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Research ArticleNovel Modulation Method for
MultidirectionalMatrix Converter
Saman Toosi,1 Norhisam Misron,1,2 Tsuyoshi Hanamoto,3 Ishak Bin
Aris,1
Mohd Amran Mohd Radzi,1 and Hiroaki Yamada4
1 Department of Electrical & Electronic, Faculty of
Engineering, Universiti Putra Malaysia (UPM), 43400
Serdang,Selangor, Malaysia
2 Institute of Advanced Technology (ITMA), Universiti Putra
Malaysia (UPM), 43400 Serdang, Selangor, Malaysia3 Department of
Biological Functions Engineering, Graduate School of Life Science
and Systems Engineering,Kyushu Institute of Technology, 2-4
Hibikino Wakamatsu-ku, Kitakyushu 808-0916, Japan
4Graduate School of Science and Engineering, Yamaguchi
University, 2-16-1 Tokiwadai, Ube-shi, Yamaguchi 755-8611,
Japan
Correspondence should be addressed to Norhisam Misron;
[email protected]
Received 21 May 2014; Revised 22 August 2014; Accepted 22 August
2014; Published 14 September 2014
Academic Editor: Fernando Lessa Tofoli
Copyright © 2014 Saman Toosi et al. This is an open access
article distributed under the Creative Commons Attribution
License,which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly
cited.
This study presents a newmodulation method for multidirectional
matrix converter (MDMC), based on the direct duty ratio pulsewidth
modulation (DDPWM). In this study, a new structure of MDMC has been
proposed to control the power flow directionthrough the stand-alone
battery based system and hybrid vehicle. The modulation method acts
based on the average voltage overone switching period concept.
Therefore, in order to determine the duty ratio for each switch,
the instantaneous input voltages arecaptured and compared with
triangular waveform continuously. By selecting the proper switching
pattern and changing the slopeof the carriers, the sinusoidal input
current can be synthesized with high power factor and desired
output voltage. The proposedsystem increases the discharging time
of the battery by injecting the power to the system from the
generator and battery at thesame time. Thus, it makes the battery
life longer and saves more energy. This paper also derived
necessary equation for proposedmodulation method as well as detail
of analysis and modulation algorithm. The theoretical and
modulation concepts presentedhave been verified in MATLAB
simulation.
1. Introduction
More than 1.3 billion people in the world are not connected toa
national grid. Although extension of the conventional elec-tricity
grid remains preferable mode of electrification, it isnot
economical for areas where the grid extension is
difficult.Currently the stand-alone power system (SAPS)
supplieslocal villages or individual users with lack access to
electricity.Typical SAPS may be powered by one or more methods
suchas microhydroturbine, wind turbine, solar panel
geothermalsource, and diesel or biofuel generator to generate
theelectricity [1].
A major requirement for stand-alone power system isto ensure
continuous power flow by storing excess energyfrom the energy
sources. For example, hybrid systems withbattery storage are
employed as an efficient and reliable stand-alone system for remote
areas [2]. Battery based systems
(BBS) are amongst the SAPS models which a battery mayemploy in
series or parallel with renewable energy source. Inbattery based
systems, the input power of the system convertsto desirable voltage
and frequency through power electronicconverters in order to supply
the system loads and charge thebattery [3, 4].
In recent years, the matrix converter becomes popular inthe
category of AC to AC converters due to the desirable fea-tures such
as sinusoidal input and output current, generationof load voltage
with arbitrary amplitude and frequency, andability to control input
power factor for any load [5]. In theearly 1980s Venturini and
Alesina proposed the principle ofMC control [6].They derived duty
ratio functions that can bemodulated by carrier signal. In this
method, the voltagetransfer ratio was limited to 0.5. Alesina and
Venturini (1981)theoretically proved that the maximum voltage
ratio, 𝑞max, isequal to 0.866 for the three-phase MC when using
balanced
Hindawi Publishing Corporatione Scientific World JournalVolume
2014, Article ID 645734, 12
pageshttp://dx.doi.org/10.1155/2014/645734
http://dx.doi.org/10.1155/2014/645734
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2 The Scientific World Journal
input voltage [7]. In 1989, Alesina and Venturini extended
thevoltage ratio from 0.5 to 0.866 by taking advantage of
thirdharmonic injection methods [8].
The “indirect transfer function”was derived byRodriguezin 1983
[9]. In this method, the matrix converter wasdescribed as virtual
configuration of pulse with modulation(PWM) rectifier and inverter
with “fictitious dc link.” Theoperational and technological
research on MC were contin-ued in different areas such as new
topology of MC [10–13],input filter design [14, 15], unbalance
operational conditions[16–18], safe and practical commutation
strategies [10, 19],new control methods [20, 21], new modulation
methods [22,23], and new application such as hybrid vehicles
[24].
Yoon and Sul (2006) [23] proposed new carrier basedmodulation
methods for conventional matrix converter. Thismethod is the same
as conventional space vector pulse mod-ulation (SVPWM) which is
used in voltage source inverter.Yoon and Sul synthesized the
sinusoidal input currentwith unity power factor by changing the
slope of carrier andthe proper offset voltage. The reference output
voltages arecalculated and compared with a discontinuous carrier to
gen-erate the gating signals. However, it is difficult to
intuitivelyunderstand the modulation principle since it employs
theoffset for references and discontinues carrier signal.
Further-more, thismethod cannot be used for theMC typologies witha
neutral connection.
The preliminary concepts of a new carrier based PWMstrategy,
named direct duty ratio PWM (DDPWM), are pre-sented by Li et al.
(2008). This method can be implementedwithout complex calculations
and lookup tables and doesnot require the reference offset voltage.
Based on the averagevalue of each output phase in one switching
period, theduty ratio values may be updated at each switching cycle
byemploying input phase voltages. Thus, the PWM signals
aregenerated by comparison of these duty ratio values with
acontinuous triangular carrier waveform. The 𝑞max of 0.866also can
be easily obtained in the three-phase system byapplying the third
harmonic injection method to the outputvoltage references.
Furthermore, the input power factor canbe controlled by changing
the slope of the carrier whilemaintaining the sinusoidal input
currents [22]. Li and Choi(2009) extended theDDPWMto various
topologies ofmatrixconverter and derived the control schemes for
alternativestructures such as single-phase and three-phase
four-legmatrix converters [25].
Multidirectional converter has recently been proposedas an
alternative power conversion concept which has bothrectifier and
inverter capability [26, 27].Most desired featuresof
multidirectional converter can be fulfilled by using
MatrixConverter structures. In theMDMC, a bidirectional switch
isused, coupled between the power source and load, to provideboth
AC and DC properties, which cannot be achieved withconventional
converters. This converter has ability to controlthe power flow and
synthesise the desired output voltageby developing the space vector
pulse width modulation(SVPWM) methods. In the SVPWM method, the
modu-lation task of the multidirectional matrix converter can
beresolved into the different imaginary stages of transforma-tion
including inverter and rectifier stage which are linked
together by an imaginary DC link. However, the MDMC isnot being
able to inject power from generator and batteryat the same time,
since several vectors are utilized in oneswitching period [28].
Previous studies [29–31] show that, inconventional battery based
system, generator should be disconnected from system when it is not
being able to supplythe demand power.
Based on the literature highlighted above, this study aimsto
inject power from battery and generator at the same timeby changing
theMDMC structure and increasing the numberof time intervals of
direct duty pulse width modulationmethod. In this study, the
proposed modulation methoddetermines the switching state of each
output phase byemploying the input DC phase voltages and input AC
phasevoltages based on per-output-phase average concept over
oneswitching period. At the first step of each switching period,
inorder to generate the corresponding PWM signals, the dutyratio
values for each output phase were calculated and theresults
compared the continuous triangular waveform. Thisnew topology and
new modulation method can increase thedischarging time of battery
in the battery based systemswhenthe discharging time is directly
proportional to the generatoroutput voltage. Therefore, the
multidirectional matrix con-verter with a new modulation method is
expected to break-through towards new technological advancements in
the areaof sustainable energy and power electronics.
2. Proposed MDMC Structure forBattery Based System
Batteries are not efficient as a whole. Some energy is lost
asheat and chemical reactions when charging and discharging.In
common, the lead acid battery’s efficiency is around 85%when state
of charge (SOC) is varied from 0 to 100% [32]. Inbattery based
stand-alone power system (BBSAPS), when thebattery is connected in
series, total electricity generation fromsystem will be stored in
battery before transmitting to theloads, while in system with
parallel battery connection onlythe excess electricity will be
saved in battery. Hence, a systemwith parallel battery connection
ismore efficient compared toa system with series battery
connection. In addition, the par-allel battery based system can be
modified by combining allconverters as a single converter which is
indicated as multi-directional matrix converter. Figure 1 shows the
comparisonof block diagram of BBSs with matrix converter and
theproposed MDMC system.
The multidirectional matrix converter is a single-stageconverter
which has a𝑚×𝑛matrix (or array) of bidirectionalpower switches to
connect an𝑚-phase voltage source to an 𝑛-phase load directly. In
general, the proposedMDMCneeds 15bidirectional switches that is one
switch between each inputand output phases. Figure 2 shows the
circuit configuration ofproposed MDMC including the positive DC
input voltage(battery), negative DC input voltage (battery),
three-phaseinput voltages (AC generator), multidirectional matrix
con-verter and resistor-inductor (𝑅-𝐿) load, and second-order 𝐿-𝐶
filter which is used at the input terminals to filter out thehigh
frequency harmonics of the input currents. In this study
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The Scientific World Journal 3
Rectifier
Generator
Battery Inverter
Matrix converter AC load
(a) BBS with matrix converter
Generator
Battery
AC loadMultidirectional matrix converter
(MDMC)
(b) BBS with multidirectional matrix converter
Figure 1: Block diagram of system with parallel battery
connection.
Generator
Battery
Vsa
Vsb
Vsc
s
s
VsP
VsN
isa Lf
Lf
Lf
Lf
Lf
+
+ −
−
+
−
Cf/2
Cf Cf Cf
R
S
T
RL−ac LL−acioR
o
o
�oR
RL−dc LL−dc
RL−dc LL−dc
SaR
SbR
ScR
SPR
SNR
SaS
SbS
ScS
SPS
SNS
SaT
SbT
ScT
SPT
SNT
Source Input filter Bidirectional switches
AC and DC load
∼
∼
∼
Figure 2: Multidirectional matrix converter circuit.
the 𝑅𝐿-dc and 𝐿𝐿-dc and the 𝑅𝐿-ac and 𝐿𝐿-ac are considered
as
DC and AC load, respectively.In the MDMC, the switching method
should have sinu-
soidalwaveforms at the arbitrarymagnitude, frequency inACside,
and clean DC voltage at the DC side.The input currentsalso should
be sinusoidal at the desired power factor. In orderto achieve this
target, a proper switching pattern should beapplied to the switches
of the MDMC in each switchingperiod.The general switching function
for the switches of theMDMC can be described as follows:
𝑆𝑖𝑗 (𝑡) = {
1, 𝑆𝑖𝑗closed,
0, 𝑆𝑖𝑗open,
𝑖 = 𝑎, 𝑏, 𝑐, 𝑃,𝑁 𝑗 = 𝑅, 𝑆, 𝑇,
(1)
where the 𝑆𝑖𝑗refers to the switch on input line “𝑖” and
output
line “𝑗.”Moreover, input phases should not be short circuited
and
output phases should never be opened due to the inductive
nature of typical loads. In this study, these two constraints
canbe expressed as below:
𝑆𝑎𝑗+ 𝑆𝑏𝑗+ 𝑆𝑐𝑗+ 𝑆𝑃𝑗+ 𝑆𝑁𝑗= 1, 𝑗 = {𝑅, 𝑆, 𝑇} . (2)
By considering two states for each switch in (1) and by
apply-ing the limitation of (2) to the switching algorithms of
theproposed MDMC, allowable combinations will be derivedbased on
the DDPWM technique. Voltages and currents ofsources and voltages
and currents of load in Figure 2 can beexpressed as vectors that
are defined by (3)where the𝑋 can beinput and output
phase-to-neutral voltage vectors or theMDMC input and output
current vectors:
𝑋𝑅𝑆𝑇
= [
[
𝑋𝑅 (𝑡)
𝑋𝑆 (𝑡)
𝑋𝑇 (𝑡)
]
]
, 𝑋𝑎𝑏𝑐𝑃𝑁
=
[[[[[
[
𝑋𝑎 (𝑡)
𝑋𝑏 (𝑡)
𝑋𝑐 (𝑡)
𝑋𝑃 (𝑡)
𝑋𝑁 (𝑡)
]]]]]
]
. (3)
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4 The Scientific World Journal
SaR = 1 SbR = 1 SbR = 1 SPR = 1 SNR = 1
SaS = 1 SbS = 1 ScS = 1 SPS = 1 SNS = 1
SaT = 1 SbT = 1 ScT = 1 SPT = 1 SNT = 1
tbR tcR tPRtNR
taS tbStcS tPS tNS
taT tbT tcT tPT tNT
Ts
TAC TDC
taR
Out
put
phas
eRO
utpu
tph
aseS
Out
put
phas
eT
Figure 3: The switching pattern in a sequence period.
The MDMC instantaneous switching function matrix can beexpressed
as follows:
𝑆 = [
[
𝑠𝑎𝑅𝑠𝑏𝑅𝑠𝑐𝑅𝑠𝑃𝑅
𝑠𝑁𝑅
𝑠𝑎𝑆𝑠𝑏𝑆𝑠𝑐𝑆𝑠𝑃𝑆
𝑠𝑁𝑆
𝑠𝑎𝑇𝑠𝑏𝑇𝑠𝑐𝑇𝑠𝑃𝑇
𝑠𝑁𝑇
]
]
. (4)
Equation (5) shows the relation between load, input voltages,and
currents, where 𝑆𝑇 is the transpose matrix of 𝑆matrix:
𝑉𝑅𝑆𝑇
= 𝑆 ⋅ V𝑎𝑏𝑐𝑃𝑁
, 𝑖𝑎𝑏𝑐𝑃𝑁
= 𝑆𝑇⋅ 𝑖𝑅𝑆𝑇. (5)
Modulation rules can be derived by applying the
differentswitching pattern to the power switches (see Figure
3).
As indicated in Figure 3, the output phase “𝑅” is con-nected to
the input phase “𝑎” during 𝑡
𝑎𝑅and when 𝑇
𝑠is the
sequence period of switching for MDMC system. It is
alsoconnected to phase “𝑏,” “𝑐,” “𝑃,” and “𝑁” during timeperiods
𝑡
𝑏𝑅, 𝑡𝑐𝑅, 𝑡𝑃𝑅, 𝑡𝑁𝑅
, respectively. Arbitrary amplitudeand frequency can be
generated bymodulating the duty cycleof the switches using their
respective switching functions.
If 𝑑𝑖𝑗(𝑡) = 𝑡
𝑖𝑗/𝑇seq, the restrictions of the duty cycle (based
on (2)) can be represented as below:
0 ≤ 𝑑𝑖𝑗≤ 1, 𝑑
𝑎𝑗+ 𝑑𝑏𝑗+ 𝑑𝑐𝑗+ 𝑑𝑃𝑗+ 𝑑𝑁𝑗= 1,
𝑖 ∈ (𝑎, 𝑏, 𝑐, 𝑃,𝑁) , 𝑗 ∈ (𝑅, 𝑆, 𝑇) .
(6)
The matrix 𝑆 can be replaced by matrix 𝐷 (3 × 5) and finallythe
low frequency transfer matrix is defined as below:
V𝑅𝑆𝑇
= 𝐷 ⋅ V𝑎𝑏𝑐𝑃𝑁
, 𝑖𝑎𝑏𝑐𝑃𝑁
= 𝐷𝑇⋅ 𝑖𝑅𝑆𝑇, (7)
where 𝑖𝑅𝑆𝑇
and V𝑅𝑆𝑇
are a set of sinusoidal currents andarbitrary amplitude,
frequency output voltages, and V
𝑎𝑏𝑐𝑃𝑁
and 𝑖𝑎𝑏𝑐𝑃𝑁
are sinusoidal input voltages and input currents atthe MDMC
terminals.
3. Modulation Method
In this modulation method, reference output phase voltagecan be
synthesized by utilizing all five input phase voltagesover one
switching period in the average sense.Therefore, theswitching
period 𝑇
𝑠is divided into two time periods, 𝑇
𝑐and
𝑇3. During𝑇
𝑐, the input phases ofACgenerator are connected
to a corresponding output terminal, and during 𝑇3the input
phases ofDCbattery are connected to a corresponding output
dR1
1 1
0
T1 T2
Tc
T3
Ts
MN
MX MX
MD
TR1 TR2 TR3 TR4 TR5 TR6
Neg
Pos
Figure 4: Output 𝑅-phase switching state in switching
pattern-I.
terminal. In addition, the time interval 𝑇𝑐is divided into
two
periods 𝑇1and 𝑇
2. Also, the MX, MD, and MN denote the
instantaneous values of maximum, medium, and minimuminput
voltages of AC generator. Furthermore, POS and NEGdenote the
instantaneous values of positive andnegative inputvoltages of DC
battery, respectively. During 𝑇
1, the line-
to-line voltage between MX and MN is used, which is themaximum
line-to-line voltage among three line-to-line inputvoltages of
generator at the sampling instant. During 𝑇
2, the
second maximum line-to-line voltage is used which is MX toMD for
switching pattern-I and MD to MN for switchingpattern-II. Finally,
during 𝑇
3the line-to-line voltage between
POS and NEG is employed.In this method, the three line-to-line
input voltages of
the generator and the input voltages of batteries are
readcontinuously at the sampling instant. Then, duty ratio
values(range between 0 and 1) are predetermined for each
outputphase at the beginning of each switching period. Also,
theduty ratio of each phase is compared with a common con-tinuous
triangular carrier waveform, in order to generate thecorresponding
six time subintervals (see Figure 4). These sixtime subintervals
determine the connection time of the cor-responding output terminal
to the input phases during oneswitching cycle. Therefore, the
desired output voltage canbe synthesized by updating the duty ratio
value during eachswitching period. In addition, the input power
factor can becontrolled by manipulating the slopes of the
triangularcarriers. Due to the time subintervals extension, this
methodis called extended direct duty pulse width
modulation(EDDPWM).
3.1. Switching Pattern-I. Figure 4 shows the switchingpattern-I,
where the 𝑅-phase duty ratio value (𝑑
𝑅1) is com-
pared with triangular carrier waveform to generate the 𝑅-phase
output voltage.The output phase is changed during theswitching
pattern-I from MN→MX→MX→MD→NEG→POS, consequently. The actual output
voltage mergeof 𝑅-phase is illustrated in Figure 6 when applying
switchingpattern-I. As illustrated in Figures 4 and 6, the output
phase“𝑅” is connected to the input phase “MN” during 𝑇
𝑅1
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The Scientific World Journal 5
dR2
1 1
0
Tc
T1 T2 T3
Ts
MN MN
MX
MD
TR1 TR2 TR3 TR4 TR5 TR6
Neg
Pos
Figure 5: Output 𝑅-phase switching state in switching
pattern-II.
and when 𝑇𝑠is the sequence switching period. And it is
connected to phases “MX,” “MX,” “MD,” “NEG,” and “POS”during
time periods 𝑇
𝑅2, 𝑇𝑅3, 𝑇𝑅4, 𝑇𝑅5, and 𝑇
𝑅6, respectively.
These six time subintervals can be represented as (8),
where𝑑𝑅1
is the 𝑅-phase duty ratio value and carrier slops aredefined as𝑚
= 𝑇
1/𝑇𝑐and 𝑛 = 𝑇
𝑐/𝑇𝑠:
𝑇𝑅1= 𝑑𝑅1𝑚𝑛𝑇𝑠,
𝑇𝑅2= (1 − 𝑑
𝑅1)𝑚𝑛𝑇
𝑠,
𝑇𝑅3= (1 − 𝑑
𝑅1) (1 − 𝑚) 𝑛𝑇𝑠,
𝑇𝑅4= 𝑑𝑅1 (1 − 𝑚) 𝑛𝑇𝑠,
𝑇𝑅5= 𝑑𝑅1 (1 − 𝑛) 𝑇𝑠,
𝑇𝑅6= (1 − 𝑑
𝑅1) (1 − 𝑛) 𝑇𝑠.
(8)
The fluctuation of the input voltage is negligible during
theswitching periods.Thus, the integration of the output
voltageV𝑜𝑅
over 𝑇𝑠can be expressed in
∫
𝑇𝑠
0
V𝑜𝑅𝑑𝑡 ≅ 𝑇
𝑅1⋅MN + (𝑇
𝑅2+ 𝑇𝑅3) ⋅MX
+ 𝑇𝑅4MD + 𝑇
𝑅5⋅NEG + 𝑇
𝑅6⋅ POS.
(9)
Based on (8) and (9), the average output voltage can beexpressed
in terms of𝑚 and 𝑛 as follows:
V𝑂𝑅=1
𝑇𝑠
∫
𝑇𝑠
0
V𝑜𝑅𝑑𝑡
≅ 𝑑𝑅1⋅ (− (1 − 𝑛)POS − 𝑛 ⋅MX + (1 − 𝑚) ⋅ 𝑛 ⋅MD
+𝑚 ⋅ 𝑛 ⋅MN + (1 − 𝑛) ⋅NEG)
+ 𝑛 ⋅MX − (1 − 𝑛) ⋅ POS.(10)
0t
Ts
�oR
MN
MX
MD
TR1 TR2 TR3 TR4 TR5 TR6
Neg
Pos
VoA
Figure 6: Output 𝑅-phase voltage synthesis in switching
pattern-I.
For the present switching cycle, the duty ratio value, 𝑑𝑅1,
can
be written as follows:
𝑑𝑅1= (V∗𝑜𝑅− 𝑛 ⋅MX − (1 − 𝑛) ⋅ POS)
× (− (1 − 𝑛)POS − 𝑛 ⋅MX + (1 − 𝑚) ⋅ 𝑛 ⋅MD
+𝑚 ⋅ 𝑛 ⋅MN + (1 − 𝑛) ⋅NEG)−1,
(11)
where the V∗𝑜𝑅
is the 𝑅-phase output voltage command whichis equal to the V
𝑂𝑅.
3.2. Switching Pattern-II. Theprocedure to drive the equationfor
switching pattern II is the same as the previous switchingpattern.
Figure 5 illustrates the case of switching patternII where the
𝑅-phase duty ratio value (𝑑
𝑅2) is compared with
triangular carrier waveform to generate the 𝑅-phase
outputvoltage. The output phase is changed during the
switchingpattern-II from MN→MX→MD→MN→NEG→POS,consequently. The
actual output voltage merge of 𝑅-phase isillustrated in Figure
7when the output phase “𝑅” is connectedto the input phases during
the time subintervals sequentially.Similarly, the integration of
the output voltage V
𝑜𝑅and the
average output voltage V𝑂𝑅
is presented as below:
∫
𝑇𝑠
0
V𝑜𝑅𝑑𝑡 ≅ (𝑇
𝑅1+ 𝑇𝑅4) ⋅MN
+ 𝑇𝑅2⋅MX + 𝑇
𝑅3MD + 𝑇
𝑅5⋅NEG + 𝑇
𝑅6⋅ POS,
V𝑂𝑅=1
𝑇𝑠
∫
𝑇𝑠
0
V𝑜𝑅𝑑𝑡
≅ 𝑑𝑅2⋅ (− (1 − 𝑛)POS − 𝑚𝑛 ⋅MX
− (1 − 𝑚) ⋅ 𝑛 ⋅MD + 𝑛 ⋅MN
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6 The Scientific World Journal
+ (1 − 𝑛) ⋅NEG)+ (1 − 𝑛) ⋅ POS − 𝑚 ⋅ 𝑛 ⋅MX + (1 − 𝑚) ⋅ 𝑛
⋅MD.
(12)
By letting the V𝑂𝑅
be equal to V∗𝑜𝑅
the duty ratio value 𝑑𝑅2
canbe written as follows:
𝑑𝑅2= (V∗𝑜𝑅− 𝑛 ⋅MX − (1 − 𝑛) ⋅ POS)
× (− (1 − 𝑛)POS − 𝑛 ⋅MX + (1 − 𝑚) ⋅ 𝑛 ⋅MD
+𝑚 ⋅ 𝑛 ⋅MN + (1 − 𝑛) ⋅NEG)−1.
(13)
3.3. Outputs Voltage Merged for MDMC. Five bidirectionalswitches
are used for each output phase to apply the switchingpattern-I and
II. The POS and NEG input phase are alwaysconstant while the MX,
MD, and MN are selected byinstantaneous comparison of the AC input
phases. When theswitching state for output phase “𝑅” is POS, NEG,
MX, MD,or MN, the output phase “𝑅” is connected to the input
phasewhich the voltage is POS, NEG, MX, MD, or MN, respec-tively.
This modulation control method can be applied totheMDMC as amodular
structure for each phase where eachoutput phase has the independent
reference control signal.This reference control signal can be
different in terms offrequency, waveform shape, and amplitude.
0t
�oR
MN
MX
MD
TR1 TR2 TR3 TR4 TR5 TR6
Neg
Pos
TsVoA
Figure 7: Output 𝑅-phase voltage synthesis in switching
pattern-II.
The duty ratio of phases 𝑆 and 𝑇 is indicated as 𝑑𝑆and 𝑑
𝑇
and can be derived in the same way of phase 𝑅 by letting
theV𝑂𝑆
and V𝑂𝑇
be equal to the 𝑆 and 𝑇 phase voltage com-mand V∗
𝑜𝑆and V∗
𝑜𝑇, respectively. Duty ratio of phases can be
expressed as follows:
𝑑𝑅=
{{{
{{{
{
V∗𝑜𝑅− 𝑛 ⋅MX − (1 − 𝑛) ⋅ POS
− (1 − 𝑛)POS − 𝑛 ⋅MX + (1 − 𝑚) ⋅ 𝑛 ⋅MD + 𝑚 ⋅ 𝑛 ⋅MN + (1 − 𝑛)
⋅NEG, for Pattern-I,
V∗𝑜𝑅− 𝑛 ⋅MX − (1 − 𝑛) ⋅ POS
− (1 − 𝑛)POS − 𝑛 ⋅MX + (1 − 𝑚) ⋅ 𝑛 ⋅MD + 𝑚 ⋅ 𝑛 ⋅MN + (1 − 𝑛)
⋅NEG, for pattern-II,
𝑑𝑆=
{{{
{{{
{
V∗𝑜𝑆− 𝑛 ⋅MX − (1 − 𝑛) ⋅ POS
− (1 − 𝑛)POS − 𝑛 ⋅MX + (1 − 𝑚) ⋅ 𝑛 ⋅MD + 𝑚 ⋅ 𝑛 ⋅MN + (1 − 𝑛)
⋅NEG, for Pattern-I,
V∗𝑜𝑆− 𝑛 ⋅MX − (1 − 𝑛) ⋅ POS
− (1 − 𝑛)POS − 𝑛 ⋅MX + (1 − 𝑚) ⋅ 𝑛 ⋅MD + 𝑚 ⋅ 𝑛 ⋅MN + (1 − 𝑛)
⋅NEG, for pattern-II,
𝑑𝑇=
{{{
{{{
{
V∗𝑜𝑇− 𝑛 ⋅MX − (1 − 𝑛) ⋅ POS
− (1 − 𝑛)POS − 𝑛 ⋅MX + (1 − 𝑚) ⋅ 𝑛 ⋅MD + 𝑚 ⋅ 𝑛 ⋅MN + (1 − 𝑛)
⋅NEG, for Pattern-I,
V∗𝑜𝑇− 𝑛 ⋅MX − (1 − 𝑛) ⋅ POS
− (1 − 𝑛)POS − 𝑛 ⋅MX + (1 − 𝑚) ⋅ 𝑛 ⋅MD + 𝑚 ⋅ 𝑛 ⋅MN + (1 − 𝑛)
⋅NEG, for pattern-II.
(14)
In the proposed method, the output voltages have been
wellsynthesised by using two out of five line-to-line input
voltagesduring each switching period, while the input currents
aredistorted. In order to improve the input current quality
andreduce the input currents distortion, five input phases
con-ducted the current during each switching period.
3.4. Inputs Current Merged for MDMC. The 𝑛 and 𝑚 canproperly be
adjusted to reduce the input current distortion in(14).This current
distortion can be reduced by controlling theinput power factor
which is directly depending on the slopeof the triangular carrier.
By maintaining the 𝑇
𝑠at a constant
value and adjusting the value of 𝑛 and𝑚 to the desired value,the
input current is synthesized.The output voltagewaveform
will not be disturbed since 𝑛 and 𝑚 are considered in
thederivation of (14).
The output currents are almost constant during theswitching
cycles; thus the input current can be merged basedon the PWM
switching pattern. These six time subintervalsfor each phase can be
expressed as follows:
𝑇𝑋1= 𝑑𝑋𝑚𝑛𝑇𝑠= 𝑑𝑋𝑇1,
𝑇𝑋2= (1 − 𝑑
𝑋)𝑚𝑛𝑇
𝑠= (1 − 𝑑
𝑋) 𝑇1,
𝑇𝑋3= (1 − 𝑑
𝑋) (1 − 𝑚) 𝑛𝑇𝑠 = (1 − 𝑑𝑋) 𝑇2,
𝑇𝑋4= 𝑑𝑋(1 − 𝑚) 𝑛𝑇𝑠 = 𝑑𝑋𝑇2,
-
The Scientific World Journal 7
𝑇𝑋5= 𝑑𝑋 (1 − 𝑛) 𝑇𝑠 = 𝑑𝑋𝑇3,
𝑇𝑋6= (1 − 𝑑
𝑋) (1 − 𝑛) 𝑇𝑠 = (1 − 𝑑𝑋) 𝑇3,
𝑋 = 𝑅, 𝑆, 𝑇.
(15)
3.4.1. Switching Pattern-I. Five inputs are connected to
theoutput terminal through the bidirectional switches. Accord-ing
to the switching state as shown in Figures 4 and 6, theoutput
phases 𝑅, 𝑆, and 𝑇 during 𝑇
𝑅1, 𝑇𝑆1, and 𝑇
𝑇1, are con-
nected to the input phase whose voltage is MN. In the sameway,
the input phase MX is connected to the output phases𝑅, 𝑆, and 𝑇
during (𝑇
𝑅2+ 𝑇𝑅3), (𝑇𝑆2+ 𝑇𝑆3), and (𝑇
𝑇2+ 𝑇𝑇3),
respectively, and the input phase MD is connected to theoutput
terminals 𝑅, 𝑆, and 𝑇 during 𝑇
𝑅4, 𝑇𝑆4, and 𝑇
𝑇4,
respectively. In addition, the input phaseNEG is connected tothe
output terminals 𝑅, 𝑆, and 𝑇 during 𝑇
𝑅5, 𝑇𝑆5, and 𝑇
𝑇5,
respectively, and input phase POS is connected to the
outputterminals𝑅, 𝑆, and𝑇 during𝑇
𝑅6,𝑇𝑆6, and𝑇
𝑇6, respectively. By
applying the average concept to each input phase, the
inputcurrent can be presented as follows:
𝑖𝑠MX𝑇𝑠 = (𝑇𝑅2 + 𝑇𝑅3) 𝑖𝑜𝑅 + (𝑇𝑆2 + 𝑇𝑆3) 𝑖𝑜𝑆 + (𝑇𝑇2 + 𝑇𝑇3)
𝑖𝑜𝑇,
𝑖𝑠MD𝑇𝑠 = 𝑇𝑅4𝑖𝑜𝑅 + 𝑇𝑆4𝑖𝑜𝑆 + 𝑇𝑇4𝑖𝑜𝑇,
𝑖𝑠MN𝑇𝑠 = 𝑇𝑅1𝑖𝑜𝑅 + 𝑇𝑆1𝑖𝑜𝑆 + 𝑇𝑇1𝑖𝑜𝑇,
𝑖𝑠NEG𝑇𝑠 = 𝑇𝑅5𝑖𝑜𝑅 + 𝑇𝑆5𝑖𝑜𝑆 + 𝑇𝑇5𝑖𝑜𝑇,
𝑖𝑠POS𝑇𝑠 = 𝑇𝑅6𝑖𝑜𝑅 + 𝑇𝑆6𝑖𝑜𝑆 + 𝑇𝑇6𝑖𝑜𝑇.
(16)
By substituting (15) into (16), the instants value of the
inputphase current during one switching cycle can be obtained
asfollows:
𝑖𝑠MX𝑇𝑠 = − 𝑇𝑐 ⋅ (𝑑𝑅𝑖𝑜𝑅 + 𝑑𝑆𝑖𝑜𝑆 + 𝑑𝑇𝑖𝑜𝑇) , (17)
𝑖𝑠MD𝑇𝑠 = 𝑇2 ⋅ (𝑑𝑅𝑖𝑜𝑅 + 𝑑𝑆𝑖𝑜𝑆 + 𝑑𝑇𝑖𝑜𝑇) , (18)
𝑖𝑠MN𝑇𝑠 = 𝑇1 ⋅ (𝑑𝑅𝑖𝑜𝑅 + 𝑑𝑆𝑖𝑜𝑆 + 𝑑𝑇𝑖𝑜𝑇) , (19)
𝑖𝑠NEG𝑇𝑠 = 𝑇3 ⋅ (𝑑𝑅𝑖𝑜𝑅 + 𝑑𝑆𝑖𝑜𝑆 + 𝑑𝑇𝑖𝑜𝑇) , (20)
𝑖𝑠POS𝑇𝑠 = −𝑇3 ⋅ (𝑑𝑅𝑖𝑜𝑅 + 𝑑𝑆𝑖𝑜𝑆 + 𝑑𝑇𝑖𝑜𝑇) . (21)
By substituting (19) into (17), the𝑚 can be obtained as
follows:
𝑚 ≡𝑇1
𝑇𝑐
= −𝑖𝑠MN𝑖𝑠MX
. (22)
Also, by calculating the 𝑖𝑠MX ⋅ 𝑇𝑠 based on (𝑖𝑠MX + 𝑖𝑠POS) ⋅
𝑇𝐶,
the 𝑛 can be obtained as below:
𝑛 ≡𝑇𝑐
𝑇𝑠
=𝑖𝑠MX
(𝑖𝑠MX + 𝑖𝑠POS)
. (23)
3.4.2. Switching Pattern-II. Like switching pattern-I, by
apply-ing the switching pattern-II which is indicated in Figures
5and 7, input phaseMX is connected to the output phases𝑅, 𝑆,
𝑇 during time subinterval𝑇𝑅2,𝑇𝑆2, and𝑇
𝑇2, respectively. Sim-
ilarly, the input phase MD is connected to the output phases𝑅,
𝑆, and 𝑇 during 𝑇
𝑅3, 𝑇𝑆3, and 𝑇
𝑇3, respectively and the
input phase MN is connected to the output phases 𝑅, 𝑆, and𝑇
during (𝑇
𝑅1+𝑇𝑅4), (𝑇𝑆1+𝑇𝑆4), and (𝑇
𝑇1+𝑇𝑇4), respectively.
Finally, the input phase NEG is connected to the outputterminals
𝑅, 𝑆, and 𝑇 during 𝑇
𝑅5, 𝑇𝑆5, and 𝑇
𝑇5, respectively,
and input phase POS is connected to the output terminals𝑅, 𝑆,
and 𝑇 during 𝑇
𝑅6, 𝑇𝑆6, and 𝑇
𝑇6, respectively. The input
currents can be presented as follows:
𝑖𝑠MX𝑇𝑠 = 𝑇𝑅2𝑖𝑜𝑅 + 𝑇𝑆2𝑖𝑜𝑆 + 𝑇𝑇2𝑖𝑜𝑇, (24)
𝑖𝑠MD𝑇𝑠 = 𝑇𝑅3𝑖𝑜𝑅 + 𝑇𝑆3𝑖𝑜𝑆 + 𝑇𝑇3𝑖𝑜𝑇, (25)
𝑖𝑠MN𝑇𝑠 = (𝑇𝑅1 + 𝑇𝑅4) 𝑖𝑜𝑅 + (𝑇𝑆1 + 𝑇𝑆4) 𝑖𝑜𝑆 + (𝑇𝑇1 + 𝑇𝑇4)
𝑖𝑜𝑇,
(26)
𝑖𝑠NEG𝑇𝑠 = 𝑇𝑅5𝑖𝑜𝑅 + 𝑇𝑆5𝑖𝑜𝑆 + 𝑇𝑇5𝑖𝑜𝑇, (27)
𝑖𝑠POS𝑇𝑠 = 𝑇𝑅6𝑖𝑜𝑅 + 𝑇𝑆6𝑖𝑜𝑆 + 𝑇𝑇6𝑖𝑜𝑇. (28)
By considering the time intervals for 𝑇𝑠and substituting
(26)
into (24), the𝑚 can be represented as follows:
𝑚 ≡𝑇1
𝑇𝑐
= −𝑖𝑠MX𝑖𝑠MN
. (29)
In addition, by calculating the 𝑖𝑠MX ⋅𝑇𝑠 based on (𝑖𝑠MX+𝑖𝑠POS)
⋅
𝑇𝐶, the 𝑛 can be obtained as below:
𝑛 ≡𝑇𝑐
𝑇𝑠
=𝑖𝑠MN
(𝑖𝑠MN − 𝑖𝑠POS)
. (30)
Furthermore, when the power factor is one in balance system,the
currents 𝑖
𝑠MN, 𝑖𝑠MX, and 𝑖𝑠POS can be replaced by voltagesV𝑠MN, V𝑠MX, and
V𝑠POS (see (22), (23), (29), and (30)). As theinput voltage is
directly sensed from the power circuit, themodulation calculation
becomes easier.
To achieve unity power factor, load can be assumed ascurrent
source in one switching cycle; accordingly, inputcurrent can be
synthesized based on the switching state of theoutput phase
current. The magnitude of each input currentvaried based on the
ratio between𝑇
1and𝑇2and ratio between
𝑇𝑐and 𝑇
3while 𝑇
𝑠is constant. On the other hand, due to the
missing of the energy storage component in MDMC, theinput and
output powers should be kept balanced all the timeat any load. The
practical selection of 𝑛 and 𝑚 for switchingpattern-I and II can be
determined by the input voltage angle𝛼𝑖, to synthesize sinusoidal
input current.The three-phase input voltages signal shown in Figure
8 is
divided into the 6 segments and each segment is divided intotwo
sectors which correspond to either switching pattern-I orII. By
letting the power factor of system equal to 𝜑, the inputcurrent
angle can be obtained as follows:
𝛽𝑖= 𝛼𝑖+ 𝜑. (31)
In the proposed modulation, input power factor is controlledby
adjusting the value of 𝑛 and 𝑚 (Table 1). Based on theavailable
maximum line-to-line voltage, the range of duty
-
8 The Scientific World Journal
Table 1: Determination of 𝑛 and𝑚 based on the input voltage
sector.
Sector 𝑛 Uniformity 𝑀 Uniformity
I-2 − sin (𝛽𝑖− 2𝜋/3)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖+ 2𝜋/3))/ sin(𝛽
𝑖− 2𝜋/3) 1–0.5 down
II-2 − sin (𝛽𝑖− 2𝜋/3)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖))/ sin(𝛽
𝑖− 2𝜋/3) 0.5–1 up
II-1 sin (𝛽𝑖)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖− 2𝜋/3))/ sin(𝛽
𝑖) 1–0.5 down
III-1 sin (𝛽𝑖)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖+ 2𝜋/3))/ sin(𝛽
𝑖) 0.5–1 up
III-2 − sin (𝛽𝑖+ 2𝜋/3)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖))/ sin(𝛽
𝑖+ 2𝜋/3) 1–0.5 down
IV-2 − sin (𝛽𝑖+ 2𝜋/3)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖− 2𝜋/3))/ sin(𝛽
𝑖+ 2𝜋/3) 0.5–1 up
IV-1 sin (𝛽𝑖− 2𝜋/3)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖+ 2𝜋/3))/ sin(𝛽
𝑖− 2𝜋/3) 1–0.5 down
V-1 sin (𝛽𝑖− 2𝜋/3)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖))/ sin(𝛽
𝑖− 2𝜋/3) 0.5–1 up
V-2 sin (𝛽𝑖)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖− 2𝜋/3))/ sin(𝛽
𝑖) 1–0.5 down
VI-2 sin (𝛽𝑖)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖+ 2𝜋/3))/ sin(𝛽
𝑖) 0.5–1 up
VI-1 sin (𝛽𝑖+ 2𝜋/3)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖))/ sin(𝛽
𝑖+ 2𝜋/3) 1–0.5 down
I-1 sin (𝛽𝑖+ 2𝜋/3)
√3
2𝐷 to𝐷 (− sin(𝛽
𝑖− 2𝜋/3))/ sin(𝛽
𝑖+ 2𝜋/3) 0.5–1 up
I II III IV V VI
0
1 1 1 1 1 12 2 2 2 2 2
Input voltage
𝛼i
Figure 8: Interval voltage sector based on the input voltage
(𝛼𝑖).
ratio is changed during time intervals 𝑇1and 𝑇
2. The range
of available voltage ratio during the 𝑇1is higher than 𝑇
2.
Therefore, the desired value of 𝑚 is varied from 0.5 to 1 ineach
sector to reach the maximum power of input source. InTable 1, the𝐷
= V
𝑠MX/(V𝑠MX + V𝑠POS) indicates the magnitudevariation of 𝑛, where
V
𝑠MX is nominal value of generator inputvoltage.
4. Simulation Result
Simulation of the proposed modulation method for MDMCis
performed by using MATLAB software. The system has
Table 2: Simulation parameter.
𝑅-𝐿 load 𝑅 = 5Ω, 𝐿 = 10mHInput voltage(line-to-neutral) 𝑉
𝑠-RMS56V
Battery voltage(line-to-neutral) 𝑉
𝑠-dc±48V
Output voltage(line-to-neutral) 𝑉
𝑜-RMS28V
Voltage ratio 𝑞 0.5Input frequency 𝑓
𝑠60Hz
Output frequency 𝑓𝑜
50Hz
been investigated to synthesize the voltage and current in
twoconditions, when the input voltage of generator𝑉
𝑠-RMS is big-ger than the battery voltage𝑉
𝑠-dc and vice versa.The switchingperiod 𝑇
𝑠is assumed to be 200𝜇s in all conditions.
4.1. Condition I. In this condition the line-to-neutral
voltageof generator𝑉
𝑠-RMS is bigger than the battery voltage𝑉𝑠-dc andbattery’s
charging (SOC) is equal to 50%. Thus, the power isinjected from
generator to the AC and DC loads. Simulationparameters for
condition (I) are shown in Table 2.
In point of view of power transferring, when the batteryvoltage
𝑉
𝑠-dc is less than the line to-neutral voltage of gen-erator
𝑉
𝑠-RMS whole load’s power demand is supplied by thegenerator.
Thus, the time interval 𝑇
3is equal to zero and
voltage ratio is varied based on the value of
generator’svoltage.
-
The Scientific World Journal 9
100
50
0
−50
−100
Switching pulse
�oR
ioR
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
10
5
0
−10
−5
AC o
utpu
t vol
tage
,E(V
)AC
out
put c
urre
nt,I
(A)
Time, t (s)
100
50
0
−50
−100
0.0190 0.0192 0.0194
Figure 9: AC voltage and current output waveform by
voltagesynthesizing.
0.0190 0.0192 0.0194
10
5
0
�oST
ioS
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Time, t (s)
100
150
50
0
100
150
50
0
DC
outp
ut v
olta
ge,E
(V)
DC
outp
ut cu
rren
t,I
(A)
Figure 10: DC voltage and current output waveform by
voltagesynthesizing.
4.1.1. Voltage Synthesizing. In voltage synthesizing
situation,the slopes of triangular waveforms are constant.
Therefore,the time intervals are considered to be 100𝜇s for 𝑇
1and
𝑇2. Figure 9 illustrates the output line-to-neutral voltage
V
𝑜𝑅
which is connected to the AC load and AC output current 𝑖𝑜𝑅.
Figure 10 represents the output line-to-line voltage V𝑜𝑆𝑇
which
0
10
5
0
−10
−5
Inpu
t vol
tage
,E(V
)
Inpu
t cur
rent
,I(A
)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Time, t (s)
100
50
−50
−100
�sa
isa
Figure 11: Input voltage and current waveform by voltage
synthesiz-ing.
100
50
0
−50
−100
Switching pulse
�oR
ioR
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
10
5
0
−10
−5
AC o
utpu
t vol
tage
,E(V
)AC
out
put c
urre
nt,I
(A)
Time, t (s)
100
50
0
−50
−100
0.0190 0.0192 0.0194
Figure 12: AC voltage and current output waveform by
currentsynthesizing.
is connected to the DC loads and DC output current 𝑖𝑜𝑅. The
red line in the expand graph indicated the switching
pulsewaveform.
Figure 11 shows the input phase voltage V𝑠𝑎
and filteredinput current 𝑖
𝑠𝑎in steady state. The simulation results
revealed that the proposed modulation method is capable
ofsynthesizing the output voltages while the distortion on theinput
current is visible in Figure 11.
4.1.2. Current Synthesizing. By changing the slope of
thetriangular carriers which is related to the value of 𝑚,
powerfactor has been controlled and the sinusoidal input
currentshave been synthesised. Figures 12 and 13 show the output
ACoutput voltage/current waveform and DC output voltage/current
waveform, respectively.
Figure 14 shows the input phase voltage V𝑠𝑎
and filteredinput current 𝑖
𝑠𝑎in current synthesizing mode. The simula-
tion result in Figure 14 shows that the current input is
wellmerged when there is no additional distortion in
outputvoltage.The simulation result for outputwaveform also
shows
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10 The Scientific World Journal
0.01900.01920.01940.0196
10
5
0
�oST
ioS
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Time, t (s)
100
150
50
0
100
150
50
0DC
outp
ut v
olta
ge,E
(V)
DC
outp
ut cu
rren
t,I
(A)
Figure 13: DC voltage and current output waveform by
currentsynthesizing.
0
10
5
0
−10
−5
Inpu
t vol
tage
,E(V
)
Inpu
t cur
rent
,I(A
)
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Time, t (s)
100
50
−50
−100
�sa
isa
Figure 14: Input voltage and current waveform by current
synthe-sizing.
that the power factor has been controlled and unity powerfactor
almost achieved.
4.2. Condition II. In the second condition when the 𝑉𝑠-RMS
is less than battery voltage (𝑉𝑠-dc) and state of charge of
battery’s is SOC = 95%, power will be injected from generatorand
battery to the AC load at the same time. The switchingsequence is
assumed to be 𝑇
𝑠= 200 𝜇𝑠. All simulation
parameters are the same as parameters in Table 2, exceptthe
input voltage (line-to-neutral) 𝑉
𝑠-RMS, which is equal to20𝑉RMS in this condition. In condition
II, the voltage ratio (𝑞)is independent of the generator input
voltage. The power ofthe generator which is transferred to the load
will be deter-mined by the differences between 𝑉
𝑠-RMS and 𝑉𝑠-dc.
4.2.1. Voltage Synthesizing. In this mode, the slopes of
trian-gular waveforms are constant. Therefore, the time
intervalsare considered to be 𝑇
1= 𝑇2= 50 𝜇s, 𝑇
3= 100 𝜇s. Figure 15
illustrated the average output line-to-neutral voltage V𝑜𝑅
which is connected to the AC load, 𝑅-phase output current
�saisa
ioR
�oR
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
30
15
0
−15
−30
30
0
−30
3
0
−3
10
5
0
−5
−10
Time, t (s)
Out
put c
urre
nt,I
(A)
Inpu
t cur
rent
,I(A
)
Out
put v
olta
ge,E
(V)
Inpu
t vol
tage
,E(V
)
Figure 15: Simulation result by voltage synthesizing.
�sa
isa
ioR
�oR
30
15
0
0
−15
−30
30
15
−15
−30
3
0
1.5
−3
−1.5
10
5
0
−5
−100.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
Time, t (s)
Out
put c
urre
nt,I
(A)
Inpu
t cur
rent
,I(A
)
Out
put v
olta
ge,E
(V) I
nput
vol
tage
,E(V
)
Figure 16: Simulation result by current synthesizing.
𝑖𝑜𝑅, input phase voltage V
𝑠𝑎, and filtered input current 𝑖
𝑠𝑎.
The simulation results showed that the proposed modulationmethod
is able to well synthesize the output voltages, whilethe distortion
on the input current is visible.
4.2.2. Current Synthesising. By changing the slope of the
tri-angular carriers (𝑛 and𝑚) based on Table 2, power factor
hasbeen controlled and the sinusoidal input currents have
beensynthesised. The simulation result in Figure 16 shows thatthe
current input is well merged when there is no additionaldistortion
in output voltage. The result indicated that thepower factor has
been controlled and unity power factoralmost achieved.
4.3. Current Control. In order to test the system
stability,reference current is changed in AC and DC sides while
theloads are constant. Figure 17 shows the simulated
responsesofMDMC systemwhen the current is changed in AC andDCside
at 𝑡 = 0.05 and 𝑡 = 0.07 s, respectively.
Figure 17 shows that the current in 𝑖𝑜𝑆and 𝑖𝑜𝑇
is constantat 𝑡 = 0.05 regardless of the changing in 𝑖
𝑜𝑅which is
increased by 0.2 pu. In addition, when the DC reference
-
The Scientific World Journal 11
ioRioS
ioT
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10
6
3
0
−3
−6Out
put c
urre
nt,I
(A)
Time, t (s)
Figure 17: Output currents waveform during load variation.
current reduced by 0.2 pu, the current in AC side
remainsconstant at 𝑡 = 0.07 s.
It can be clearly seen from Figure 17 that the system isable to
track the variation of reference current, and currentoutput of each
terminals is completely independent of otheroutput current
terminals. Moreover, the simulation resultsexhibited that the
undershoot/overshoot and steady-stateerror for output currents is
acceptable for low power batterybased system.
5. Conclusions
This study represents a structure for multidirectional
matrixconverter which is suitable for battery based system.This
newMDMC configuration reduces the cost and size of the system.This
study also presents a novel DDPWMmethod to controlthe power flow
from generator and battery to the load. Thisnewmodulationmethod
used the concept of the average volt-age per switching period and a
continuous carrier formultidi-rectionalmatrix converters. By
applying the proper switchingpattern and determining the duty ratio
for each switch, thevoltage of each output terminal has been well
synthesized. Inaddition, by changing the slope of the carriers
whichis related to the value of 𝑛 and𝑚, power factor has been
con-trolled and the sinusoidal input currents have been
synthe-sised.
The feasibility of the proposed MDMC structure andEDDPWM
technique has been verified by MATLAB simula-tion. Results of this
study revealed that the proposed carrierbased modulation technique
can be used for the applicationwhere battery is essential. This
method can easily control thepower factor andmerged the output
voltage and input currentwithout any lookup tables. Since this new
modulation hasa good flexibility and applicability, it can be
effectivelyapplied in a system with a connection between the input
andoutput neutrals with a desired output voltage and
frequency.Furthermore, battery discharging time has been increased
byletting power flow from both generator and battery to theload,
simultaneously.The simulation results of this study alsorevealed
that the current response in AC and DC of theMDMC system with
proposed EDDPWMmethod is accept-able for low power battery based
systems.
Conflict of Interests
The authors declare that there is no conflict of
interestsregarding the publication of this paper.
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