novel modulation method for multidirectional matrix converter...novel modulation method for...

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

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

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)


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


dR2

1 1

0

Tc

T1 T2 T3

Ts

MN MN

MX

MD


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


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


+ (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


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


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


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,


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


𝑇4,

respectively. In addition, the input phaseNEG is connected tothe output terminals 𝑅, 𝑆, and 𝑇 during 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


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


𝑇5, respectively,

and input phase POS is connected to the output terminals𝑅, 𝑆, and 𝑇 during 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


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


𝑖))/ sin(𝛽

𝑖− 2𝜋/3) 0.5–1 up

II-1 sin (𝛽𝑖)

√3


𝑖− 2𝜋/3))/ sin(𝛽

𝑖) 1–0.5 down

III-1 sin (𝛽𝑖)

√3


𝑖+ 2𝜋/3))/ sin(𝛽

𝑖) 0.5–1 up

III-2 − sin (𝛽𝑖+ 2𝜋/3)

√3


𝑖))/ sin(𝛽

𝑖+ 2𝜋/3) 1–0.5 down

IV-2 − sin (𝛽𝑖+ 2𝜋/3)

√3


𝑖− 2𝜋/3))/ sin(𝛽

𝑖+ 2𝜋/3) 0.5–1 up

IV-1 sin (𝛽𝑖− 2𝜋/3)

√3


𝑖+ 2𝜋/3))/ sin(𝛽

𝑖− 2𝜋/3) 1–0.5 down

V-1 sin (𝛽𝑖− 2𝜋/3)

√3


𝑖))/ sin(𝛽

𝑖− 2𝜋/3) 0.5–1 up

V-2 sin (𝛽𝑖)

√3


𝑖− 2𝜋/3))/ sin(𝛽

𝑖) 1–0.5 down

VI-2 sin (𝛽𝑖)

√3


𝑖+ 2𝜋/3))/ sin(𝛽

𝑖) 0.5–1 up

VI-1 sin (𝛽𝑖+ 2𝜋/3)

√3


𝑖))/ sin(𝛽

𝑖+ 2𝜋/3) 1–0.5 down

I-1 sin (𝛽𝑖+ 2𝜋/3)

√3


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.


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


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


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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