Journal of Engineering Science and Technology
Special Issue on Applied Engineering and Sciences, October (2014) 1 - 10
© School of Engineering, Taylor’s University

CONFIGURATIONS COMPARISON OF MULTI DIRECTIONAL
MATRIX CONVERTER FOR LOW POWER APPLICATION
S. TOOSI1,*, M. NORHISAM1,2, T. HANAMOTO2, I. ARIS1,
M. A. M. RADZI1, H. YAMADA2
1
Department of Electrical & Electronic, Faculty of Engineering,
Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
2
Department of Biological Functions and Engineering, Graduate School of Life Scienceand Systems, Engineering, Kyushu Institute of Technology, Kyushu 804-8550, Japan*Corresponding Author: saman_tosi_e@yahoo.com

Abstract
Four different topologies of Multi Directional Matrix Converters (MDMC) arecompared for use in low power applications. In the proposed small-scale powersystem the MDMC configuration with 12 bidirectional switches combined thedesirable characteristics of the AC/AC conventional Matrix Converter (MC)and AC/DC single phase to single phase matrix converter. The indirect methodwith Space Vector Pulse Width Modulation (SVPWM) technique applied to the
proposed MDMC configurations in order to control the power direction frompower sources to loads. These four configurations have been simulated by
MATLAB software and results are presented and discussed. Analyses andsimulation results show that the MDMC with 12 bidirectional switches can run
over a large input voltage and frequency range while controlling the power flow
direction, compensate the fluctuating power and maintaining the excellent
quality of output waveform in case of THD and DC current ripple.
Keywords: Matrix converter, Multi directional matrix converter, SVPWM, Smallscale power system.

1. Introduction
With increasing demand of electricity in the recent decade, renewable energy is
become interesting as significant alternative sources of energy. Many factors suchas impact of fossil-fuel resource on environmental, increasing the cost of fuel oil
and diminishing fossil-fuel resource are responsible for this development [1-2].
1

2

S. Toosi et al.

Nomenclatures
dα, dβdµ, dγ
fi
fo
Iα
Iβ
Ll
mc
mv
Rl
Tα, TβTµ, TγT0Vab, Vbc, Vbc
Vod
Vors,Vost, Votr
Voq
Vs-RMS

Duty cycle of current vector Iα and Iβ respectively
Duty cycle of voltage vector vµ and vγ respectively
Input frequency of the MDMC
Output frequency of the MDMC
Closest clockwise state vector to reference current vector
Closest anticlockwise state vector to reference current vector
Output load inductance
Modulation index of current source rectifier
Modulation index of voltage source inverter
Output load resistanceTime spent in vector Iα and Iβ respectively
Time spent in vector vµ and vγ respectively
Time spent in zero vector
Input line-to-line voltage
d-axis input voltage
Output line-to-line voltage
q-axis input voltage
Input line-to-line voltage in RMS

Greek Symbols
θCSR
The angle between the reference vector and the closest clockwise state vector in current source rectifierθVSI
The angle between the reference vector and the closest clockwise state vector in voltage source inverter
One of the major requirements for small scale power generation system is toensure continuous power flow by storing excess energy from the energy source[3]. Small scale power systems with battery storage and power converter are
efficient and reliable stand-alone system for remote areas [4]. In recent years,
the matrix converter become popular in the category of AC/AC converters due
to its desirable features such as sinusoidal input and output current, generatingof load voltage with arbitrary amplitude and frequency and ability to controlled
input power factor for any load [5]. The principle of MC control proposed by
Venturini and Alesina in the early 1980’s which known as a “direct transfer
function” approach with voltage transfer ratio restriction to 0.5 [6]. The term
direct transfer function means that the energy does not appear in the form of dc
in the conversion process.
The “indirect transfer function” was derived by Rodriguez in 1983 [7]. In thismethod, the matrix converter was described as virtual configuration of pulse
width modulation (PWM) rectifier and inverter with “fictitious dc link”.
Switching is arranged in this method, so most positive and most negative input
lines will be connected to each output line by using PWM technique, as
conventionally used in standard voltage source inverter (VSIs) [8].
Between direct and indirect method, the indirect method, have the capability
to implementing Pulse Width Modulation (PWM) and Space Vector PWM(SVPWM) techniques to the switches of the MC which can reduced THD and

Journal of Engineering Science and Technology

Special Issue 10/2014

Configurations Comparison of Multi Directional Matrix Converter for Low . . . . 3

losses in system. the voltage ratio of MC can reach to the 0.866 with taking theadvantage of SVPWM technique [9].
The multi directional matrix converter for 2kW standalone power system withbattery storage is expected to be a breakthrough towards new technologicaladvancements, in the area of sustainable energy. Therefore, four possible
configurations have been proposed based on conventional Matrix converter
configuration [6], and all configurations simulated by MATLAB software andresults are presented and discussed.

2. System Structure
In the proposed small-scale power system, the Variable speed turbine is connectedto the three phase 2 kW permanent magnet generator which can generate voltage up
to 80 V, the output of generator is connected to the input side of MDMC. In anotherside the DC output of MDMC used for battery charging and AC output connected
to transformer with ratio of 1:10 in order to top up the voltage amplitude based on
the Malaysia standard (240 V). The Schematic diagram of the proposed stand-alone
system with battery and MDMC is shown in Fig. 1.
The proposed MDMC configurations are made based on the MC structure.
Performance of matrix converter is strictly depending on the high switchingfrequency switches topology and the modulation strategy employed to control
theses bidirectional switches. The indirect method is Appropriate method In
order to implement the Pulse Width Modulation (PWM) and Space Vector pulse
width modulation (SVPWM) techniques to the MC [9]. Therefore, the proposed
MDMCs should be able to control the power flow from generator or battery to
the AC load regarding to the concept of fictitious rectifier-inverter pair and dclink of indirect method. In another hand the DC output voltage of the MDMC
should deliver a clean regulated voltage output with sinusoidal input current.

Fig. 1. Schematic Diagram of the Proposed Stand-Alone System.
The proposed MDMC concept structure with four input and three outputs areillustrated in Fig. 2. The input side of the MDMC is connected to the three phase
generator and imaginary battery when the system is on discharging mode. In
another side the output of MDMC is connected to the single phase AC load andthe real battery when the system is on charging mode.

Journal of Engineering Science and Technology

Special Issue 10/2014

4

S. Toosi et al.

Fig. 2. Schematic Diagram of Multi Directional Converter.

3. MDMC Modulation Methods
Different imaginary stages of transformation are considered in indirect switching
matrix approach. This transfer switching matrix, are considered as: rectification
stage and inverter stage. In the rectification stage, a fictitious dc link with a dc
voltage of constant local average will be provided. Then, the fictitious dc voltage
is connected to the battery in case of battery charging as well as converted to thesingle-phase AC voltage in the case of AC load on inverter stage.
The SVPWM technique is a renowned method in control of DC/AC inverters
and also AC/DC converters [10]. The SVPWM reduced the number of switching ineach time sequence and represent the voltages and currents in two-dimension
reference frames instated of three-dimensional abc frames. Firstly, Huber andBorojevic applied the SVPWM to the matrix converter in the same way that it isapplied to DC/AC converter with taking advantage of indirect matrix switchingapproach [11, 12]. The concept of the indirect method for all proposed MDMC
structure have been illustrate in imaginary switches part of Tables 1(a) and 1(b),with six imaginary switches for the rectifier part and six imaginary switches for the
inverter. Furthermore, Tables 1(a) and 1(b) indicates the current flow through theinverter stage during the two 180o sectors.
The first part of all multi directional converters can be considered as a current
source rectifier (CSR) with an imaginary dc-link voltage, Vpn, which is illustrated
in Fig. 3. The implementation of SVPWM for the current source rectifier issimilar in all configuration of MDMC. Any of the three-phase quantities in abcframe can be transforming to the dq coordinate with accomplished of dq-frametransformation. Three-phase output ac voltages of generator Vab, Vbc and Vca are a
set of quantized values in abc coordinate at each state which is transformed to the
fixed two-dimensional dq-frame as shown in Eq. (1) [13].
2 1

 =

3
0

2
2
( )
(− ) 
33   22( ) (− ) 
3
3

(1)

By calculating the switching state vector for allowed input currents of thecurrent source converter in each switching state, will result, eight space current
vectors consist of six non-zero space switching current vectors, I1, I2,...,I6, andJournal of Engineering Science and Technology

Special Issue 10/2014

Configurations Comparison of Multi Directional Matrix Converter for Low . . . . 5

two zero current space current vectors, I0 and I7. Figure 3 illustrates the eight
Input current space vector in complex plane where the two zero space current
vectors, are located at the origin of the frame and the rest six vectors can form ahexagon centred at the origin of the dq frame [14].
The continuous desired input currents should be synthesized using the two
active vectors next to the reference vector and a zero vector. If the reference
vector located in sector 1, between non-zero vectors,  and# , the Is-ref canbe represented as Fig. 4. During each switching period, Ts, the Is-ref is calculated
by Tα ,T β and T0 where Tα is the time spent in vector Iα and T β is the time spentin vector Iβ and the rest is the time T0 which dedication to a zero vector.
These three time periods can be stated by duty cycles using trigonometricidentities as shown in Eq. (2) where the mc is the modulation index of the current
source converter.
%& = ' sin * − -./0 1 . %3 = 4& %3,$ %5 = ' sin(-./0 ) . %3 = 45 %3+% = 4 %3 = %3 − (%& + %5 )+4& = ' sin( − -./0 ),7$ 45 = ' sin(-./0 ) ,0 ≤ ' ≤ 1
4 = 1 − (4& + 45 )(2)

The second part of imaginary switches of MDMCs can be considered asvoltage source inverter (VSR). It is necessary to replace θCSR in Fig. 4 with output
space vector θVSI angle voltage and subscripts α and β in duty cycles with
subscripts µ and:, three duty cycles of VSR of MDMC can be described by
Eq. (3) as follow.

%; = '< sin * − -=/> 1 . %3 = 4; %3
4; = '< sin( − -=/> )3
3$ % = ' sin(- ) . % = 4 %7$ 4 = ' sin(- ) ,0 ≤ '< ≤ 1
?

<

=/>

3

? 3

%< = 4< %3 = %3 − (%; + %? )

?

<

=/>

4< = 1 − (4; + 4? )(3)In all configurations of MDMC with indirect method, it is supposed to have atarget constant current space vector, for the rectifier part which contains six 60°
sectors. Furthermore, in inverter stage there are two 180o sectors for AC and DC
outputs. In this study, 12 sectors in total have been determined for MDMCs
outputs. By considering these 12 sectors and regarding to the three phase to threephase matrix converter modulation proposed by Huber et.al in 1995 [12], theproposed modulation process can be perform by using five combined duty cycles
as shown in Eq. (4). These combinations can be considered in each sequence.
4&; = 4& × 4;

45; = 45 × 4;

4&? = 4& × 4? (4)45? = 45 × 4?

4 = 1 − (4&; + 45; + 45? + 4&? )Journal of Engineering Science and Technology

Special Issue 10/2014

6

S. Toosi et al.

Iβ=I

I

π /6

5π / 6θ
7π / 6

1

dβIβ

π /2

s− refCSRdα I α11π / 6Iα = I

9π / 6

6

Fig. 4. Is-ref Synthesis
Using Vectors AB and AC .

Fig. 3. Input Current Space
Vector in Complex Plane.

Table 1a. MDMC Configurations and
SVPWM Switching Method (Inverter Stage).
MDMC
Name

AX2

AC loadAC loadAX1
DC loadDC loadSchematic
Diagram of
MDMC

MDMC with Conventional MC
Structure and Two Auxiliary
Switches (II)MDMC with Conventional MC
Structure (I) [7].

Ax2

n

Van

Vbn

ia

ib

Vcn
Ax1

Imaginary
Switches

a
p

ic
b

AC
c

r
+

DC
s

Vpn
n

-

Sector0-π

π - 2πJournal of Engineering Science and Technology

Special Issue 10/2014tConfigurations Comparison of Multi Directional Matrix Converter for Low . . . . 7

Table 1b. MDMC Configurations and
SVPWM Switching Method (Inverter Stage).
MDMC
Name

MDMC with DC Load insideof MC Structure (III)MDMC with 12
Bidirectional Switches (IV)

Schematic
Diagram of
MDMC

Imaginary
Switches

Sector0-π

π - 2π4. Results and Discussion
Simulation of MDMC configurations I, II, III and IV are performed byusing MATLAB and the result are shown in Figs. 5-8 respectively. The
simulation parameters are shown in Table 2. The switching period Ts is 166 µs,
and battery’s charging is SOC=95%, thus power injected from generator to the
DC and AC loads.
Table 2. Simulation Parameters.
Parameters
Value
Rl=2.4 Ω , Ll=10 mH
Rl - Ll load
Input voltage
28 V(line-to-line RMS) Vs-RMS
180 HzInput frequency fi
50 Hz
Output frequency fo

Journal of Engineering Science and Technology

Special Issue 10/2014

8

S. Toosi et al.

Figures 5-8 illustrate the output AC-side line-to-line voltage vors whichconnected to the AC load in all configuration, r-phase output ac-side current ior,
output battery-side voltage vost and t-phase output current iot. The total harmonic
distortion (THD) of the output currents is processed by FFT analysis feature of
MATLAB and result expressed in Table 3. Finally all configurations compared toeach other based on Table 3 contents such as number of bidirectional switches
which directly affect to the total cost of system and efficiency, total harmonic
distortion and ability of configuration to inject power from DC side to the system
when the power of generator is not sufficient to supply the AC load.
Regarding to output wave form result and contents of the Table 3, theconfiguration IV have the lowest THD in the case of AC current output andlowest ripple in DC current output with ripple of 1.4% average DC current. inanother hand the quality of waveform is acceptable for the configuration III with
THD = 1.67% in the case of AC current output, but the ripple in DC current is
not acceptable for battery charging when it’s around 61% of average DC current.
In point of view of injecting power from the battery source to the system basedon Table 3 and wave form result of simulation, configuration IV have the best
performance and more freedom to control the power flow in all direction. The
simulation results in Figs. 7 and 8 illustrate that configuration IV can inject thepower to/from DC continuously when the configuration III is be able to transfer
power to the DC side in 60o of each period at desired output frequency.
Number of the switches has direct effect on system losses and price.
Therefore, in point of view of losses and price, configuration I and II with 9 and11 bidirectional switches respectively are more cost efficient than configuration
IV. Furthermore, configuration III has lower losses compare to the configuration
IV. With using indirect method and SVPWM technique, MATLAB simulation
result revealed that the configuration I and II are not capable to inject power fromDC side to system, since several vectors are utilized in one switching period. In
addition, the output DC current has been distorted in configuration I and II due tothe connection point of the battery. This distortion is happen when the voltage
cannot apply to the DC load continuously.
Three-phase to single-phase converters always pay attention to how to compensate
the fluctuating power. In this paper, the MDMCs compensate the fluctuating powerwith draw the fluctuating power from the generator, i.e., the inertia of the generator
acts as an energy buffer for compensating the fluctuating power.
Table 3. Comparison of MDMC Configurations.
Configuration
THD
DC Current(Iave± percentage of ripple)
Number of bidirectionalswitches
Extra switches
Ability to flow power fromDC side to AC sideI
15.02%
1.24±
95%
9II
19.14%
2.75±
15%
9

III
1.67%
1.15±
61%
9

IV
1.61%
2.74±
1.4%
12

0
No

2
No

0
Yes

0
Yes

Journal of Engineering Science and Technology

Special Issue 10/2014

Configurations Comparison of Multi Directional Matrix Converter for Low . . . . 9

Fig. 5. Output Wave Form of
MDMC Configuration (I).

Fig. 6. Output Wave Formof MDMC Configuration (II).

Fig. 7. Output Wave Formof MDMC Configuration (III).

Fig. 8. Output Wave Form of
MDMC Configuration (IV).

5. Conclusions
The multi directional matrix converter offers superior technical characteristics for
low power system with battery storage, especially without bulky DC-bus capacitors
at the DC-side. This study also presents a SVPWM method for all proposed
configuration and compared the result in terms of quality of waveform, losses andefficiencies. The presented results show, that the output voltages and currents ofproposed configurations can be synthesize by using the indirect method and taking
the advantage of the SVPWM technique.
The feasibility of the proposed MDMC structures and SVPWM technique has
been verified by MATLAB simulation. Analyses and simulation results shows that
the MDMC with 12 bidirectional switches can run over a large input voltage andfrequency range while controlling the power flow direction, compensate thefluctuating power, and maintaining the excellent quality of output waveform in caseof THD and DC current ripple.
Journal of Engineering Science and Technology

Special Issue 10/2014

10

S. Toosi et al.

References1.

Haidar, A.M.A.; Senan, M.F.M.; Noman, A.; and Radman, T. (2012).
Utilization of pico hydro generation in domestic and commercial loads.
Renewable and Sustainable Energy Reviews, 16(1), 518-524.
2. Aravind, C.V.; Al-Atabi, M.; Ravishankar, J.; Malik, A.; Arkar; andAmbikairajah, E. (2013). Eco-tourism sustainability through pv technology: acomprehensive review. Journal of Engineering Science and Technology(JESTEC), 8(6), 654-669.
3. Khan, M.J.; and Iqbal, M.T. (2005). Pre-feasibility study of stand-alone
hybrid energy systems for applications in Newfoundland. Renewable Energy,30(6), 835-854.
4. Colle, S.; Abreu, S.L.; and Ruther, R. (2004). Economic evaluation andoptimization of hybrid diesel/photovoltaic systems integrated to utility grids.
Solar Energy,76(1-3), 295-299.
5. Wheeler, P.W.; Rodriguez, J.; Clare, J.C.; Empringham, L.; and Weinstein,
A. (2002). Matrix converters: a technology review. IEEE Transactions on
Industrial Electronics, 49(2), 276-288.
6. Venturini, M.; and Alesina, A. (1980). The generalised transformer-A new
bidirectional sinusoidal waveform frequency converter with continuously
adjustable input power factor. Power Electronics Specialists Conference,
1980, 242-252.
7. Rodriguez, J. (1983). A new control technique for AC-AC converters.
Proceedings of IFAC Control in Power Electronics and Electrical Drives
Conference, 203-208.
8. Oyama, J.; Higuchi, T.; Yamada, E.; Koga, T.; and Lipo, T. (1989). New
control strategy for matrix converter. 20th Annual IEEE on PowerElectronics Specialists Conference, 1, 360-367.
9. Huber, L.; and Borojevic, D. (1989). Space vector modulator for forced
commutated cycloconverters. IEEE Conference on Industry Applications
Society Annual Meeting, 1, 871-876.
10. van der Broeck, H.W.; Skudelny, H.-C.; and Stanke, G.V. (1988). Analysis
and realization of a pulsewidth modulator based on voltage space vectors.
IEEE Transactions on Industry Applications, 24(1),142-150.
11. Casadei, D.; Serra, G.; Tani, A.; and Zarri, L. (2002). Matrix converter
modulation strategies: a new general approach based on space-vector
representation of the switch state. IEEE Transactions on Industrial
Electronics, 49(2), 370-381.
12. Huber, L.; and Borojevic, D. (1995). Space vector modulated three-phase to
three-phase matrix converter with input power factor correction. IEEE
Transactions on Industry Applications, 31(6), 1234-1246.
13. Toosi, S.; Mehrjou, M.R.; Karami, M.; and Zare, M.R. (2013). Increase
performance of IPMSM by combination of maximum torque per ampere andflux-weakening methods. ISRN Power Engineering, Article ID 187686, 1-10.
14. Holtz, J. (1992). Pulsewidth modulation-a survey. IEEE Transactions on
Industrial Electronics, 39(5), 410-420.

Journal of Engineering Science and Technology

Special Issue 10/2014