Behavior of a Matrix Converter with aFeed Back Control in an Input Side
Junnosuke Haruna and Jun-ichi Itoh
Nagaoka University of Technology, 1603-1 Kamitomioka-cho Nagaoka City Niigata, 940-2188, Japan
itoh@vos.nagaokaut.ac.jp
Abstract--This paper discusses about characteristics of amatrix converter where a current feedback is applied to the
input side. When the impedance of the power grid is high,such as a generator, the control stability of the matrix
converter will be deteriorated. One of the solutions to thisproblem is to apply an input current stability control that is
proposed. However, the efficiency of the generator will
decrease at light load and heavy load. In this paper, thebehavior of the input current control is analyzed, then thevector control is applied to the input side in order to obtaina stable operation and the maximum efficiency according to
the pole position of the generator. This study confirms thevalidity of the vector control for the matrix converter input
side with experimental results. The input current THD
2.8% is obtained under a RL load.
Index Terms-- matrix converter, synchronous reactance,
input current stability control, input current feed backcontrol

I. INTRODUCTION
Recently, matrix converters, that can directly convert
AC power supply voltage into AC voltage of variable
amplitude and frequency without large energy storages,
such as electrolytic capacitors, have been actively studied[1-11]. Matrix converters have advantages in thefollowing aspects; size reduction, light-weight, long-lifeand high efficiency power supplies, compared with theuse of a PWM rectifier and an inverter system.
Matrix converters are mainly considered for motor
drive system applications, such as elevators and air
conditioners. Lately, applications for grid connection
have been considered, such as micro-gas turbines, wind
power systems, engine generators and so on. Moreover, amatrix converter for Hybrid EV is also considered. In
these applications, the generator is connected to the input
side of the matrix converter.
An impedance of the generators is higher than thecommercial power grid. When the generator is connectedto the matrix converter, a synchronous reactance isseveral dozen percent, the terminal voltage of thegenerator and the input current are unstable due to theresonance between the synchronous reactance and the
input capacitor. Especially, when an output power iscontrolled to constant by the current regulator, negative
resistance characteristic appears in the input side [1]. The
stability control method of the input current, which isconsidering the high line impedance, has been alreadyproposed in [3]. However, when under extremely highimpedance power source, such as a generator, is used as
the input, that effect has not been reported.

On the basis of these problems, the stability control
method for the input current considering synchronous
reactance of the generator has been already proposed byauthors. The conventional method, which is proposed in[1], achieves suppression in the input current oscillationand the variable speed drive of a motor using a damping
control on a rotating frame known a d-q frame.
On the other hand, the input current command of theconventional method consists of open loop control whichis calculated from the terminal voltage of the generator.
Open loop control is a simple construction. However,unity power factor control between an induced electro
motive force (EMF) and the input current is difficult forlight and heavy load because a filter capacitor current
affects the input power factor for light load. In addition,
the voltage drop due to the synchronous reactance also
affects the input power factor under a heavy load.
This paper discusses the relationship among the input
current, the filter capacitor current and the input power
factor for induced EMF for a matrix converter in order toclarify the behavior of the input current. Next, this paper
applies a vector control for the generator side using input
current feedback. In this proposed method, the oscillationof the input filter is suppressed; and the input power
factor between the induced EMF and the input current is
controlled to unity regardless of the load amplitude.
Lastly, the control characteristics of the matrix converter
where the generator is connected as input, theexperimental results are demonstrated as follows; (1) the
fundamental operation with R-L load, (2) the input
current distortion characteristics, (3) the relations among
the load power, the input power factor and the amplitudeof input current. The experimental results confirmed thevalidity of the proposed system.
II. INPUT POWER FACTOR FOR LIGHT AND HEAVY LOAD
Fig. 1 shows the circuit diagram of a matrix converterwith the generator as an input. The bi-directionalswitches, which consist of reverse-blocking IGBTs (RBIGBT), are connected between the input phase and output
phase. The synchronous reactance of the generator issubstituted by an input filter reactance. The input filter isconstructed by only filter capacitor.
Generally, when a 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 is connected in series to the filter capacitor.
Second, the damping resistor is connected in parallel tothe filter reactor. For the series connection, the power
consumption of the resistor becomes larger because thecapacitor current has large harmonics components at
switching frequency. Therefore, the damping resistor isusually connected in parallel to the filter reactor.
However, for the generator input, the damping resistor
can not be inserted to the synchronous reactance inparallel practically.
Fig. 2 shows a configuration of the input filter of thematrix converter with the generator as the input. Fig. 2 (a)shows the single equivalent circuit of the matrix
converter where Vr and Vs is the input phase voltage, Vg isthe induced EMF of the generator, Vc is the terminal
voltage of the generator, Iin is the input current, Imc is thePWM current of the matrix converter, Ic is the filter
capacitor current, Vmc is the output voltage, Lx is
synchronous reactance of the generator and Cf is the filter
capacitor. From Fig. 2 (a), a block diagram of the input
filter is introduced as shown Fig. 2 (b).
A transfer function from the PWM current to the input
current in Fig. 2 (b) is calculated by
1
Lx C f
I in
=
(1).
1
I mc
s2 +
Lx C fA damping factor does not appears in (1) because thedenominator does not contains the fist order of Laplacians, so the filter resonance between the synchronous
reactance Lx and the filter capacitor Cf will continue thenthe system becomes unstable. Therefore, a control
scheme to suppress the resonance is required for the input
side control.
Fig. 3 shows a block diagram of the conventional
stability control on the d-q frame [1]. Vcr, Vcs, Vct are thethree phase terminal voltage of the generator, θvc is phaseangle of the terminal voltage of the generator, θpfc is 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,
the fundamental frequency component of the terminal
voltage on the d-q frame becomes a constant value, i.e.
DC signal. In addition, harmonics components appear as
a ripple. Therefore, the distortion component of theterminal voltage can be removed by using a low passfilter (LPF) which has a long time constant. After that,the distortion component is subtracted to the input current
command Iin*.
On the other hand, the input current command of
conventional method is constructed on an open loop
control. The input current Iin is not controlled directly by
the input current command Iin*. Therefore, it becomesdifficult since the PWM current of the matrix converter
Imc is decided by the filter current Ic and the disturbances,which is generated by commutation error.
The relationship among the input current Iin, the PWM

Fig. 1. System configuration diagram of the matrix converter with thegenerator as input.

(a) Single phase equivalent circuit.

(b) Block diagram of input filter.
Fig. 2. Configuration of input filter.

Fig. 3. Conventional input current stability control.

V&g

V&c

V&g

V&c

I&in
I&mc
I&c

I&in
I&

I&mc

c

Fig. 4. Relationship among the input current, the input PWM current andthe input filter current of the matrix converter.

current of the matrix converter Imc and the filter current Ic
is calculated by
I in = I mc + I c(2).
Fig. 4 shows the phasor diagram of the relationshipamong the input current Iin, the PWM current of thematrix converter Imc and the filter current Ic in case of thelight and heavy load. In this paper, an EMF power factor
is defined as the power factor between the induced EMF
Vg and the input current Iin. When the EMF power factor
is controlled to unity, the d-axis component of the input
current Iin does not occur. Then, the amplitude of theinput current Iin becomes the minimum value. Therefore,
the maximum efficiency of the generator can be obtained.
In the heavy load in Fig. 4, the filter current Ic can beneglected because the amplitude of the input current Iin ismuch larger than the filter current Ic. Therefore, the EMF
power factor can be controlled to unity nearly. However,in the light load, the filter current Ic can not be neglected
because the ratio of the Ic to Iin is larger. Then, the phaseangle between the PWM current of the matrix converter
Imc and the input current Iin becomes larger. That is, theEMF power factor can not be controlled to unity.
On the other hand, the output voltage of the matrix
converter Vout is described by
Vout = λVg cos θ(3),where λ is the modulation index and cosθ is the EMF
power factor. Therefore, voltage transfer ratio, which isdefined as the ratio between the induced EMF Vg and theoutput voltage Vout, depends on the EMF power factor.
Consequently, the voltage transfer ratio decreases and thegenerator loss increases due to the increase of the input
current.
For example, in the view of applications, that theefficiency at light load is important, such as HEV, an
improvement of the EMF power factor at light load isrequired.
III. FEED BACK CONTROL OF INPUT CURRENT
This chapter describes the proposed input current
vector control for the generator side using an input
current feedback. In this proposed method, the oscillationof the input filter is suppressed by the current regulator;
and the EMF power factor is controlled to unity
regardless of the load amplitude.
Fig. 5 shows a block diagram of the input filter andcurrent control. The input current Iin is controlled to astable condition by the feedback control that is
calculating the error between the input current command
Iin* and input current Iin. The input current command Iin*is given to obtain the unity EMF power factor; i.e. id* =0.
Fig. 6 shows the phasor diagram of the relationshipamong the input current Iin, the PWM current of thematrix converter Imc and the filter current Ic using theunity EMF power factor control in the light load. The
input current Iin can be controlled directly by using thecurrent feedback. As a result, the amplitude of the input
current is optimized. It should be noted that the input
current command Iin* is considered like a reluctancetorque in non-salient-pole-type synchronous generator.
In order to suppress the resonance of the input filter,the control parameter in the automatic current regulator(ACR) needs to be designed. An input side of a matrix
converter is same as a current source type rectifier. Then,the filter voltage feedback is corresponding to the reactor
current feedback on a voltage source type converter.
However, the input current feedback on the matrix
converter requires a differential component to express anequivalent component for the filter voltage dimension.

Td s
Iin*

+
Iin

Kp

+
+

1 +
Ti s

Imc
-

Ic
+
Iin

Vg
+

Vc
-

1
Cf s

1
Lx s

Iin

Fig. 5. Block diagram of input current feed back control.
q&
VgjωLx I&in
V&c

I&in
I&c

I&mc

θ pfc
d

Fig. 6. Relationship among input current, input PWM current and input
filter current of input filter with proposed input current feed back control.

That is, a PID controller is needed. Next, the stabilizationof the input current with a PID control is considered.
From Fig. 5, 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
(4),
=
*
1
K
+
K
Ki
I in
p
s+
s3 + d s2 +Lx C fLx C fLx C fwhere s is Laplacian, Kp is a proportional gain, Ki is an
integral gain and Kd is differential gain.
When Ki and Kd equal to zero (i.e. P control), the firstorder s term becomes zero. Therefore, the damping factor
is zero. In addition, when the Ki does not equal to zero (PIcontrol), second order s term disappears. Therefore, thesystem is still unstable by PI control. However, when the
Kd is added even if the Ki equals to zero (PD control), thedamping factor can be set. Therefore, in the input current
control system on the rotating frame, the stabilization issecured by Kd and steady state error is eliminated by Ki.
From (4), the sate equation of the current control isgiven by⎤⎡1
0 ⎥ ⎡ x1 ⎤ ⎡0⎤⎡ x1 ⎤ ⎢ 0⎥⎢
p ⎢⎢ x2 ⎥⎥ = ⎢ 0(5),0
1 ⎥ ⎢⎢ x2 ⎥⎥ + ⎢⎢0⎥⎥iin*
1
+
K
K
K
p
⎥
⎢
i
d
⎢⎣ x3 ⎥⎦ ⎢⎣1⎥⎦⎢⎣ x3 ⎥⎦⎢L C
Lx C fLx C f ⎥⎦⎣ x f⎡ x1 ⎤⎡ Ki
Kp
Kd ⎤⎢ ⎥
iin = ⎢−
(6),
−
−
⎥ x2
Lx C fLx C f ⎥⎦ ⎢ ⎥⎢⎣ Lx C f⎢⎣ x3 ⎥⎦
where x1, x2 and x3 is state variable. In order to evaluate
the damping factor quantitatively, root locus of the PI
control and the PID control is obtained from (5).
Fig. 7 shows the root locus of the PI control and the
PID control when Kp equals 0.1 pu, Ti equals 1 ms and Td
equals 1 ms. Proportional gain Kp is normalized by theamplitude of the output current. In PI control, a realcomponent of the root locus is positive. In addition, an
imaginary component is large. Therefore, the system thatuses PI control is oscillating and unstable. 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 is suppressedby using the PID control.
The proportional gain Kp, the integral action time Ti
and the derivative action time Td can be designed from
Fig. 7. In this paper, the stabilization of the proposed
input vector control is discussed by the roots placed near
the real axis. The damping factor can be calculated incomparison with the roots and the second order standard
form equation. When an angle between the root and theorigin is 45 degree, the damping factor becomes 0.7 inthe second order. In this paper, the damping factor isadjusted to 0.7 from Fig. 7. As a result, the derivative
action time Td is set to 1ms.
Fig. 8 shows a details configuration of input current
feedback control. The phase information of induced EMF
is required to control the input power factor between the
induced EMF and the input current. This induced EMF
information is detected from a pole position sensor. It
should be noted that the phase information of induced
EMF can be estimated from the input current iin, theterminal voltage of the generator vc, the synchronous
reactance Lx and a generator frequency fin. The induced
EMF phase and generator frequency are calculated fromthe pole position sensor and digital Phase Locked Loop
(PLL). The integral block to calculate the phase angle θinis reset to zero by rising the u-phase pulse of the poleposition sensor. The input current command id* equals to
0 pu and iq* equals to 1 pu respectively. A coordinatetransformation of the input current is used as θin, which is
calculated by PLL. Then the input current phase iscontrolled to the same phase as the induced EMF of thegenerator regardless of the load amplitude.
The q-axis command iq* is always set to 1 in thematrix converter because the amplitude of the input
current is dominant by the output active power and the
input power factor. Therefore, the amplitude of the input
current is required to normalize the input current. The
amplitude of the input current can be introduced from the
input power and the output power to neglect the converter
losses. The input power and output power are describedby (7) and (8) respectively;
pout = vu*iu + vv*iv + vw* iw(

pin = I amp v i + v i + v i
*

*
gr r

vv*,

*
gs s

*
gt t

)

(7),
(8),

vw*

where vu ,are three phase output voltage
commands, iu, iv, iw are the three phase output current, vgr,vgs, vgt are the three phase induced EMF of the generator,
ir, is, it are the input current and Iamp is the amplitude of
the input current. The induced EMF vgr, vgs, vgt of thegenerator can be calculated by the frequency and theinduced EMF constant in generator parameters. From (7)and (8), the amplitude of the input current is calculatedbyv *i + v *i + v* i
I amp = u u* v v* w w *(9).
v gr ir + v gs is + v gt it
In this system, when the resonance frequency of the
input filter is set high enough than the operation
frequency of the generator, the filter capacitance becomes
smaller due to large synchronous reactance under same
resonance frequency. Then the ripple of the terminal

Fig. 7. Block diagram of input current feed back control.
Table 1. Parameters of the synchronous generator.

Table 2. Experimental conditions.

Fig. 8. Configuration diagram of input current feed back control.

voltage becomes larger. Consequently, the switchingdevises might break down due to the problem of overvoltage. Therefore, in this system, the filter capacitance is
set to a large value to reduce the ripple of the terminal
voltage of the generator and resonance frequency.
IV. EXPERIMENTAL RESULTS(a) Without stability control.

(b) Proposed input current vector control.
Fig. 9. Experimental results with RL load.

Generator current THD [%]This chapter discusses the validity of the proposed
input current feed back control by the experiments. Table
1 shows the parameters of the synchronous generator.
The experiment set-up uses an interior permanent magnet(IPM) generator. The IPM generator has harmonics
distortion in the induced EMF of the generator. It should
be noted that the harmonics distortion of the induced
EMF is neglected. The generator speed is constant ofrated speed. The output voltage control is an open loop
V/f control in [12]. Other experimental parameters areshown in Table 2.
Fig. 9 shows the experimental results where thegenerator as an input with a R-L load. Fig. 9 (a) shows
the input and output waveforms with the conventional
control method. Fig. 9 (b) shows the waveforms using the
proposed input current control.
In Fig. 9 (a), the large oscillation occurs in the input
terminal voltage and the input current. Additionally, theoutput waveforms have a distortion due to the resonancebetween the input filter capacitor and the synchronous
reactance. The total harmonic distortion (THD) of the
input current is 10.7% and the THD of the output current
is 4.2%.
As for Fig. 9 (b), the oscillation of the input side isdrastically suppressed in comparison with Fig. 9 (a).
Moreover, the distortion of the output side is eliminated.
The THD of the input current is 2.8% and the THD of
output current is 1.7%. The THD of the input current
reduced by quarter and the THD of the output current
reduced by half with the proposed input current feed backcontrol. These results lead to the conclusion that the
proposed control is extremely effective for a generator.
Fig. 10 shows the plot diagram based on theexperimental results that contain the input current THD
characteristic of the following controls; the conventional
control, the proposed control, and the non-stability
control. In non-stability control, as the load increases, theinfluence of the input filter resonance becomes larger
because the damping factor is only a winding resistance.
Therefore, the input current distortion will increase. In
addition, the input current distortion of the conventional
control is improved. However, the input current distortionof the conventional method becomes larger in heavy load
regions. That is, in the heavy region of conventional
control, the voltage drop due to the synchronous
reactance becomes larger. Therefore, the output voltage
command becomes over modulation. On the other hand,in the proposed method, the input current distortion is
drastically improved at all load regions because the EMF
power factor is controlled to unity and q-axis input

Fig. 10. Generator current THD characteristic by conventional method
and proposed method.

current is always zero. Therefore, the maximum voltage
transfer ratio can be obtained. As a result, the input
current does not distorted.
Fig. 11 shows the relationship between the load power
and the input power factor (not the EMF power factor)
between the generator terminal voltage and the input
current. Figs. 11 (a) and 11 (b) show the power factor
characteristic at the light load and the heavy load
respectively.
In the light load region, the EMF power factor isclosed to the input power factor because the phase angleθpfc between the induced EMF and the terminal voltage ofthe generator is near to zero from Fig.4 (b).
From Fig. 11 (a), the proposed method shows that the
EMF power is closed to the unity power factor in thelight load region. As for the conventional, the input
power factor is smaller in compared to the proposed

5

1.2↓Proposed control

1

4

0.8
0.6

3

↑Conventional control
Conventional control↓2

0.4↑Proposed control

1

0.2
0

200

400

600
800
Load power [W]1000

1200 0(a) Light load.
1.2

14↑Proposed control
Conventional control↓

12↑Proposed control

0.6

8

0.4

6
4

0.2
0
1000

10

Generator current [A]

0.8

18
16

Conventional control↓

1Input power factor

method. This is because the input power factor can not be
controlled due to the current influence at filter. The input
current of the proposed control is smaller than that of theconventional control. The proposed control can reducethe copper loss to one-third of the conventional method at
maximum point of the light load.
On the other hand, in the heavy load region, the input
power factor will decrease because θpfc increases at theheavy load. Then the input power factor should becontrolled to a lead phase.
As for Fig. 11(b), the input power factor of theconventional method can be controlled to unity. However,
the amplitude of the input current also increased. In thecase for proposed method, the input current is also
increase but the increment ratio is lower than theconventional method. This is because the reactive current
in the proposed method can be always controlled to zeroand the EMF power factor is controlled to unity. But for
conventional control, the reactive current (d-axis current)
increases at heavy load because the input power factor iscontrolled to unity. The proposed control can reduce thecopper loss by 26% of the conventional method at
maximum point of the heavy load.

2
1500

2000

2500

3000

3500

0
4000

Load power [W](b) Heavy load.

V. CONCLUSIONSIn this paper, the problem of the power factor between
the induced EMF and the input current where the load islight or heavy has been clarified. In order to solve thisproblem, this paper applies the input current feedback
control into the input side of the matrix converter with thegenerator as an input. In addition, a state equation is
introduced from the transfer function in order to analyze
the stability of derivative element of proposed input
current control.
This paper confirms the operation of the proposed
control by the experiment. The results show as follow;(1) The THD of the input current reduce to a quarter.
(2) Proposed control can correct the EMF power
factor at light load and heavy load.
(3) Proposed control can reduce the copper loss by
one of the third of the conventional method at the
maximum point.
The experimental results lead to a conclusion that the
input current feedback control for the matrix converter
where the generator performs as an input is a valid
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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