Direct Power Control Based Matrix Converter and Its Operation Characteristics
Toshihiko Noguchi, Somei Nakatomi, and Daisuke Takeuchi
Nagaoka University of Technology
1603-1 Kamitomioka, Nagaoka 940-2188, JAPANtnoguchi@vos.nagaokaut.ac.jp

I. INTRODUCTION
In general, an AC/DC/AC power conversion is extensively
used in a variety of power system applications, industry
applications, transportation systems, and etc., which requires a
rectifier, a DC bus, and an inverter to obtain arbitrary AC
power from a utility power source. Since two-stage power
conversion is indispensable in such conventional systems,
however, total power conversion efficiency from the utility
power source to a load is normally around 90 % at most and it
is rather difficult to improve the efficiency higher than 95 %.
Furthermore, the conventional system requires a bulky
energy-buffering device such as an electrolytic capacitor tosmooth DC bus voltage, which prevents physical size
reduction and longer product life of the whole apparatus. In
recent years, therefore, matrix converters have intensively
been studied and many researchers have published a numerous
number of papers on the matrix converters because it makes adirect AC/AC power conversion possible without anyenergy-buffering devices.
The authors have been investigating a direct power control(DPC) strategy of power converters and its application tovarious power conversion systems. This strategy features
relay (bang-bang) control of instantaneous active and reactive
power, which is accomplished by a direct selection of an
optimum switching state of the power converter. The DPC
system requires none of a current minor loop, rotational
coordinate transformation, and a linear regulator such as a PI
element to control the power converter. Therefore, thestrategy allows an ultimately high-speed power control
response, which leads to minimization of the energy-buffering
device, and is likely suitable to control of the matrix converter

because it requires an extremely high-speed response in power
management due to its particular circuit topology with noenergy-buffering devices.
This paper describes the DPC strategy applied to the matrix
converter, and presents the system configuration andperformances, which includes a theoretical aspect of the
proposed control strategy, a feasibility study throughcomputer simulations and real performance evaluation with a
1.5-kW experimental setup.
II. SYSTEM CONFIGURATION AND CONTROLALGORITHM OF DPC BASED MATRIX CONVERTER
A. Switching State of Matrix Converter
The proposed DPC based matrix converter employs avirtual AC/DC/AC power conversion approach to determine
the switching state of the matrix converter at every moment.
This approach divides the matrix converter into two parts, i.e.,a virtual front-end AC/DC rectifier and a virtual DC/AC
inverter, and synthesizes the switching state of the matrix
converter from the both switching states of the virtual rectifier
and the virtual inverter.
Fig. 1 illustrates a matrix converter, where va, vb, and vc are
input voltages from the utility power source and vu, vv, and vw
are output voltages to the load. The relationship between the
input voltages and the output voltages can be expressed as (1),using a set of switching states of the matrix converter.
⎡ vu ⎤ ⎡ S au⎢ ⎥ ⎢⎢ v v ⎥ = ⎢ S av⎢⎣v w ⎥⎦ ⎢⎣ S aw

S bu
S bv
S bw

S cu ⎤ ⎡v a ⎤⎥⎢ ⎥S cv ⎥ ⎢vb ⎥ . ········································ (1)S cw ⎥⎦ ⎢⎣ v c ⎥⎦In the above equation, each switching state takes a value ofeither “1” or “0”, according to the “ON” or “OFF” state ofeach bidirectional device, respectively.
On the other hand, an AC/DC/AC power conversion systemcomposed with a three-phase PWM rectifier and a three-phase
Sau
va

Sav
Saw

vb

vc

Input Filter

Abstract – This paper proposes a novel control strategy of amatrix converter, which features direct instantaneous-activeand reactive-power control of the converter. The power candirectly be regulated by selecting an optimum switching statewith a relay (bang-bang) control algorithm; thus an ultimately
high-speed response of the power control is achieved. A
theoretical aspect of the control is discussed, and some computer
simulation results are presented to confirm the basic
controllability of the technique. In addition, several operation
characteristics are examined through experimental tests, using a
1.5-kW prototype. The maximum efficiency and total input
power factor of the experimental setup were 95.4 % and 99.9 %at 1.5-kW load with 30-Hz output frequency, respectively. Also,
the total harmonic distortion of the input current was 5.9 % at
the rated load condition. These results prove feasibility andeffectiveness of the proposed strategy.

Sbu
Sbv
Sbw
Scu
Scv
Scw

Fig. 1. Simplified circuit diagram of matrix converter.

1-4244-0136-4/06/$20.00 '2006 IEEE

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vu
vv
vw

to have short-circuit among power source terminals nor
open-circuit at the output terminals because the load isregarded as an inductive component. Therefore, a front end of
the virtual AC/DC/AC power conversion system isnecessarily a current-source type rectifier, while an output
stage of the virtual AC/DC/AC power conversion system has
to be a voltage-source type inverter. The switching state of theactual matrix converter can be determined by (5) as if there are
two independent conventional power converters to becontrolled, i.e., the virtual current-source PWM rectifier andthe virtual voltage-source PWM inverter. Fig. 3 illustrates a
block diagram of the matrix converter controller on the basisof the virtual AC/DC/AC power conversion system. In thispaper, a DPC based current-source PWM rectifier and acurrent-controlled voltage-source PWM inverter are
introduced to satisfy the above requirements and to determine
the switching state of the matrix converter at every moment.

va
vb
vc

Input Filter

vdcp
Sap

Sbp

Sup

Scp

Svp

Swp
vu

vdc

vv
vw

San

Sbn

Scn

vdcn

Sun

Svn

Swn

Fig. 2. AC/DC/AC power conversion system.

Matrix Converter

vv
vw

Load

vc

vu

Input Filter

va
vb

9
Eq. (5)
6
Virtual Rectifier
Control

6
Virtual Inverter
Control

B. Control of DPC Based Virtual Current-Source PWM
RectifierFig. 3. Virtual AC/DC/AC conversion based matrix converter control.

PWM inverter is depicted in Fig. 2, where vdcp and vdcn
represent a high-side voltage and a low-side voltage of therectifier output with respect to a neutral point of the DC bus.
Therefore, the output voltages of the rectifier are expressed as(2), using its set of switching states.
⎡v dcp ⎤ ⎡ S ap⎢⎥=⎢
⎣v dcn ⎦ ⎣ S an

S bp
S bn

⎡v a ⎤
S cp ⎤ ⎢ ⎥⎥ vb . ······································· (2)S cn ⎦ ⎢ ⎥⎢⎣ v c ⎥⎦In a similar manner, the relationship between the output of theinverter and the DC bus voltages can mathematically bedescribed as (3).
⎡ vu ⎤ ⎡ S up⎢ ⎥ ⎢⎢ v v ⎥ = ⎢ S vp⎢⎣v w ⎥⎦ ⎢ S wp⎣

The DPC technique is applied to the virtual current-source
PWM rectifier because of its extremely high-speed response
in power management. Fig. 4 indicates a block diagram of thedirect power controller. As shown in the figure, instantaneous
active power P and instantaneous reactive power Q are
calculated from the voltages and the currents of the utility
power source.
⎡ P ⎤ ⎡vα⎢ ⎥ = ⎢v
⎣Q ⎦ ⎣⎢ βv β ⎤ ⎡iα ⎤⎥ ⎢ ⎥ , ····················································· (6)− vα ⎦⎥ ⎣⎢i β ⎦⎥where vα and vβ are two-phase voltages and iα and iβ are
two-phase currents obtained by the following coordinatetransformations:

S un ⎤⎥ ⎡v ⎤
S vn ⎥ ⎢ dcp ⎥ . ·············································· (3)v
S wn ⎥⎦ ⎣ dcn ⎦

⎡vα ⎤
⎢ ⎥=
⎣⎢v β ⎦⎥

2 ⎡1
⎢
3 ⎣0

By substituting (2) into the above equation, therefore, theoutput AC voltages to the load can be expressed as a functionof the input AC voltages from the utility power source, using a
product of two sets of switching state matrices as follows:

⎡iα ⎤
⎢ ⎥=
⎢⎣i β ⎥⎦

2 ⎡1
⎢
3 ⎣0

⎡ vu ⎤ ⎡ S up⎢ ⎥ ⎢⎢ v v ⎥ = ⎢ S vp⎢⎣v w ⎥⎦ ⎢ S wp⎣

S un ⎤⎥ ⎡S
S vn ⎥ ⎢ ap
S
S wn ⎥⎦ ⎣ an

S bp
S bn

⎡v a ⎤
S cp ⎤ ⎢ ⎥⎥ vb . ······················ (4)S cn ⎦ ⎢ ⎥⎢⎣ v c ⎥⎦In order to obtain the same input-and-output relationship as
shown in (4) with that of the matrix converter expressed by (1),the following equation must be held among the switching statematrices:⎡ S au⎢⎢ S av⎢⎣ S aw

S bu
S bv
S bw

S cu ⎤ ⎡ S up
⎥ ⎢S cv ⎥ = ⎢ S vp
S cw ⎥⎦ ⎢⎣ S wp

S un ⎤⎥ ⎡S
S vn ⎥ ⎢ ap
S
S wn ⎥⎦ ⎣ an

S bp
S bn

S cp ⎤⎥ . ········· (5)S cn ⎦In the matrix converter shown in Fig. 1, it is necessary never⎡v a ⎤−1 2− 1 2 ⎤⎢ ⎥⎥ vb , and ························· (6a)3 2 − 3 2⎦ ⎢ ⎥⎢⎣ v c ⎥⎦⎡i a ⎤− 1 2 ⎤⎢ ⎥⎥ ib . ································ (6b)3 2 − 3 2⎦ ⎢ ⎥⎢⎣ic ⎥⎦−1 2

In general, a current-source PWM rectifier requires an input
LC filter, which may cause current waveform distortions dueto the LC resonance. Therefore, it is necessary to dump the
LC resonance with a power feedback compensation, which iscomposed by differential elements kd. This compensator adds
a dumping factor to the transfer function between the AC
power source and the DC bus of the virtual PWM rectifier.
The instantaneous active power command P* is obtained
from a product between the load power PL and a normalized
virtual DC bus voltage as shown in (7). The load power PL
can simply be obtained from voltage commands and current
feedback signals in the virtual inverter, while the normalized
virtual DC bus voltage is derived from the detected
power-source voltages.

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6
Switching TableSp Sq Θn

vα
vβ
iα
iβ

P
Q

Eq. (6)ia
ib
ic

3φ →2 φ 3φ →2 φ

va
vb
vc

s

kd

s

kd

sp
sq

PL
vin

iu* +
iv

π
6

Θ2
Θ3
Θ4

Fig. 5. Quantized phase of power-source voltage vector.
Sy

Sw

Θ1

Sx

Θ2

Θ3

Θ4

Θ5

Θ6

Su

Sv

Sz

1

0

PON

OPN

NPO

NOP

ONP

PNO

1

1

PNO

PON

OPN

NPO

NOP

ONP

0

0

SOO

OOS

OSO

SOO

OOS

OSO

0

1

ONP

PNO

PON

OPN

NPO

NOP

Sp
1

ΔP

1

0
P

Θn

Sq

1 α

ΔQ

6
5

0
*

P

Q

2
3β
4

Q

*

vw

+
+
+

PL

+-

+-

vv*
vw*

Three-Phase
carrierP(2n − 3) ≤ Θ n <π
6( 2n − 1) Q n = 1, 2, L , 6 . ···················· (8)By using the quantized signals Sp, Sq and Θn, the mostappropriate switching state of the virtual PWM rectifier is
uniquely determined to restrict the control errors ∆P and ∆Q
within the predetermined hysteresis bandwidth. In order toachieve this relay control operation, an optimum switchingstate table shown in Fig. 6 is employed to select a uniqueoptimum switching state of the virtual PWM rectifier,according to a combination of the quantized signals Sp, Sq andΘn. In the table, a switching state “P” indicates that high side
device is turned on and that low side device is turned off, and“N” indicates vice versa. Another switching state “O”
corresponds to a state that both of high- and low-side devices
in a specific leg are simultaneously turned off, while “S”
means a short circuit situation by turning on the high- and thelow-side devices in one of the three legs at the same time.
Since the DPC system is in principle based on a relay
control algorithm, it is significant to investigate relationshipbetween the switching state and behaviours of theinstantaneous active and reactive power, i.e., time derivatives
dP/dt and dQ/dt derived as functions of the switching state of
the virtual PWM rectifier as follows:

β

Sp Sq

P

vv

+-

expressed as

vs

Θ5

iw

P

vu*

Fig. 7. Block diagram of current controller for virtual voltage-source PWM
inverter.

α

Θ6

+

iw* +

Fig. 4. Block diagram of direct power controller for virtual current-source
PWM rectifier.

Θ1

*

iv

6
Latch

Trigger

vu

iu

∆P ∆Q
++ +
++
+
Eq. (7)
P* Q* vin

Logic

vs

Sv S w⎧
dP I rms ⎡=−) cos θ⎢− 3I rms + 2 I dc ⎨( S u −
Cf ⎣
dt
2
2
⎩

Fig. 6. Optimum switching state table and comparators for quantization.

⎧⎡ 1 − 1 0 ⎤ ⎡cos ωt
⎤⎫
⎪⎢
⎥⎢
⎥⎪
∗
P = PL max ⎨⎢ 0
1 − 1⎥ ⎢cos(ωt − 2π 3)⎥ ⎬ . ················ (7)⎪⎢ − 1 0
1 ⎥⎦ ⎢⎣cos(ωt − 4π 3)⎥⎦ ⎪⎭⎩⎣On the other hand, the instantaneous reactive power command
Q* is provided from the outside of the controller, and isnormally set at zero to achieve a unity total power factor
operation.
Control errors ∆P = P*−P and ∆Q = Q*−Q are quantizedwith hysteresis comparators, generating signals Sp and Sq. A
phase angle of the power-source voltage vector is also
quantized to 6 sectors Θn as shown in Fig. 5, where α-axis and
β-axis denote real and imaginary parts of the vector,
respectively. The quantized phase Θn is mathematically3⎪⎫⎤+( S v − S w ) sin θ ⎬⎥
2
⎪⎭⎦⎥

dQ
=
dt

2 I rms I DC ⎧⎪ 3
( S v − S w ) cosθ
⎨−
Cf
⎪⎩ 2
S
S
⎫
+ ( S u − v − w ) sin θ ⎬22⎭, and ····· (9). ························· (10)In the above equations, Irms, IDC, θ, and Cf are an rms value ofthe power source current vector, virtual DC bus current, anargument of the power source voltage vector and acapacitance of the LC filter, respectively.
According to polarities of the time derivatives dP/dt and1874

(a) Power source voltage, input current, output voltage, and load current
waveforms.

(a) Power source voltage, input current, output voltage, and load current
waveforms.

(b) Frequency spectrum of input current.

(b) Frequency spectrum of input current.

(c) Frequency spectrum of load current.
Fig. 8. Simulation result at 30-Hz and 1.5-kW output.

(c) Frequency spectrum of load current.
Fig. 9. Simulation result at 100-Hz and 1.5-kW output.

TABLE I ELECTRIC PARAMETERS OF POWER CIRCUIT.
Power source voltage
Input filter inductance Lf
Input filter capacitance Cf
LoadReactive power command

200 V, 50 Hz
2.7 mH20 µF
12.5 Ω, 3.7 mH
0 var

dQ/dt solved as (9) and (10), one of the switching states of thevirtual PWM rectifier can uniquely be determined to restrict
the control errors ∆P and ∆Q within the hysteresis bandwidth,
which leads to determination of the contents of the optimum
switching state table.
C. Control of Virtual Voltage-Source PWM Inverter
Fig. 7 shows a block diagram of a controller for the virtual
voltage-source PWM inverter with current minor loops. As
shown here, the inverter output voltage commands vu*, vv* andvw* are obtained from control errors between the current
feedback signals iu, iv, iw and their commands iu*, iv*, iw*. The
voltage commands are converted to PWM signals with a
sub-harmonic modulation technique, where three-phase
triangular-wave signals are employed as a PWM carrier. The

PWM technique using the three-phase carrier does not
generate zero-voltage vectors that cause a freewheeling mode
among the three-phase load terminals; hence this approachguarantees continuity of the virtual DC bus current. If there isan interruption in the virtual DC bus current for any reasons, adetrimental waveform distortion will appear in the input
current of the virtual PWM rectifier. To the contrary, whilethe virtual PWM rectifier generates a zero-current vector bymaking a short circuit across the virtual DC bus (afreewheeling mode), the virtual DC bus voltage becomes zero,
which detrimentally affects the output of the virtual PWM
inverter. To minimize an effect of the interference, therefore,
an exceptional treatment is given to the optimum switchingstate table and the virtual PWM inverter is prohibited tochange its switching state when the short circuit occurs acrossthe virtual DC bus. This special restriction mode is easily
detected from the control signals Sp and Sq of the virtual PWM
rectifier.
As described in the previous section, the load power PL iscalculated to provide the virtual PWM rectifier with the
instantaneous active power command P* as shown in (11).

1875∗
PL = vu∗ iu + v v∗ iv + v w
i w . ················································· (11)(a) Power source voltage, input current, output voltage, and load current
waveforms.

(a) Power source voltage, input current, output voltage, and load current
waveforms.

(b) Frequency spectrum of input current.

(b) Frequency spectrum of input current.

(c) Frequency spectrum of load current.
Fig. 10. Experimental result at 30-Hz and 1.5-kW output.

(c) Frequency spectrum of load current.
Fig. 11. Experimental result at 100-Hz and 1.5-kW output.

III. COMPUTER SIMULATION RESULTS
Computer simulations were conducted with PSIM software
to investigate the basic operation performance of the proposed
strategy. The electric parameters of a power circuit used in thesimulations are listed in TABLE I. Fig. 8 and Fig. 9 show
operation waveforms and frequency spectra of the input andthe output currents at 30 Hz output and 100 Hz output,
respectively. In both cases, the load was 1.5 kW and thereactive power command was 0 var. As is indicated in the
figures, the unity total input power factor operation isachieved at the grid frequency of 50 Hz, and sinusoidal input
current waveforms are confirmed in both test conditions. In
addition, the sinusoidal output currents are provided to theload at both commanded frequencies of 30 Hz and 100 Hz as
well. The FFT analysis results of the input and the output
currents indicate that most of the harmonics is less than 1 %,which demonstrates excellent performance of the proposed
strategy.
IV. EXPERIMENTAL SETUP AND RESULTS
A 1.5 kW prototype was developed to confirm

experimentally feasibility and effectiveness of the DPC based
control of the matrix converter. The prototype has the same
specifications and parameters used in the computer
simulations. Fig. 10 and Fig. 11 show experimental results
obtained under the identical test conditions as those of thesimulations. As can be seen in these figures, the input current
is in phase with the power source voltage and is controlled tobe sinusoidal in both cases of the 30 Hz output and the 100 Hz
output. The measured frequency spectra of the input current
include slightly larger harmonics than those of the simulation
results, but few conspicuous peaks are observed over the wide
range of frequency band in both cases. On the other hand, theoutput currents are well controlled at the commanded
frequency of 30 Hz and 100 Hz and have quite low harmonic
spectra less than 1 %, which is confirmed by the current
waveforms as well as the FFT analysis results.
Fig. 12 and Fig. 13 show characteristics of the total input
power factor and the total efficiency, respectively. The
maximum total input power factor was 99.9 % and the
maximum total efficiency was 95.4 % under the conditions ofboth 30-Hz and 100 Hz output frequencies and 1.5-kW load.
The frequency change of the output currents does not affectvery seriously on the overall operation performance. Fig. 14
represents the total harmonic distortion of the output currents,

1876the total efficiency of such an AC/DC/AC power conversion
system can achieve nearly 90-% efficiency at most. From theviewpoint of the total efficiency between the AC power source
and the AC load, however, the proposed system has a great
advantage over the conventional system, which is the most
attractive point.
VI. REFERENCES

Fig. 12. Characteristics of total input power factor.

Fig. 13. Characteristics of total efficiency.

Fig. 14. Characteristics of total harmonic distortion of input current.

which show the minimum value of 5.9 % was measured at
1.5-kW rated load. However, the total harmonic distortion
characteristics become worse up to approximately 30 % as theload power is reduced. Further performance improvement is
expected in the light-load range in the future works.
V. CONCLUSION
This paper proposed a novel control strategy of a matrix
converter, which featured direct control of the instantaneous
active and reactive power on the basis of a relay (bang-bang)
control algorithm. A theoretical aspect of the proposed
technique was discussed prior to the computer simulations andexperimental tests. By using a 1.5-kW experimental set up,
excellent controllability of the input current was confirmed,
resulting in 99.9-% total input power factor and low input
harmonics less than 1 % regardless of the output frequency.
Also, well-controlled output currents were observed at thedesired frequency independently of the fixed utility powersource frequency. As a result, the maximum efficiency of
95.4 % was accomplished at the rated load of 1.5 kW throughthe experiments. Even assuming that both of the conventional
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