current feedback with avector control for the generator side, the oscillation in the
input filter can be suppressed. However, the output current
oscillation occurs when the high response output current
control at the same time due to no energy buffer in the matrix
converter. The proposed stability control is the output current
control including a damping factor for the input filter
oscillation. This proposed method can achieve a stable
operation for the generator side and the motor drive at thesame time. In this paper, root placement is used to discuss thestability of the proposed controls. In addition, this paper
confirms the validity of the proposed controls in a matrix
converter with a generator and a motor by demonstrating thesimulation and experimental results.

I.

INTRODUCTION

Recently, matrix converters, that can directly convert AC
power supply voltage into AC voltage of variable amplitudeand frequency without the large energy storages, such as
electrolytic capacitors, have been actively studied [1-10].
Matrix converters have advantages in the following aspects;
size reduction, light-weight, long-life and high efficiency
power supplies, comparing with the PWM rectifier and an
inverter system.
Matrix converters can be applied in motor drive systems,
such as elevators and air conditioners. Lately, it also has
been considered to apply for grid connection such as microgas turbines, wind power systems, and engine generators.
Moreover, application of the matrix converter in the Hybrid
EVs is also being considered. In these applications, thegenerator is commonly connected as the input side of thematrix converter.
Generally, the impedance of the generator is higher thanthe commercial power grid. When the generator is connectedto the matrix converter, a synchronous reactance is several
dozen percent, the terminal voltage of the generator and the

input current are unstable due to the resonance between thesynchronous reactance and the input capacitor. Especially,
when an output power is controlled to constant by the current
regulator, negative resistance characteristic appears in the
input side [1]. The stability control method of the input
current, which is considering the high line impedance, hasbeen already proposed in [5]. However, when an extremely
high impedance power source, such as a generator, is used as
the input, that effect was not reported. In addition, thevoltage transfer ratio of the matrix converter decreases
because the voltage drop by the synchronous reactance is notneglected. Moreover, the reactive current of the generator
will increase which results the copper loss increased also.
In order to solve these problems, a stability control
methods with the synchronous reactance of the generator
have been proposed for the input current [2] by the authors.
This control method has an input current feedback tosuppress the oscillation between the synchronous reactanceof the generator and the filter capacitor. The oscillation of
the input filter could be suppressed; and the input power
factor between the induced EMF and the input current is
controlled to unity regardless of the load amplitude by using
the input current feedback control method. As a result,distortion in the generator side could be suppressed. In
addition, the voltage transfer ratio and reactive current of thegenerator are also compensated by the input power factor
control. However, when an output current feedback control
and the proposed method are applied at the same time toachieve the high performance motor control, the system
becomes unstable. In order to prevent unstable situation, theoutput current control response is limited.
This paper achieves the high performance motor driveand stable operation of the generator side by using a
proposed output current control including a damping factor.
In this method, the stability control for the generator side isadded to the output current control. The input current
command is constructed on an open loop control as same as
the conventional input current control of the matrix converter.

The reason of the input current feedback control ant thevalidity of the proposed method will be confirmed bydemonstrating the simulation and the experimental results. In
this paper, the characteristics of the input current feedback
control where the generator is connected as the input, aredemonstrated as follows; (1) the fundamental operation with
R-L load, (2) the relations among the load power, the input
power factor and the amplitude of input current at the lightload. (3) Operation with a motor load. As for the proposed
output current control method, the following results will beshown in sequence. (1) the fundamental operation with an
induction motor load, (2) torque step response results.
II.

=
R
S
T

G

U
V
W

M

Generator
Filter capacitor
Matrix converter
Figure 1. System configuration diagram of the matrix converter with thegenerator and the motor.

MATRIX CONVERTER WITH THE GENERATOR
Lx

Figure 1 shows the circuit diagram of a matrix converterwith the generator as an input. The bi-directional switches,
which consist of reverse-blocking IGBTs (RB-IGBT), areconnected between the input phase and output phase. The
synchronous reactance of the generator is substituted by an
input filter reactance. The input filter reactance is substituted
by using the synchronous reactance of the generator. The
input filter is constructed by only filter capacitor.
Generally, when the matrix converter is connected to a
power grid, the input filter resonance is suppressed by adamping resistor. There are two types of connection pattern
for the damping resistor. First, the damping resistor isconnected in series to the filter capacitor. Second, thedamping resistor is connected in parallel to the filter reactor.
For the series connection, the power consumption of thedamping resistor becomes larger because the capacitor
current has large harmonics components. Therefore, thedamping resistor is usually connected in parallel to the filter
reactor. However, the damping resistor cannot be inserted tothe synchronous reactance in parallel to a generator
practically.
Figure 2 shows a configuration of the input filter of thematrix converter with the generator as the input. Figure 2 (a)shows the single equivalent circuit of the matrix converter
where Vr and Vs are the input phase voltage, Vg is the induced
EMF of the generator, Vc is the terminal voltage of thegenerator, Iin is the input current, Imc is the PWM current of
the matrix converter, Ic is the filter capacitor current, Vmc is
the output voltage, Lx is synchronous reactance of thegenerator and Cf is the filter capacitor. From Figure 2 (a), a
block diagram of the input filter is introduced as shown in
Figure 2 (b).
A transfer function from the PWM current to the input
current in Figure 2 (b) is calculated by
1
Lx C f
I in=
I mc s 2 + 1
Lx C f

V&g

I&in

V&c

I&mc

I&c

Cf

(a)

Equivalent circuit of the input filter.

(b)

Block diagram of the input filter.

Figure 2. Configulation of the input filter.

A damping factor does not include in (1) because thedenominator does not contains the first order of Laplacian s,so the filter resonance between the synchronous reactance Lx
and the filter capacitor Cf will continue then eventually thesystem becomes unstable. Therefore, a control scheme tosuppress the resonance is required for the input side control.
III.

PROBLEM OF INPUT FEEDBACK CONTROLIn the stabilization method, which use an input current
feedback [2], the oscillation of the input filter is suppressedby the current regulator; and the EMF power factor iscontrolled to unity regardless of the load amplitude.
However, when this control is applied with an output current
control, the system becomes unstable. In this chapter, thestability of the system is discussed when the input current
control and the output current control are used at the sametime.

Figure 3 shows the block diagram of the input filter andinput current control. The input current Iin is directly
controlled to a stable condition by the feedback control thatis calculating the error between the input current command*(1). Iin and input current Iin. In order to suppress the resonance of
the input filter, a PID controller is required.

Figure 4 shows the phasor diagram of the relationshipamong the input current Iin, the PWM current of the matrix
converter Imc and the filter current Ic in case of the light load.
Figure 4 (a) shows the phasor diagram without the proposed
control and Figure 4 (b) shows the phasor diagram applies
with the proposed control. In the light load, the ratio of Ic to
Iin is larger than the heavy load. Then, the phase angle
between Imc and Iin becomes larger. Therefore, the phaseangle of Iin cannot control to the same phase of Vg. On theother hand, In Figure 4 (b), Iin can be controlled directly byusing the current feedback. As a result, the efficiency of thegenerator is optimized in the light load.
From Figure 3, the transfer function from the input
current command Iin* to the input current Iin is described by

Kp
Kd 2
Ki
s +
s+
Lx C fLx C fLx C f
I in
=
*
1
+
K
Kd 2
Ki
I in
p
s3 +
s +
s+
Lx C fLx C fLx C fFigure 3. Input current feedback control for the generator side.

q
V&g

I&in
I&c

(2),

where s is Laplacian, Kp is a proportional gain, Ki is an
integral gain and Kd is differential gain.

qjωLx I&in&
V&g jωLx I in

V&c

V&c

I&in

I&mc

(a) Without any control.

d

I&c

I&mc

d

(b) Input current feedback control.

Figure 4. Relationship among the input current, the input PWM current
and the inut filter current.

Figure 5 shows the root placement of the input current
feedback control with the PI control and the PID control. In
the PI control, a real component of the root placement is
positive. In addition, an imaginary component is large.
Therefore, the system that uses PI control is oscillating andunstable. On the other hand, in the PID control, all imaginary
component moves to the negative side and is smaller than the
PI control. Therefore, the oscillation of the input side can besuppressed by the PID control.
Figure 6 shows the experimental results where thegenerator as an input with a R-L load. Figure 6 (a) shows the
input and output waveforms without any stability control
method. Figure 6 (b) shows the waveforms using the input
current feedback control. In Figure 6 (a), the large oscillation
occurs in the input terminal voltage and the input current. As
for Figure 6 (b), the oscillation of the input side is drasticallysuppressed in comparison with Figure 6 (a). Moreover, thedistortion of the output side is eliminated. The THD of the
input current is 2.8% and the THD of output current is 1.7%.
These results lead to the conclusion that the proposed control
is extremely effective for a generator.
Figure 7 shows the relationship between the load power
and the input power factor between the generator terminal
voltage and the input current. As for the conventional, theinput power factor is smaller in compared to the input current
feedback control. This is because the input power factor
cannot be controlled due to the current influence at filter.
The amplitude of the input current with the input current
feedback control is smaller than that of the conventional
control. The proposed control can reduce the copper loss.
Figure 8 shows the simulation results of the motor loadwith input current feedback control and an output current

Figure 5. Root placement of the proposed input current feedback control
with PI control and PID control.

vector control. Each waveform has very large distortion andthe input current and the output current cannot be controlledaccording to the references. As a result, the system becomes
unstable.
In this case, the system has two current controllers at theboth of the input and the output side. Each current controller
tries to control the active power independently. However, thematrix converter cannot control the active power of the input
and the output side independently because the matrix
converter is a direct AC/AC power converter that does not
has any energy storages. Therefore, a power supply directly
proves the active power to the output side. In this case, theactive power is decided by the motor load torque and speed.
However, in the generator side, the input current feedback
control required to control the active power to suppress the
distortion component of the input side. Consequently, theinstantaneous active power between the input and the output

TABLE I.

TABLE II.

IPM GENERATOR PARAMETERS.

EXPERIMENTAL CONDITION OF INPUT CURRENTFEEDBACK CONTROL.

(a) Experimental results without proposed control.

1.2

5↓Proposed control

1

4

0.8
0.6

3

↑Conventional control
Conventional control↓2

0.4↑Proposed control(b) Experimental results with proposed control

0200

Figure 6. Experimental results with RL load using proposed input current
feedback control.

current control is different. Therefore, operation of eachcontroller interferes. As a result, the system becomes
unstable.
IV.

PROPOSED OUTPUT CURRENT CONTROL INCLUDINGDAMPING FACTOR

This chapter describes the proposed output current
control including the damping factor. In this proposed
method, the output current and oscillation of the input filter
are controlled at the same time.
The output voltage of the matrix converter is directly
converted from the input voltage. When the input voltage has
distortion, consequently the output voltage will be affected
and distorted. Thereby, the output current will be distorted
too. Thus, the input current is distorted and the distortion of
the terminal voltage will be increased. Therefore, thedistortion of the input side is affecting the output sidesimilarly. In the proposed system, the current controller must
be applied to only one side of the matrix converter to avoid
interferes of the controller. Generally, high performance
controller is required for adjustable speed drive. Therefore,
in this paper, the stability control for the input side isintegrated o the output current control. The input current

1

0.2
400

600
800
Load power (W)1000

1200 0Figure 7. Experimental results of input power factor characteristics withproposed input current control.
150
0
-150
6
0
-6
200
0
-200
5
0
-5
6
0
-6

Back e.m.f. of generator (phase, estimate) [V]Input current [A]Output voltage (line-to-line) [V]

Output current [A]dq-axis output current [A]

0.1 [s/div]

Figure 8. Simulation results of with the motor load using the input current
feedback control and the vector control.

stability control constructed by the open loop control isalready proposed by the authors [1]. In order to achieve thestable operation and output current control, the input current
stability control is combined to the output current control.

Figure 9 shows a block diagram of the conventional
stability control on the d-q frame. Vcr, Vcs, Vct are the threephase terminal voltage of the generator, θvc is the phase angleof the terminal voltage of the generator, θpfc is the input
power factor control command, Kd is the damping gain of
conventional stability control and Ir*, Is*, It* are the input
current command. In the conventional stability control, thefundamental frequency component of the terminal voltage on
the d-q frame becomes a constant value, i.e. DC signal. In
addition, harmonics components are appearing as a ripple.
Therefore, the distortion component of the terminal voltage
can be removed by using a low pass filter (LPF) which has along time constant. After that, the distortion component is
subtracted to the input current command Iin*.

Vcr
Vcs
Vct

Figure 12 shows a details configuration of output current
control including the damping factor. As well as the
proposed input feedback control, the phase of the induced
EMF is detected by the pole position sensor for controllingthe input power factor to unity. The phase angle of the input
Generator

Damping control

Ir*
Is*
It*

dq
/
3

+
+
Input power factor control

pfc

Figure 9. Block diagram of the input current stability control.

+
*

Iu

+
1
In

Kd

-

1
1+sTlpf

+

Kp
1
sTi

Iu

+
+

Figure 10. Block diagram of the proposed output current control.

PI control
Proposed control

4000

2000

-3x106 -1200

-900

-100

-200

0

-4000
Figure 11. Root placement of the proposed input current feedback control
with PI control and proposed control.

current command is calculated from the digital PLL. The
input current command idin* is always fixed to 0 pu and iqin*
equals to 1 pu respectively. Phase angle of an output sidemotor is calculated from motor encoder. Output current
command and phase angle of the output side are used for the
proposed output control. In this control, Automatic Speed
Control (ASR) and Automatic Flux Control (AFR) can beapplied to decide the d-q axis output current command. In
addition, the ASR, AFR and ACR PI gain can be designed

Matrixconverter

Pole position
sensor18
idin*=0
iqin*=1
fin

dq
/
3

∫
in

ir*,is*,it* 3

IM

SwitchingsignalSwitchingsignalcal. (ref.3)

100

-2000

Filter capacitor

G

PLL

3
/
dq

vc

Figure 10 shows the block diagram of the proposed
output current control where Tlpf is the time constant of the
LPF, Kd is the damping gain, Kp is the proportional gain of
the output current control and Ti is the integral action time.
Proposed control is the combination of input current stability
control and the output current control. The proposed control
is applied on the d-q frame. First of all, the error between
output current command and output current will becalculated. Next, the ripple of the output current error due tothe oscillation in the input filter is completely removed by
the low pass filter. After that, the fundamental component of
the output current is controlled by the PI controller. The
ripple component is controlled by the damping gain Kd.
Finally, the damping factor is added to output of PI
controller. As a result, the output current control anddamping control for the input side can be achieved at thesame time.
Figure 11 shows the root placement of the output current
between the PI control and proposed control. In the PI
control, a real component of the root placement is positive.
Therefore, the system that uses PI control is oscillating andunstable. On the other hand, in the proposed control, allimaginary component moves to the negative side. Therefore,
the oscillation of the input side is successfully suppressed byusing the proposed control.

Damping control
+
Kd
+
LPF
+

3
/
dq

iqout

idout

out

dq
3
/
vu*,vv*,vw* 3

ACR
ACR

∫

+

+

idout

PLL

*

iqout*

Figure 12. Control block diagrams of the proposed stability control

fout

Proposed output current control

TABLE III.

TABLE IV.

INDUCTION MOTOR PARAMETERSIMULATION PARAMETERS(a) Without proposed output current control.
TABLE V.

EXPERIMENTAL PARAMETERS

based on the specification of the motor. The damping gain Kd
and Time constant of LPF Tlpf can be designed by the root
placement as shown in Figure 11.
V. SIMULATION AND EXPERIMENTAL RESULTS WITHPROPOSED OUTPUT CURRENT CONTROL INCLUDINGDAMPING FACTOR
This chapter demonstrates the simulation andexperimental results by using two proposed control methods.
Table III and IV are used for the simulation with theproposed output current control including the damping factor.
In addition, Table III and V are used for the experimental
results with the proposed output current control.
Figure 13 shows the simulation results of the matrix
converter with the generator and the motor. Figure 13 (a)shows the input and output waveforms without the proposed
output current control method. Figure 13 (b) shows the
waveforms using the proposed output current control. In
Figure 13 (a), the large oscillation occurs in the input
terminal voltage and the input current. d axis and q axis
current also contains of the large distortion. On the other
hand, in Figure 13 (b), the oscillation of the input side isdrastically suppressed in comparison with Figure 13 (a).
Moreover, the distortion of the output side is eliminated. The
THD of the input current is 3.4%. These results lead to the(b) With proposed output current control.
Figure 13. Simulation results with the generator and the motor using
proposed output current control.

conclusion that the proposed control is extremely effective
for the generator and the motor.
Figure 14 shows the experimental results of the matrix
converter with a large inductance grid power supply and theinduction motor. Figure 14 (a) shows the input and output
waveforms without the proposed output current control
method. Figure 14 (b) shows the waveforms using the
proposed output current control. In this experimental result,the commercial grid and large inductance are used in the
input side to simulate an operation of the generator becauseof the limitation of experimental condition. In addition, the
ASR is added to the input of the q-axis current command of

Figure 12. The parameter of ACR and ASR is shown in
Table V.
In Figure 14 (a), the large oscillation occurs in the input
terminal current. The THD of the input current is over 35%.
As a result, the system becomes unstable without the stability
control as shown in Figure 13 (a). On the other hand, inFigure 14 (b), the input and output waveforms can becontrolled to the sinusoidal by the proposed output current
control. Especially, the large oscillation of the input current
can be suppressed. The THD of the output current is 13.8%.
As a result, the system becomes stable by using the proposed
output current control. It should be noted that the input
waveform happens with some distortion due to thecommutation error. This problem can be solved by thecommutation error compensation method [11].

(a) Without proposed output current control.

Figure 15 shows a torque step response result. In thecenter of this result, the load torque changes from 0% to
100%. Spike voltage and current did not happen on thesewaveforms after the torque steps up. So, the system can be
kept to the stable condition even if the load torque changes
suddenly. These results lead to the conclusion that the
proposed output current control including the damping factor
for the input filter oscillation control can suppress theoscillation in the input current and also drive the induction
motor under a variable speed.
VI.

CONCLUSION

This paper discusses about the control strategy for amatrix converter with a generator and a motor. By using the
input current feedback control, the stable operation of thegenerator was confirmed. However, the output current
control is applied to control the motor, thus the system
becomes unstable due to the interference of the controller. In
order to solve this problem, this paper proposed the output
current control including the damping factor can control the
motor current. The proposed control can achieve the stable
operation of the generator and the high performance motor
drive at the same time. The validity of the proposed method
is confirmed with simulation and experimental results. These
results lead to the conclusion that the proposed output
current control including the damping factor is extremely
effective for the motor drive application with the generator
as input.

0

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0

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Load torque 0%

Load torque 100%0
Input voltage (phase) (500 V/div)0
Input current (10 A/div)
Output voltage (line-to-line) (250 V/div)

Output current (20 A/div)
100 (ms/div)

Figure 15. Torque step response result with the proposed output control.

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