A Novel Control Strategy for a Combined System
Using Both Matrix Converter and Inverter
without Interconnection Reactors
Jun-ichi Itoh and Hiroshi Tamura* Nagaoka University of Technology

Department of Electrical Electronics and Information Engineering1603-1 Kamitomioka-machi, Nagaoka city Niigata, Japan
itoh@vos.nagaokaut.ac.jp

Abstract— This paper proposes the control strategy of amatrix converter and a voltage type inverter in parallelsystem which becomes unnecessary of interconnection
reactors. The proposed control strategy divides theoperation time of each converter to every carrier cycle.
Further the output voltage of the combined system and thepower distribution ratio of each converter are controlled,
simultaneously. In addition, the sinusoidal input current
waveform is obtained. The operation time of each converter
is divided in one carrier cycle. Thus, interconnection
reactors are not required. These new proposals are
confirmed by the simulation and experimental results.

I.
INTRODUCTION
Recently, to improve the global environment problem,
power converters require high efficiency. In particular,
there has been a strong demand for high efficiency anddownsizing of three-port interconnection converters withan AC and a DC power source such as, hybrid electricvehicles systems consisting of a generator, motor andbattery, and the power grid back up systems using anengine generator and a battery [1].
Generally, a PWM rectifier, a DC chopper and an
inverter system are used as a combined system of an AC
and a DC power source. However, an electrolytic
capacitor is needed as an energy buffer for DC link partin this system. The electrolytic capacitor results that thecircuit is large-size, short lifetime and high cost. One ofpossibility to solve these disadvantages is application of
matrix converters, which can directly convert AC to AC
without the need of large electrolytic capacitors [2-3].
However, it is difficult to apply a matrix converter to aninterconnection system consisting of an AC and a DC
power source, because matrix converters have no DC linkpart in the main circuit.
There are some approaches to interconnection systems
using other type matrix converters known as indirect
matrix converters [4]. The indirect matrix converter has a
DC stage without a capacitor and can also obtain highefficiency in comparison with conventional systems thatconsist of a PWM rectifier and an inverter. However, theefficiency of a conventional matrix converter using nine
AC switches is higher than an indirect matrix converter.
On the other hands, there is another approach using anine-switch matrix converter was proposed in Ref. [5]. A
voltage type inverter is connected to input side of amatrix converter. However, in conventional systems,
there are problems such as large-sized and needed
maintenance because the snubber circuit is needed in a
direct power converter. The snubber circuit causes large
volume and high cost.
This paper proposes a novel control strategy for athree-port system of AC to AC and DC to AC conversion
using a nine switch matrix converter and an inverter. The
inverter with the battery is connected in parallel to thematrix converter in place of a snubber circuit. In otherwords, the proposed system is a delta configuration
system among a generator, a battery, and a motor. Thissystem can realize the most efficient power conversion
between each power source because there is only one
power converter between each power source. Moreover,the proposed system does not require an interconnection
reactor, because the matrix converter operation isperfectly divided from the inverter operation by a gateblocking signal.
There are two methods to control a matrix converter
known as a indirect control [6-7], and a space vector
PWM[2-3]. The operation time of each converter must be
switched at high speed in order to keep a sinusoidal wave
form for the input current. The indirect control is used tothe matrix converter because a triangular wave
comparison control [8] is used for parallel inverter. Then,the operation time of each converter is divided for every
carrier cycle. An operation time division ratio is
determined from output voltage and a power distribution
ratio of each converter.
This paper describes the features of the proposedsystem and the proposed control method, and provides
experimental results to demonstrate the validity of the
proposed system.
II.

THE CONVENTIONAL CONFIGURATION

A. A PWM rectifier and inverter system
Fig.1 shows a conventional PWM rectifier and inverter
system with DC chopper for a DC power source. Thissystem requires a large electrolytic capacitor in DC linkpart. This system is very flexible for the input and output
voltage condition. However, the problem for anelectrolytic capacitor in DC link part is large volume,
short lifetime in high temperature and high cost.
B. A system using an indirect matrix converter
Fig. 2 shows the system using an indirect matrix
converter. A DC/DC converter is added between an
AC/DC converter and a DC/AC converter in this system
configuration. The advantage of this system is that theefficiency is higher than a conventional PWM rectifier
and inverter system. In addition, an indirect control islower cost than a conventional matrix converter using
nine-switch because a conventional IGBT module can beapplied. Thus, easy commutation can be achieved because
pulse pattern of the AC/DC converter does not require
overlap time. However, the efficiency of this system islower than the conventional matrix converter. Because thenumber of power conversions is needed twice between
each power source.

interconnection reactors are large and heavy. In addition,
the interconnection reactor results losses increasing.
III. THE PROPOSED CONFIGURATION
Fig.5 shows the configuration of the proposed system.
The proposed system is a delta configuration system
which is connected by the diode rectifier, the inverter andthe matrix converter. Then, this system can directly
convert among each power sources of a generator, abattery, and a motor. In this paper, the power converter
between the generator and battery is used as the dioderectifier because the generator mainly charges the power
to the battery. It is noted that if the system requires thegenerator is driven by the battery, the PWM rectifier canbe applied.
The most significant characteristic in the proposal
system is that the proposed system does not require theinterconnection transformers or reactors at the connection
point of the matrix converter and inverter because the time

C. A system connecting an inverter to input side of amatrix converter
Fig.3 shows the system connecting an inverter to the
input side of the matrix converter. The characteristic of
this system is that an input filter becomes unnecessary.
However, the efficiency between the battery and the load
is not so high because this system requires twice power
conversion between a battery and load. In addition, thesnubber circuit becomes large in order to absorb theenergy of an inductive load in the protect operation of thematrix converter.
D. A general parallel system of a power converter
Fig. 4 shows the configuration of a conventional
parallel connection system using interconnection reactors.
A parallel connection system can easily increase thepower rating. Interconnection reactors suppress the shortcircuit between parallel converters [9-13]. However,Fig.3 System configuration of the combined system of a matrix
converter with an inverter at the input side

Fig.4 Parallel multiplexing system using interconnection
reactors.

Fig. 1 Conventional PWM rectifier and inverter system with dc
chopperFig.2 System configuration with an indirect matrix converter

Fig.5 The proposed system using a matrix converter and an
inverter without interconnection reactors.

sharing operation of the matrix converter and inverter isachieved during one carrier cycle. Furthermore, the chiptemperature of a switching device in the system can be
kept at low temperature because the output current of the
proposed system can be distributed to the matrix converter
and the inverter. Therefore, the current rating of aswitching device can be reduced according to each output
power ratio. Moreover, it is not necessary to include thesnubber circuit for the matrix converter because the circuitof battery and inverter works as regenerative snubber
circuit for the matrix converter. Therefore, thecommutation of the matrix converter can be simplified
from four steps to two steps because the pulse timing of
the matrix converter may have a dead time period.
Consequently, the number of drive circuits of the matrix
converter can be reduced from eighteen to nine because
the same gate signal can be used for a couple of theswitching device in the same arm. However, the matrix
converter and inverter are prohibited to be active at thesame time because the short circuit occurs between thegenerator and the battery. Moreover, the battery voltage isconstrained to larger than the maximum line voltage of thegenerator.
IV. THE PROPOSED CONTROL STRATEGYThis paper proposes the control strategy of the matrix
converter and inverter system, which does not requireinterconnection reactors. In addition, we control the output
voltage of each converter and the power distribution ratioof the combined system simultaneously. Moreover, theoperation time of the matrix converter and the inverter isdivided for every carrier cycle so that the input current isheld to a sinusoidal wave form.
Fig.6 shows the control block diagram of the proposed
combine system. The power distribution ratio is controlled
by the operation time division of each converter. The
output voltage is obtained by average output voltage of
inverter and matrix converter. Thus, a variation triangle
carrier, which has difference slope between up and down
as reported in [4], is used in order to maintain thesinusoidal input current waveform.

Fig.6 Control block diagram of the proposed system.

Fig.7 Relationship of the output voltage between the proposedsystem and each converter.

Egenerator =200[V]300

Edc =350[V]Uncontrollable range

247
200
173

Controllable range
100

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

*
mc

Fig.8 Output voltage range for the proposed system.

A. The simultaneous control method for the output
voltage and the output power ratio
Fig.7 shows the relationship between the output voltage
and the operation time ratio for the proposed combined
system. The output voltage is decided by the averagevalue of the output voltage between the matrix converter
and the inverter. Therefore, when the operation time ratio
for the matrix converter is defined as αmc and theoperation time ratio for the inverter is defined as 1-αmc in
one carrier cycle, the output line voltage is obtained by (1).
Vsysout = α mcVmcout + (1 − α mc )Vinvout= α mc λ mc E generator + (1 − α mc )λinv

E dc
2(0 ≤ λ ≤ 0.866, 0 ≤ λ ≤ 1, 2 E
mc

inv

3
2

generator(1)< E dc)where, Vsysout is the output line voltage of the proposedsystem, Vmcout is the output line voltage of the matrix
converter, Vinvout is the output line voltage of the inverter,
λmc is the modulation index of the matrix converter, λinv isthe modulation index of the inverter, Egenerator is the line
voltage of the generator, and Edc is the battery voltage.
Fig.8 shows the output voltage range for the proposedsystem. In the proposed system, the battery voltage isconstrained by larger than the maximum line voltage ofthe generator. Thus, the range of the output voltage isdefined from zero volts to battery voltage.
The power distribution ratio is calculated bymultiplying the output voltage and operation time ratio.
Generally, the instantaneous power from the symmetricalstar configuration power supply to the balance starconfiguration load is given by (2).
P = 3VI cos ϕ(2)where, P is the output power, V is the output phasevoltage, I is the output current, and cosφ is the load power
factor.
In a proposed system, the load current and the load
power factor of the matrix converter are equal to that of
the inverter due to the parallel connection. Therefore, thePmc ==

α mcVmcout + Vinvout
α mc (Vmcout − Vinvout )2 2α mc λmc E generator + 3λinv Edc(

α mc 2 2λmc E generator − 3λinv Edc)(3)

where, Pmc is the power distribution ratio for the matrix
converter, Pinv is the power distribution ratio for the
inverter, Vmcout is the output line voltage of the matrix
converter, and Vinvout is the output line voltage of theinverter.
Thus, the output voltage of the proposed system isconstrained by the power distribution ratio. To control the
output voltage and the power distribution ratio at the sametime, the output voltage command and operation time ratioof the matrix converter is leaded by (4) and (5) from (1)and (3). It is noted that the modulation index of the matrix
converter can be calculated by (4-2).
*
Vmcout=***mc sysout invout***
sysoutmc
invoutP V(0 ≤ V

*
mcout

λ

*
mc

=

V

)

*
*
3Pmc
Vsysout
λ*inv E dc

(

)

*
*
E generator 2 2Vsysout
Pmc− 1 + 3λ*inv E dc

}

(4-2)

(0 ≤ λ ≤ 0.866), (0 ≤ λ ≤ 1)
*
mc

*
inv

*
*
Pmc
Vinvout(5)****
Vmcout− Pmc
Vmcout− Vinvoutwhere, V*mcout is the output line voltage command forthe matrix converter, V*invout is the output line voltage
command for the inverter, V*sysout is the output line voltage
command for the proposed system, λ∗mc is the modulationindex for the matrix converter, and λ∗inv is the modulationindex for the inverter.
Fig. 9 shows the relation of the output voltage
command between the inverter and the matrix converter
according to each power distribution ratio when the output
voltage command of the proposed system is set to 100 [V].
This figure means that, for example, if the voltage
command of the inverter is set to 150V, and the power
distribution ratio is set to 0.5, then the matrix converter
voltage command have to be set to 75 [V] to obtain100[V] of the output voltage for the proposed system. The
power distribution ratio is independently controlled when
the output voltage command of the proposed system
equals to each of the converter. However, the voltage
command of each converter is restricted by the power
distribution ratio in other operation point. It should be
noted that each output voltage command should be set tothe same value when the system output voltage command
is lower than the maximum voltage of each converter.

α mc =(

Operation time
distribution ratio
andbasic carrier

1
mc

0

1
Dmc

Duty signal ofthe matrix converter
Duty signal of
the inverter

1-Dmc

Carrier forthe matrix converter

Carrier for
the inverter

E ⎞⎛*≤ 0.866 E generator , ⎜ 0 ≤ Vinvout≤ dc ⎟
2⎠⎝{

Fig.9 Relation of the output voltage command between the
inverter and the matrix converter.

(4-1)(P − 1) + V

V

V*mcout [V]power distribution ratio of the matrix converter isexpressed by (3) when the instantaneous power isassumed that the constant during one carrier cycle.
Pmc : (1 − Pmc ) = α mcVmcout : (1 − α mc )Vinvout)

Fig.10 Pulse generation strategy using the variation carrier

B. The generating method of the variation carriercorresponding to the operation time division ratio
Fig.10 shows the pulse generation strategy using thevariation carrier in proportion to the operation time ratio.
The selected signal of the operation converter is obtainedby comparing the operation time ratio command with abasic triangle carrier. During one cycle of the basic carrier,the operation time is distributed the inverter and matrix
converter. The relation between the operation time ratio of
each converter and the selection can be expressed in (6).
(6)
Dmc : 1 − Dmc = α mc : 1 − α mc
where, Dmc is the operation time ratio of the matrix
converter.
Special triangle carriers are made for the each converter
during one cycle of the basic carrier. The slope of eachspecial carrier is proportion to each operation time ratio.
In the proposed strategy, the change of each converter isachieved at the point of each converter is output a zerovoltage vector. This is to avoid the jump and vibration of
the output current.
V. SIMULATION RESULTS
Table 1 shows the simulation parameters. The output
voltage command of the system is set to 140 [V]constantly, and the power distribution ratio was changed
from 0.8 to 0.3 at 100 [ms]. It is noted that the dead timeand commutation time of each converter are neglected inorder to investigate the basic operation of the proposedsystem.
Fig.11 shows the output voltage, current and power
waveforms of the proposed system. The sinusoidal
waveform of the voltage and current are obtained without
unexpected jump or vibration at the operation change

Simulated Motor
Simulated Generater

TABLE I.
Input AC voltage

MatrixConverterS

200[V]

Input frequency

50[Hz]

DC voltage

350[V]

Output voltage command of the combined system

140[V]

Output voltage command of the MC

140[V]

Output voltage command of the INV

140[V]

Output frequency command

60[Hz]

Output power distribution ratio command( P*mc)

0.8,0.3

Resistance (load)

5[Ω]
5[mH]

Reactor(load)

U

R

SUMIRATION PARAMETERS

T

V
W

Variable AC regulator

Inverter

Simulated Battery

Fig.12 The configuration of the experimental system.
TABLE II.
EXPERIMENT PARAMETERS

Output line voltage[V]Input AC voltage

141
0

-141
Output phase current[A]15050[Hz]

DC voltage

255[V]

Output voltage command of the combined system

90[V]Output voltage command of the MC

90[V]Output voltage command of the INV

90[V]Output frequency command

35[Hz]

Dead time

2.5[µs]0~1

Output power distribution ratio command( P*mc)

-15

10

140[V]

Input frequency

Resistance (load)

12.5[Ω]
5[mH]Reactor(load)

Iutput phase current[A]0Distortion points

-10
2000

Output average power[W]Ptotal=1748[W]Pmc=1401[W]

Pinv=1171[W]1000

Pmc=577[W]Pinv=347[W]080

Output voltage(100V/div) 0

Ptotal=1748[W]100
Time[ms]120

Output current
0(5A/div)

Fig.11 Simulation results of the proposed system

point. Moreover, the power distribution ratio of eachconverter agrees with the each command.
When the power distribution ratio is 0.8, 0.05[%] and1.2[%] of the total harmonic distortion (THD) are
obtained for the output current and the input current,
respectively. After the power distribution ratio is changed
from 0.8 to 0.3, 0.6[%] and 1.1[%] of the THD are
obtained for the output current and the input current,
respectively.
VI. EXPERIMENT RESULTS
Fig.12 shows the configuration of the experimental
system in order to confirm the basic operation. The battery
is simulated by the combination of a variable AC regulator
and a diode rectifier. The generator is also simulated by avariable AC regulator.
Table 2 shows the experiment parameters. The power
distribution ratio was set equal to the operation time
division ratio in order to clarify the relation between the
output voltage of the proposed system, the power
distribution ratio of the each converter and the operation
time division ratio and the harmonic distortion of thecurrent.
Fig.13 shows the waveform of the output voltage, andoutput current, and the input current during a single
operation of the matrix converter (MC). The output

Iutput current
0(5A/div)
10ms/div

Fig.13 The waveform of the output voltage, the output current,
the input current when the single operation of the matrix
converter.

voltage is only observed by using the low pass filter set
cut-off frequency of 1 kHz. 1.63[%] and 1.2[%] of the
THD are obtained for the output and input current,
respectively. The output power is 628[W]. The output
voltage waveform has been distorted by the commutation
error as shown in Fig.13. It is noted that the commutation
error of the proposed system is the same as theconventional matrix converter. That is, a conventional
commutation error compensation method as proposed in[14] can be applied.
Fig.14 shows the waveform of the output voltage andoutput current during single operation of the inverter(INV). 2.55[%] of The THD is obtained for the output
current at 628[W] of the output power.
Fig.15 shows the waveform of the output voltage,current and the input voltage when the power distribution
ratio command is set to 0.5. Each input-and-output
waveform can be controlled to sinusoidal wave. The THDof the input current is 3.9[%]. However, the THD of theoutput current is 9.62[%], and has deteriorated comparedwith the case where only each converter operates. One ofOutput voltage
0(100V/div)

Output current
0(5A/div)

10ms/div

Fig.15 The waveform of the output voltage, the output current
and the input current when the output power distribution ratio
command is 0.5.

Output voltage (V)the reasons of increasing the THD is the voltage error
between the inverter and the matrix converter.
Fig.16 shows the relationship between the output
voltage and the power distribution ratio of the proposedsystem. The dotted line indicates the ideal value, and theblack spot indicate the measurement values. The output
voltage of the proposed system decreases when the power
distribution ratio command is larger than 0.4 as shown in
Fig.16. The cause of this result is also the voltage error by
the dead-time of the inverter and the commutation of thematrix converter.
Fig.17 shows the comparison between the ideal value
and the measurement value of each output power. The
measured output power agrees well with the powercommand. However, the measurement value of each
output power decreases more than the ideal values when
the power distribution ratio command is larger than 0.4.
The reason is because the decrement in the output voltageof the proposed system described in Fig. 16. Therefore, if
the decrement of output voltage of the proposed system
can be improved, the output power can follow the powercommand, too.
Fig.18 shows the relationship between the power
distribution ratio, the THD of the output and input current.
The THD of the output current becomes 5[%] or less, all
the power distribution ratios. On the other hand, the THDof the input current become less than 15% at over 0.2 ofthe operation time ratio of the matrix converter. The
reason can be explained that the fundamental componentof the input current against an input filter current isdecreased when the input current is decreased in the small
operation time ratio. However, the distortion component isalmost the same. That is, the THD is increased relatively
because the distortion component was not changed but thefundamental component is decreased.

Iutput current
0(2A/div)

Fig.16 The relationship between the output voltage and theoutput power distribution ratio of the proposed system.

Output power (W)Fig.14 The waveform of the output voltage and the output
current when the single operation of the inverter.

Fig.17 The comparison between the ideal output power value
and the measurement value of each output power.

25
Current THD[%]

VII. CONCLUSION
This paper proposed a control strategy of a matrix
converter and an inverter parallel system with no requiresof interconnection reactors. In the proposed system, theoperation time of each converter was divided by every
carrier cycle, and the output power of each converter andthe output voltage of a proposed system were controlled
simultaneously. The input current also was controlled tothe sinusoidal wave.
The features of the proposed system are as follows:i) By using the proposed control strategy,
Interconnection reactors and transformers for aparallel multiplexing system become unnecessary.

Input current THD

Output current THD

30

20
15
10
5
0

0

0.1

0.2

0.3

0.4

0.5

0.6

Power distribution ratio (Pmc =

0.7

0.8

0.9

1

mc)

Fig.18 The relationship between the output power distribution
ratio and the THD of input and output current.

ii) The current rating of IGBT can be reduced
according to the output power ratio of eachconverter.
iii) The drive circuits of the matrix converter are
reducible from eighteen to nine because thecommutation of the matrix converter can be
simplified from four steps to two steps.
iv) The combined system can be miniaturized because a
special snubber circuit for matrix converter is notneed to be added.
The utility of the proposed control method wasconfirmed by the simulation and the experiment, and thegood results were obtained. In the future works, the deadtime error correction for the variation carrier will be
examined to improve the THD of the output and input
voltage, the input current.
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