A Control Strategy for a Matrix Converter
under a Large Impedance Power Supply
Junnosuke Haruna

Jun-ichi Itoh

Nagaoka University of Technology
1603-1 Kamitomioka-cho Nagaoka City Niigata, Japan
itoh@vos.nagaokaut.ac.jp
Abstract - This paper proposes a control strategy for a matrix
converter with an input power supply such as generator.
Currently, applications for grid connection have been consideredsuch as micro-gas turbines, wind power systems, engine
generators and so on. However, very large impedance power
supply such as the generator has not been sufficiently examined.
Especially the PM generator which is used in various
applications has large synchronous reactance. Terminal voltageof the generator is not stable due to resonant phenomena between
synchronous reactance and an input capacitor. Therefore, theinduced electromotive force (e.m.f.) in the generator is estimatedusing a band pass filter (BPF). In addition, stabilization control
on a rotating frame is also proposed for the input terminal
voltage. In addition, this paper suggests an optimum input
power factor control because the output voltage is smaller thanthe output voltage command when a conventional power factor
control is used. By using the stabilization control, the input
current THD of 4.2% is obtained through experimental results.
Moreover, the validly of the optimum input power factor control
is also confirmed by the experimental results.
Index Term—Matrix converter, Generator, Synchronous
reactance, Stabilization control and Optimum input power factor
controlI.

INTRODUCTION

Recently, matrix converters, that can directly convert an AC
power supply voltage into an AC voltage of variable
amplitude and frequency without large energy storage, such as
electrolytic capacitor, have been actively studied [1-14].
Matrix converters can contribute to the realization of down
sized, light-weight, long-life and high efficiency power
supplies, compared with the use of a PWM rectifier andinverter system.
However, matrix converters are mainly considered for
motor drive system applications, such as elevators and air
conditioners [11]. In addition, other recent applications forgrid connection have been considered, such as micro-gas
turbines, wind power systems, engine generators and so on.
The behavior of matrix converters under the large line
impedance of a power grid have been investigated [10].
However, very large impedance power supplies, such as
generators have not been sufficiently examined.
For example, it has not been sufficiently discussed that theterminal voltage of the generator is not stable due to resonant
phenomena between synchronous reactance and the input
capacitor.
For the conventional control, input current
commands for the matrix converter are directly calculated by
the input terminal phase voltages. As a result, the vibration of

the input voltage influences the output voltage and the input
current waveform. In order to suppress current distortion andover voltage of switching devices, a stabilization method forthe matrix converter using the generator has been required.
The stabilization control method of the input current underconsiders the high line impedance has been already proposed
in Ref. [9]. Even if the input voltage suddenly changes, theinput current without the vibration can be kept because
effective power and reactive power are controlled byinstantaneous value. However, that effect has not beenreported in case of large impedance, such as the generator
input. In addition, the performance of the proposed method
decreases when the power supply frequency widely changes
because the stabilization control is achieved on a rest frame
and uses a band pass filter.
Moreover the control method of the generator using thematrix converter has not been discussed, yet. The output
voltage of the matrix converter depends on an input power
factor because a voltage transfer ratio is limited by the input
power factor. Therefore, the input power factor control has toconsider from the point of view of the maximum voltage
transfer ratio.
This paper proposes the control strategy for the matrix
converter with the input power supply, such as generator. In
this paper, the stabilization control on a rotating frame is
proposed for the terminal voltage. In addition, optimum input
power factor control is considered. This paper discusses thecontrol characteristics of the matrix converter based on
simulation and experimental results as follows; (1)fundamental operation with an R-L load and an induction
motor load, (2) the acceleration characteristics of the generator(3) terminal voltage control with input current phase control,and (4) relation among the input current phase, induced
electromotive force, the terminal voltage and the output
voltage. The results of the simulation and the experimentconfirmed the validity of the proposed system.
II. STABILIZATION CONTROL
A. Problems of the generation system
Fig.1 shows a circuit diagram of the matrix converter withthe generator as the power supply. Input impedance of thegenerator is very large because synchronous reactancedominants the input impedance. The synchronous reactanceof the generator is substituted by an input filter reactance.

PM Generator

Table 1. Simulation conditions.

Fig.2 shows the simulation results for the generator power
supply with the parameters given by Table 1. The large
oscillations in the input voltage and current occur. In addition,
the terminal voltage (as same as capacitor voltage) rises over
400V. Because the input current distortion affects theterminal voltage, after that the terminal voltage distortion
affects the input current of the matrix converter. As a result,the system approaches to unstable because a damping factor of
the system decreases.
Fig.3 shows a block diagram showing the transfer functionof the input filter. The transfer function shown in Fig.3 isdescribed by Eq. (1). When the synchronous reactance of thegenerator is large, the ripple of the terminal voltage becomeslarge. Therefore, the control system becomes unstable as thedamping term (Y0-K)/Cf in Eq. (1) decreases according to theincrease in the ripple factor K.
Vc
1
1=
Vs L f C f s 2 + (Y0 − K ) s + 1
Cf
Lf C fFig.1 Circuit diagram of the matrix converter with the generator.

600

Terminal voltage (phase) [V]

0
-600
3

Input current [A]

0
-3
60

Output voltage (phase) [V]0(1)

where Vs is the input voltage, Vc is the terminal voltage, Lf isthe synchronous inductance, Cf is the filter capacitor, Y0 is thesteady state values of the load power, and K is the ripple
values of the load power.
B. Damping control of the input current
In order to obtain the input current command without the
distortion factor, the phase information of the terminal voltage
has to be detected exactly. The distortion factor of theterminal voltage can be removed using the band pass filter(BPF). In this case, a cut-off frequency of the BPF accords
with the terminal voltage frequency. Therefore, the design of
the BPF is difficult because the cut-off frequency of the BPF
has to be adjusted by the output frequency of the generator.
On the basis of these problems, this paper suggests thestabilization control method using an adaptive BPF on arotating frame known a d-q frame.
Fig.4 shows a block diagram of the stabilization control
with the adaptive BPF on the d-q frame. The fundamental
frequency component on the d-q frame becomes a constantvalue, i.e. DC signal. In addition, harmonics components
appear as a ripple on the AC component. Therefore,
harmonics components can be completely removed by using a
low pass filter (LPF) which has long time constant. One of
the advantages of the proposed method is that the adjustmentof cut-off frequency in LPF is not required depending on thegenerator speed because the fundamental frequency
component of the input signal automatically is converted to a
DC signal on the rotating frame.

-6010Output current [A]0-10100ms/div

Fig.2. Input / output waveforms with the generator.

Fig.3. Block diagram with transfer function of the mission input filter.
Damping control
+

Kd

-

vcr
vcs

vcdhpf

vcd

3
/
dq

vct

vcq
cap

LPF

+

i r*

+

vcdlpfdq/
3

Damping control

is*
it*

+
pfc

+

Input power factor control
Fig.4. Block diagram of the stabilization control.

The proposed damping control is realized as shown in Eq.
(2). The input current commands are then obtained by the
inverse transformation of the rotating frame as shown in Fig.4.
1 − sTK d
1
1
**
Ic =
Vc − K d (Vc −Vc (2)Vc ) =
1 + sT
1 + sT
1 + sT
where, T is the time constant, Kd is the damping factor, Ic**isthe input current command of the matrix converter, and Vc isthe terminal voltage.
Fig.5 shows a block diagram with the transfer function of
the input filter after the proposed stabilization control. The
transfer function from Vc to Vs shown in Fig.5 is described by
Eq. (3). As a result, the stability of the system increases as thedamping term of Eq. (3) becomes Yo/Cf
1 + KL f s
Vc
1=1
Vs L f C f 2 Yo
(3)
s +
s+
Lf C fCf

C. Stabilization control for the output voltage
Fig.6 shows a control diagram of the output voltage
command with ripple compensation where vcdlpf ， vcqlpf ， vcd
and vcq are taken from Fig.4. The output voltage of the matrix
converter is also influenced by the input voltage. When the
ripple of the input voltage remains, the oscillation appears in
the output voltage. Therefore, the output voltage command in
the matrix converter is compensated by the magnitude of theterminal voltage. A mean value vcns and the instantaneous
value vins of the magnitude of the terminal voltage arecalculated using Eq. (4) and (5). The compensation gain vripple
is obtained from vcns divided by vins. For example, if vcns isgreater than vins, then vripple is over 1.0, and the output voltage
command is decreased.
vcns = vcdlpf + vcqlpf
2

vins = v cd + vcq
2

2

2

(4)

Fig.5. Block diagram of input filter in the proposed method.
vd*vq

f/V conv.

vu*
dq
/
3

*

vv*
v w*

vcdlpfvcqlpfMaximum vcns
Value cal.

vcd
vcq

Maximum
Value cal.

vripplevins

Fig.6. Control diagram of the output voltage command compensation.
R

XL

E0

Iin

Vc

MC

Fig.7. An equivalent circuit at single phase of the generator.

(5)

III. OPTIMUM CONTROL OF THE INPUT POWER FACTOR
In this chapter, we discuss the relation among the input
power factor control, the input terminal voltage, and theoutput voltage. First, the relation between the terminal
voltage and induced e.m.f. is considered. The input terminal
voltage is influenced by the input power factor in case of thelarge impedance power supply, such as the generator.
Fig.7 illustrates an equivalent circuit of a single phase forthe input side. The generator is expressed by using theinduced e.m.f. E0, the terminal voltage Vc, the stator resistor R
and the synchronous inductance XL. The matrix converter MC
can control the input power factor freely.
Fig.8 shows a vector diagram when the input power factor
is controlled at a phase lag and a phase lead when the valuesof R, which is much smaller than the synchronous reactance,
can be neglected. It should be noted that the input power
factor is decided by the θpfc as shown in Fig.4.
The input terminal voltage Vc that is smaller than the e.m.f.
E0 is obtained in case of a lag power factor as shown in Fig.8(a) θpfc<0 (Lag control)(b) θpfc<0 (Lead control)
Fig.8. Relationship among the power factor, the terminal voltage and e.m.f.

(a). In contrast, the input terminal voltage becomes larger
than e.m.f. in case of a lead power factor as shown in Fig.8 (b).
In these cases, an effective power P and a reactive power S are
obtained by Eq. (6) and (7)S = vc (i p + jiq )(6)
P = E0 i p(7).

From the Eq. (6) and (7), the input power factor cos θ is
calculated as shown in Eq. (8).
cos θ =

E0 i pP=
S v i2 + i2
c
d
q

(8)

Next, the relation between the terminal voltage, e.m.f. andthe output voltage is considered. A maximum voltage transfer
ratio of the matrix converter is limited to 0.866 of the input
terminal voltage because the minimum envelop with a fullwave rectification of the line voltage of the input terminal is
3 / 2 . In addition, the voltage transfer ratio depends on the
input power factor. AS a result, the maximum voltage Vout isconstrained as shown in Eq. (9)Vout = 0.866Vin λ cos θ(0≤λ≤1) (9)where Vout is the output voltage, Vin is the input voltage, λ isthe modulation index, and cosθ is the input power factor.
Finally, the maximum output voltage of the matrix
converter is obtained by Eq. (10) using Eq. (8) and (9).
ip
Vmax = 0.866vc cos θ = 0.866
E0(10)
id2 + iq2
Therefore In Eq. (10), when id=0, the voltage transfer ratio
becomes the maximum value. In other words, in order toobtain the maximize voltage transfer ratio of the matrix
converter, the e.m.f. phase agrees with the terminal voltage
phase.
IV. SIMULATION RESULTS
Simulations using PSIM (Power Sim Inc.) is introduced inorder to confirm the validly of the proposed stabilization
control. Table 1 shows the simulation conditions. A
commutation time is neglected in these simulations.
A. Generator power supply with a R-L Load
Fig.9 shows the simulation results for a generator power
supply with a R-L load. The generator speed is constant.
Good sinusoidal waveforms are obtained for the output
voltage, input and output current. The total harmonic
distortion (THD) of 2.9% and 4.9 % are obtained for the input
and output currents, respectively.
B. Acceleration characteristics with motor load under constantgenerator speed
Fig.10 shows the acceleration characteristics with an
induction motor load. The output frequency commandincreases from 0 to 25Hz. It was confirmed that the motor
speed follows the acceleration. The input current distortion
factor in the stationary state is 9.9%, and the output is 2.8%.
It should be noted that the input current distortion factor ishigh because the induction motor has no-load.
C. Generator acceleration results with a R-L load
Fig.11 shows the acceleration characteristics of thegenerator with damping control. After the generator is started,
the terminal voltage increases slowly. The output voltage andinput current follow the speed of the generator. If thegenerator accelerates without damping control, the terminal
voltage rises to 600V and control becomes unstable. However,
the maximum terminal voltage has reached over 300V
although the damping control is applied. This course is thatthe input filter ripple remains in the transient state. In order toTerminal voltage (phase) [V]

200
0
-200
6

Input current [A]

0
-6
100

Output voltage (phase) [V]

0
-100
10

Output current [A]

0
-10
200

Terminal voltage (BPF) [V]0-200100ms/div

Fig.9. Simulation results of generator power supply with R-L load.
Output frequency* [Hz]
25
0
300
0
-300

Terminal voltage (phase) [V]

0.6 Input current [A]0-0.6

Output voltage (line) [V]

200
0
-200
4
0
-4
200

Output current [A]Motor speed [rpm]0500ms/div

Fig.10. Simulation results of acceleration with motor load.

2000
0
400

Generator speed [rpm]Terminal voltage (phase) [V]

0
-300
1.5

Input current [A]

0
-1.5
100

Output voltage (line) [V]

0
-75
6

Output current [A]0-6500ms/div

Fig.11. Simulation results of generator acceleration with R-L load.

suppress the terminal voltage, the design of the input filter anddamping control will be optimized.
It should be noted that the simulation results agree well withthe experimental results. Therefore the experimental results
using the generator can be estimated by the simulation results.

(a) Experimental result without damping control(c) Experimental result with damping control

100

100

10

10

1

1

0.1

1

3

5

7

9

11

13

15

17

19

21

23

25

0.1

1

3

5

7

9

11

13

15

17

19

21

23

25

(b) FFT result of input current of (a).
(d) FFT result of input current of (d).
Fig.12. Experimental results with large impedance power supply.

Large
impedance
power supply

Table 2. Experimental conditions.

V. EXPERIMENTAL RESULTS
A. Stabilization control
Fig.12 shows the experimental results of a large impedance
power supply with a R-L load. The experimental parametersof Table 2 were used. Fig.12 (a) and Fig.12 (c) shows
waveforms of the input and output voltage and current, Fig.12(b) and Fig.12 (d) are the harmonics analysis results using fast
Fourier transform (FFT) of the input current. A large
reactance was connected between the power supply and thematrix converter in order to simulate a generator.
In case of Fig.12 (a) and (b), the stabilization control is notapplied. Therefore, each waveform has large oscillation.
12.2% of the input current THD is obtained. The frequency
components of 12th and 14th are especially large. This reason
is that the resonant frequency of the input filter, which
consists of the filter capacitor and the synchronous reactance,
is 565Hz to which the 11th and 14th frequency is close.
In case of Fig.12 (c) and Fig.12 (d), the stabilization control
is applied. The large oscillation components are decreased incomparison with Fig.12(a). The input current THD of 4.2% is
obtained.
The input current THD is decreased byapproximately 30% by using the stabilization control. The
frequency components from 9th to 19th are drastically(a) θpfc equals 20 [deg] (optimum value).

(b) θpfc equals 60 [deg] (over).
Fig.13. Input / output waveform at input power factor.

eliminated. Therefore, the stabilization control can greatly
suppress the filter resonance. The upper limit of thesuppressed frequency components is decided by the responseof the damping control.
These results lead to the conclusion that the stabilization
control is extremely effective for a large impedance power
supply such as a generator.
B. Optimum input power factor control
Fig.13 shows experimental results for a large power supply
with a R-L load using the stabilization control and the
optimum input power factor control. This case also uses large
reactor instead of the synchronous reactance of the generator.
The output voltage command was set to 65V.
When the input power factor angle θpfc equals 0deg, whichmeans unity power factor for the input terminal, the output
voltage of 60V is obtained. Although the output command is
65V, the output voltage according to the command is notprovided because the terminal voltage decreases under the lagphase.
When θpfc equals 20deg, the output voltage of 64.8 V is
obtained as shown in Fig.13 (a). In this case, the phase of the
input current agrees with the phase of the induced e.m.f.
which is simulated by the power supply. As a result, theoutput voltage rises by 4.8V and equals the voltage command.
Fig.13 (b) shows the result of the over power factor control.
When θpfc is controlled beyond the optimum point, the output
voltage is remarkably drops. In addition, the input current
THD becomes worse because the over modulation occur due
to the low input power factor.
Fig.14 shows the relation between the phase angle θpfc andthe ratio of the terminal voltage and the induced e.m.f., theratio of the output voltage and the induced e.m.f. The
maximum value of the Vu/E0 is obtained at θpfc=20deg asshown in Fig.14. Therefore, when a generator is used as thepower supply, the input current phase should be controlled at
the same phase as the induced e.m.f. in order to obtain the
maximum voltage transfer ratio.
On the other hand, the quantity of the terminal voltage rises
over the optimum point of θpfc. In addition, Vcr/E0 becomesover 1.0. As a result, the maximum value of the Vcr/E0 of 1.21
is obtained. The terminal voltage decreases in large leadphase because the input current can not be controlled due tothe over modulation.
VI. CONCLUSION
This paper proposes a new control strategy for the matrix
converter with the input power supply such as a generator.
The problem of the large impedance power supply is low
stability because the damping resistor in the input filter can
not be used. To solve this problem, this paper proposed thestabilization control on the rotating frame. In addition, therelation among the input power factor, the terminal voltage,
output voltage and the induced e.m.f. was analyzed, and the
optimum power factor control is also proposed.
The experimental and simulation results lead to theconclusion that the matrix converter is valid for the large input
impedance power supply such as the generator using theFig.14. Relationship among terminal voltage, output voltage and backelectromotive force.

proposed stabilization control and the optimum power factor
control.
This study was supported by Industrial Technology Grant
Program in 2005 from New Energy and Industrial Technology
Development Organization (NEDO) of Japan.
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