Research ArticleEqualization Technique for Balancing the ModulationRatio Characteristics of the Single-Phase-to-Three-PhaseMatrix Converter

Vengadeshwaran Velu1 Norman Mariun2 Mohd Amran Mohd Radzi2

and Nashiren Farzilah Mailah2

1School of Science and Engineering Manipal International University 71800 Nilai Malaysia2Faculty of Engineering Universiti Putra Malaysia 43400 Serdang Selangor Malaysia

Correspondence should be addressed to Vengadeshwaran Velu vengadeshwaranvelumiuedumy

Received 1 July 2015 Revised 26 December 2015 Accepted 28 December 2015

Academic Editor Michele Risi

Copyright copy 2016 Vengadeshwaran Velu et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Three-phase system has numerous advantages over the single-phase system in terms of instantaneous power stability and costThree-phase systems are not available in every location particularly in remote rural areas hill stations low voltage distributionhomes and so forth Having a system that is capable of converting directly the readily available single-phase system to three phaseswill have greater usability in various applications The routine techniques adopted in the direct ac-ac single-phase-to-three-phaseconverters do not yield the best desired outputs because of their complexity in the segregation process and bidirectional nature of theinput signal Other initiatives use ac-dc-ac converters which are huge and costly due to dc link energy storage devices Further noneof these systems provide a convincing result in producing the standard three-phase output voltages that are 120∘ away from eachother This paper proposes an effective direct ac-ac single-phase-to-three-phase conversion technique based on space vector pulsewidthmodulation basedmatrix converter system that produces a convincing three-phase output signals from a single-phase sourcewith balancedmodulation index characteristicsThe details of the scientific programming adopted on the proposed technique werepresented

1 Introduction

Conversion of single phase to three phases (SP2TP) is alwaysan interesting task in the ac-ac converters sector Havinga converter that takes a single-phase source as an inputand produces three phases balanced as output helps to runthree-phase loads under single-phase source Single-phase-to-three-phase matrix converter is one of the most advanceddirect ac-ac converters which can be designed for the conver-sion of the single-phase system to three-phase system Thisconverter has high prospects in those applications where onlysingle-phase source is available such as home remote townand mobile power source When the ratings of the single-phase induction motor are greater than 05 kW it becomesuneconomical to operate at higher load conditions [1] Single-phase-to-three-phase converters are widely used in electric

locomotives and rural areas where only single-phase poweris available due to technical or economic reasons [2] Con-ventional single-phase-to-three-phase converters produceunbalanced voltages which have negative effects on the loadThe impact of having unbalanced voltages on the inductionmotor load results in the production of negative sequencevoltages which in turn causes excessive losses overvoltagesmechanical oscillations and interference with control cir-cuits Among the various types of converters conversion ofsingle-phase system to three-phase system is regarded as themost complex one The major difficulty of such converters isthe alternating and bidirectional nature of the input signalwhich is required to be segregated into three output signalsAdvanced scientific programming methods help to solve thiscomplex engineering problem Matrix converter is designedusing the IGBT based bidirectional switches for direct ac-ac

Hindawi Publishing CorporationScientific ProgrammingVolume 2016 Article ID 6187926 10 pageshttpdxdoiorg10115520166187926

2 Scientific Programming

Three-phase loadsSingle-phasealternating

sourceSP2TP matrix

converter system

Figure 1 SP2TP matrix converter system [9]

conversionsThe bidirectional switches are designed in such away that they should not short-circuit the voltage sources andopen-circuit the current sources [3] On the other hand theac-dc-ac converter adopts rectifier-inverter concepts wherethe single-phase ac voltage is converted to dc voltage in thefirst stage and in the second inverter stage the dc voltageis inverted back to three-phase voltages Despite the THDlosses of ac-dc-ac converter are much lesser compared todirect ac-ac converter other issues such as additional costdue to bulk storage devices are major drawbacks Thus thedirect ac-ac converters are more compact in size and costFor many years simple carrier based sinusoidal based PWMmodulation schemes are used inmany applications [4] How-ever advance switching algorithm such as space vector basedPWM modulation scheme can be employed to segregatethe input signal along with the bidirectional IGBT switchesbased matrix converter to produce the required three-phaseoutput waveforms Using scientific programming methodsadvanced modulation scheme can be implemented usingstate-of-the-art engineering simulation application and inter-facing with the digital signal processor and other controlcircuits in real time Space vector pulse widthmodulation is aunique technique that makes the switching complexity of ac-ac converters much easier Employing the space vector PWMtechnique for the single-phase-to-three-phase conversion isthe main contribution of the paper Adjustable speed drivesare considered matured due to advances in power semicon-ductor devices and lower cost Active devices continue toimprove whereas the passive devices such as energy storagecapacitor occupy huge system volume weight and reliability[5] Similar research initiative suggests that matrix convertercan be operated under buck-boost mode with variable fre-quencies but under Z-Source topology [6] Cycloconvertersbased static converters produced balanced output voltagesbut suffer from high low order harmonics [7] Anotherinitiative suggests having two capacitor converters for morebalanced operation of induction motor using single-phasesupply [8] which are tedious and unreliable However allthese drawbacks can be overcome by incorporating advanceprogramming techniques based on space vector PWM Thispaper provides the design details of the space vector PWMprogramming based simulation model of the single-phase-to-three-phase matrix converter system and its performanceunder different load conditions

2 SP2TP Matrix Converter System

Conventionally the four-quadrant matrix converter usesnine bidirectional switches which are constructed using 18unipolar turn-off IGBTs and 18 reverse blocking diodes [10]

However the proposed design only uses six bidirectionalswitches in the construction of the matrix converter Figure 1shows the block diagram of the single-phase-to-three-phase(SP2TP) matrix converter system The SP2TP system adoptsthe direct ac-ac conversion technique that converts the single-phase alternating source voltage to three-phase alternatingvoltages that differ by 120∘ from each otherThe SP2TP systemis designed using six bidirectional switches with two switchesbeing used for each phase

3 Design of Matric Converter andControl System

Space vector pulse width modulation technique can bedefined as the combined effect of the three-phase voltages orcurrents into an equivalent single space vector componentderived from all the three-phase quantities at that instantThe derived equivalent vector component is termed as spacevectorThere are a number of space vectormodulation (SVM)techniques available [11] The ultimate object of the SVM isto produce output voltage and currents nearing unity powerfactor However due to number of hardware limitationsattaining unity power factor becomes more difficult [12]This paper attempts to describe the most stable and simplestSVM technique for direct ac-ac conversions Space vectormodulation technique adopts the Rotating Magnetic Fieldtheory in which the instantaneous resultant flux of the threealternating fluxes that are 120∘ away produces the rotatingfield at synchronous speedThe theoretical background of thespace vector algorithm is given below

The three-phase sinusoidal currents are representedmathematically as follows

119894119886= 119868119898sin120596119905

119894119887= 119868119898sin (120596119905 minus 120)

119894119888= 119868119898sin (120596119905 minus 240)

(1)

In such three-phase system the three sinusoidal currentsproduce three sinusoidal alternating fluxes that are equal inmagnitude and 120∘ away from each other At the momentwhen the ldquo119886-phaserdquo current ldquo119894

119886rdquo carries amaximumvalue and

equals ldquo119868119898rdquo then the currents in other phases ldquo119894

119887rdquo and ldquo119894

119888rdquo are

negative with the magnitudes of

119894119887= 119868119898sin (minus30)

119894119888= 119868119898sin (minus150)

(2)

Thus the resultant flux produced by the varying fluxes at anyinstant is equal to 15 times the maximum flux (120601

119898) Con-

sidering all instants within a period will yield the condition

Scientific Programming 3

120601m 120601m2120601r = 32120601m

Figure 2 Resultant unit space vector

that the resultant unit vector always equals the value of 15120601119898

and traces a circle for every period of reference cycle Figure 2represents phasor diagram of the resultant flux

For any three-phase sinusoidal excitations the maximumflux density produces sinusoidal distribution of fluxes withthe maximum values that traces a circle A similar rotatingresultant flux can also be produced using two-phase systemwhere the two voltages are equal in magnitude and differby 90∘ [11] These fluxes can also be represented as 120572 and 120573components Superimposing on the three-phase fluxes theflux produced in the 120572 direction and the flux produced inthe 120573 direction can be estimated as follows The ampere-turnproduced by the 120572 and 120573 components of the resultant flux canbe expressed as

119873119894120572= 119873119894119886(119905) + 119873119894

119887(119905) cos 120 + 119873119894

119888cos 240

119873119894120573= 119873119894119887(119905) sin 120 + 119873119894

119888sin 240

(3)

The 120572 and120573 components of the resultant flux space vector canbe expressed in complex form as

119873119894120572(119905) + 119895119873119894

120573(119905) = 119873 [119894

120572(119905) + 119895119894

120573(119905)] = 119873119894

119877 (4)

where ldquo119894119904rdquo is the current reference space vector which can be

represented as

119894119877= [119894120572+ 119895119894120573] =

10038161003816100381610038161198941198771003816100381610038161003816 119890119895120596119905

(5)

Similarly the voltage reference space vector also can berepresented as

119881119877= [119881120572+ 119895119881120573] =

10038161003816100381610038161198811198771003816100381610038161003816 119890119895120596119905+120579

(6)

Thus the flux space vector is produced by the current spacevector However this current space vector is produced by anequivalent voltage space vector [13] In PWM operation theaverage variation is circular The PWM scheme should besuch that the tip of the space vector with the average variationshould trace a circle with uniform velocity equal to the inputfrequency For any sinusoidal three-phase excitations the tipof the average value of the space vector of the alternatingquantity traces a circle with uniform velocity

Figure 3 represents the circuit diagram of the single-phase-to-three-phase matrix converter circuit with the bidi-rectional switches Each pole will have two states say 1 and 0If the top switch is ON then it is represented as ldquo1rdquo whereasthe bottom switch is ON then it is represented as ldquo0rdquo Foreach pole there are two states so for the three phases thereare eight states (23states)

The operating conditions of the 8 states are represented as000 001 010 011 100 101 110 and 111 where 000 and 111 are

3-phaseinduction

motor load

VAC

Figure 3 Single-phase-to-three-phase matrix converter with bidi-rectional switches

100

110

010

011

001

101

111

000

Figure 4 Switching states in SVPWM

zero states 000 means that all the three bottom switches areON and the output terminals are shorted to bottom switchesOn the other hand 111 means that all the three top switchesare ON and the output terminals are shorted to the topswitches The states other than 000 and 111 are active statesThe condition of various active states is shown in Figure 4

Downward arrow represents that the upper switch isclosed and bottom switch is open in any particular pole andthe upward arrow represents that bottom switch is closed andtop switch is open in any particular pole Similarly three-phase voltages can be represented as a resultant voltage 119881

119877

that travels in a circle [14] The circular path is divided intosix sectors to represent the six active states 119881

0 1198811 1198812 119881

7

represent the voltages of the eight possible states betweeneach sector as shown in Figure 5

4 Scientific Programming

6

5

4

3

2

1

120573

120572

010 (V3) 110 (V2)

VR100 (V1)

001 (V5) 101 (V6)

000 (V0) and 111 (V7)

011 (V4)

Figure 5 Sector representation of space vector modulation

At any particular moment the resultant voltage vector119881119877

can be produced by appropriately firing the sector voltagesat the given proportional time that depends on the samplingfrequency Sampling time 119879

119904is the maximum time allocated

to complete the switching of states to produce the particularinstant resultant voltage vector In sector-1 the sequence oftriggering would be V

0V1V2V7V7V2V1V0 however the

sum of the time taken for this triggering sequence should beequal to twice the sampling time [15] The switching controlof the PWM should be programmed in such a way to producethe space vector of voltage which traces a circle with uniformvelocity

The radii of the hexagon are equal to the voltage spacevector For a two-level inverter all the six active voltagevectors lie along the radii of the hexagon It is also calledas six-step inverter [16] In order to generate switchingsequences 119881

119877should trace the circle with uniform velocity

If 119881119877is in sector-1 and rotating at uniform speed high

frequency sampling signals are used to sample the rotatingreference space voltage vector 119881

119877 Low sampling periods

will enhance the quality of the space vector PWM signalsThe average value is closest to the sinusoidal On the otherhand having high frequency will also increase the losses soan optimum sampling frequency has to be chosen Whilesampling until the next status is reached the amplitude andangle of 119881

119877are assumed to be constant During that period it

switches between the boundary active vectors of the sectorand with the zero vectors The sampling period should bedesigned such that volt-sec (119881

119877-119879119904) balances the required

amplitude of the voltage at that particular moment [17] Thecomponents of 119881

119877-119879119904along alpha and beta should be volt-

sec equal to the volt-sec of active vectors of the particularsection and to that of the zero vectors If 119881

119877in sector-

1 and the boundary voltage space vectors are 1198811and 119881

2

respectively then the sampling period 119879119904can be represented

by

119879119904= 1198791+ 1198792+ 1198790 (7)

where 1198791 1198792 and 119879

0are the sampling period for the active

vectors 1198811and 119881

2and the zero vectors respectively [11]

Generally the average value of the resultant voltage vector isrepresented as follows

int

119879119904

0

119881119877119889119905 = int

11987902

0

1198810119889119905 + int

11987902+119879119899

11987902

119881119899119889119905

+ int

11987902+119879119899+119879119899+1

11987902+119879119899

119881119899+1

119889119905

+ int

119879119904

11987902+119879119899+119879119899+1

1198817119889119905

(8)

and the sampling time 119879119904is

119879119904= (1198790+ 119879119899+ 119879119899+1) (9)

The average voltage of the zero vectors (1198810and 119881

7) is zero

Thus the fictitious time of the reference voltage vector can berepresented as follows

(119881119877119879119904) = [119881

120572+ 119895119881120573] 119879119904= (119881119899119879119899) + (119881

119899+1119879119899+1) (10)

By substituting the values of119881119899and119881119899+1

the reference voltagevector can be represented in the 120572120573 components as

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

119879119904

=2

3119881119878

[[[[

[

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

cos (119899 minus 1) 1205873

sin (119899 minus 1) 1205873

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119879119899+

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

cos (119899) 1205873

sin (119899) 1205873

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119879119899+1

]]]]

]

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

119879119904=2

3119881119878

[[[[

[

cos (119899 minus 1) 1205873

cos (119899) 1205873

sin (119899 minus 1) 1205873

sin (119899) 1205873

]]]]

]

1003816100381610038161003816100381610038161003816100381610038161003816

119879119899

119879119899+1

1003816100381610038161003816100381610038161003816100381610038161003816

(11)

where ldquo119881119878rdquo is the RMS value of the source input voltage of

the converter and 119899 = 1 2 3 represents the sector Thetriggering times for the various sectors can be expressed interms of 120572120573 components as

1003816100381610038161003816100381610038161003816100381610038161003816

119879119899

119879119899+1

1003816100381610038161003816100381610038161003816100381610038161003816

=radic3

2

119879119904

119881119878

[[[[

[

sin (119899) 1205873

minus cos (119899) 1205873

minus sin (119899 minus 1) 1205873

cos (119899 minus 1) 1205873

]]]]

]

sdot

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

(12)

For any given reference space vector 119881119877 corresponding

119881120572and 119881

120573components can be calculated from which the

duration of the active vectors in the respective sector canbe estimated The ultimate task of segregating the availablesingle-phase waveform into three different waveforms thatare 120∘ away from each other is achieved through the switch-ing timings estimated from (12) Scientific programming is

Scientific Programming 5

Figure 6 Segregation of input signal

used to produce the triggering pulse durations to turn on thesix bidirectional switches appropriately Figure 6 shows thestages of segregation that takes place at every 1205873 degrees forall the three phases At any instant any one of the phases has23rd of its maximum value and the other two phases have13rd of its maximum value in either direction

4 Simulation of SP2TP MatrixConverter System

MatlabSimulink application is used for the modelling andsimulation of the proposed algorithmThedesigned Simulinkmodel is then converted into C++ coding for hardwareimplementation using digital signal processor and IGBT coreand driver circuits Figure 7 shows the variousmodules of thespace vector pulse width modulation section of the converterin which the desired output magnitude frequency and theconverter input voltage are taken as reference

The reference three-phase sinusoidal signals are con-verted to two-dimensional 120572-120573 components with the sectorinformation A ramp signal is used for the sampling ofspace vector at high frequency According to the sector theswitching timing for each bidirectional switch is estimatedThere are six PWM signal outputs for the six bidirectional

switches of thematrix converter Table 1 shows the simulationspecification of the proposed model of the matrix convertersystem

In the Simulink model of the matrix converter circuitsix bidirectional switches are used to construct the matrixconverter module Each bidirectional switch is designedusing two IGBTs switched with reversing blocking diodesand the snubber circuits as shown in Figure 8 A three-phasebalanced resistive load is used to study the output signals

5 Simulation Results of Matrix Converter

The simulation results of the proposed design are studiedfor the suitability and implementation for the practicalapplications The standard 240V 50Hz single-phase supplyis applied as the input to the matrix converter systemBoth the space vector modules and the matrix convertermodules produce the expected outputs Figure 9 shows theoutput phase voltages of the matrix converter system andall the three-phase voltages are 120∘ away from each otherThe combined waveform resembles the three-phase systemwaveforms

Figure 10 shows the output line to line voltages of thematrix converter which are found to be sinusoidal and stable

6 Scientific Programming

Switching timecalculator

Trig

Sector Gate timing

Ramp generator

Ramp

Trig

Gates logic

Ramp

Gate_timing

L1a

L1b

L2a

L2b

L3a

L3bab vector

sector

Angle Sector

ab transform

Angle

ab_V

Sine wave

DSP

Scope8Scope1

Scope[s6]

[s5]

[s4]

[s3]

[s2]

[s1]

50

415

1

3-phase sin generatorFreq_com

Dir

Vcom Vabc Vabc

Vbus bus a_b_Vbus

Figure 7 Simulation of space vector PWM algorithm for SP2TP matrix converter

Table 1 Simulation parameters of the matrix converter system

Simulation parametersModulation scheme Space vector PWMCarrier wave Ramp signalCarrier amplitude (119881cm) 1 VCarrier frequency (119891

119888

) 4500HzCarrier wave ratio = (119891

119888

)(119891119903

) 90Modulation index = (119881rm)(119881cm) 10119881ref amplitude (119881rm) Sinusoidal 1 V119881ref frequency (119891119903) and angle 50Hz zero3-ph ref amplitude 415V3-ph ref frequency amp angle 50Hz zeroNumber of samples per cycle 90Sampling time period (119879

119904

) 2222 120583sSeconds per degree 0617120583sNumber of degrees per sample 4Sampling time per sector 333ms

The combined waveform exactly behaves like a three-phasesystem voltages

Figure 11 shows the input and output voltages of thematrix converter under unity power factor load A starconnected balanced resistive network is used as a unity powerfactor loadThe power factor of the input voltage and currentis found to be at unity No phase angle difference is observedbetween the input and 119877-phase output currents

Figure 12 shows the input and output voltages of thematrix converter under lagging power factor load A starconnected balanced119877-119871 load is used as a lagging power factorload The output currents are found to be 120 degrees awayfrom each other andmore smoother compared to the resistiveload

In order to determine the appropriate conditions in viewof obtaining the balanced output voltages the simulations

Table 2 Output voltages under the effect of varying modulationindex at 50Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 020 2319 1611 22201271 1797 040 1159 8052 1110847 1198 060 7719 5364 7394635 899 080 5789 4023 5546508 719 100 4627 3215 4433424 599 120 3852 2677 3692363 513 140 3297 2291 316318 449 160 2884 2004 2765282 399 180 2561 1779 2456254 359 200 2303 160 2209

were performed under different modulation indexes Thestudy on the modulation index characteristics is found tobe the vital factor that governs the magnitude of the outputvoltagesThemodulation index of the space vector pulse withmodulation can be defined as the ratio of the product ofsquare root times the space vector reference voltage to that ofthe input supply voltages The modulation index is expressedas

Modulation Index (Mi) = radic3119881ref119881119878

(13)

The RMS values of the output voltages under the effect ofvarying the modulation index are tabulated in Table 2 Itscorresponding modulation index characteristics are shownin Figure 13 The three output voltages are found to beunbalanced Two of the output voltages are at equal valueswhereas one of the phases is having relatively low voltageoutput

From the modulation index characteristics it is foundthat the output line to line voltages are inversely proportionalto the modulation index used in the space vector modulation

Scientific Programming 7

v

Scope9

Scope6

Scope4 Scope3

Scope2

s6s5

g

s4g

s3s2

g

s1

g

RMS5RMS

RMS4RMS

RMS2RMS

RMS1RMS

R3+

R2+

R1+

From5[s6]

From4[s5]

From3[s4]

From2[s3]

From1[s2]

From[s1]

Display3

Display2

Display1

Display

AC voltagesource

+

+ minus

+minus

++ +

+

minusminus minus

minus

i

g +minus

g +minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

+ minusi

+ minusi

+ minusi

Figure 8 Simulation of SP2TP matrix converter with unity power factor load

Table 3 Output voltages under the effect of varying modulationindex at 200Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 02 2090 2075 20561271 1797 04 1044 1037 1027847 1198 06 6958 6906 6843635 899 08 5217 5179 5131508 719 1 417 4139 4101424 599 12 3472 3446 3411363 513 14 2971 2949 2922318 449 16 2599 258 2556282 399 18 2308 2291 227254 359 2 2075 206 2041

algorithm The lower the modulation indexes the higherthe RMS values of the output voltages However the lowermodulation index means the higher input supply voltage Soto increase the input voltage additional step-up transformersare to be used

The model was studied under wide range of referencefrequencies of space vector algorithm In order to obtainbalanced output voltages the reference frequency of the spacevector algorithm has to be increased beyond 150Hz Whenthe reference frequency is varied the simulation model altersthe triggering pulses duration and corresponding controlsignals are produced in the digital signal processorsThus theoutput voltages of the converter are altered correspondinglyTable 3 shows the magnitude of the line to line outputvoltages of the matrix converter under 200Hz operation

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Output phase voltages

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

Time offset 0

minus500

0

500

minus500

0

500

minus500

0

500

minus500

0

500

Figure 9 Output phases voltages of SP2TP matrix converter withunity power factor load

and its corresponding modulation characteristics show morebalanced output voltages

The modulation index characteristics obtained with thereference frequency of the program as 200Hz are shown inFigure 14 The RMS values of the output voltages are foundto be balanced and proportional to each other at all values ofmodulation index

8 Scientific Programming

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

Output line to line voltages

Line voltage Vab

Line voltage Vbc

Line voltage Vca

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

Figure 10 Output line voltages of SP2TP matrix converter withunity power factor load

Single-phase input voltage

Three-phase output voltages

Input and output currents

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus400

minus200

0

200

400

minus400

minus200

0

200

400

minus5

0

5

Figure 11 Voltages and currents under unity power factor load

Scientific programming model provides more flexibilityto choose a wide range of reference frequencies so thatconverter can be tuned to generate range of voltages atdifferent frequencies However it is limited by the hardwarerealization issues The appropriate modulated index andreference frequency have to be selected for the desired outputvoltages of the matrix converter

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus505

minus5000

500

minus5000

500

minus2000

200

minus505

minus505

minus505

Three-phase output currents

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Line current Ia

Line current Ib

Line current Ic

Figure 12 Voltages and currents under lagging power factor load

05 1 15 2 250Modulation index

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

VabVbcVca

Figure 13 Modulation index characteristics at 50Hz referencefrequency

6 Hardware Experimentation of MatrixConverter System

The hardware realization of the proposed model is shownin Figure 15 The Code Composer Studio application is usedfor the real-time interface with the digital signal processor toproduce the space vector algorithm based IGBT gate signals

Scientific Programming 9

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

05 1 15 2 250Modulation index

VabVbcVca

Figure 14 Modulation index characteristics at 200Hz referencefrequency

MCB

DSP

Gate driver core and base board

3-phase squirrel cage induction

motor

IGBT bidirectionalswitches

Voltage transducer

Miniature circuit breaker

SP2TP matrix converter hardware implementation schematic

Figure 15 Hardware realization of matrix converter system

The gate drive circuits and base board circuits are used toprovide the appropriate gate voltages to the bidirectionalswitches The developed hardware model is tested underdifferent power factor loads

Figure 16 shows the actual hardware experimental setupof the single-phase-to-three-phase matrix converter systemIGBT based bidirectional switches are used to design thematrix converter system Texas Instrument DSP and theConcept IGBTCoreDrives are used for the control operationSynchronization circuit is used to synchronize the sinusoidalsupply voltage with the control signals

The RMS values of the practical hardware circuits areslightly lower than the simulation circuits Figure 17 showsthe practical line to line voltages compared with the simula-tion data The variation is mainly due to the presence of oddharmonics in the hardware circuits

Figure 18 shows the percentage total harmonic distortion(THD) of the 119877-phase voltage under unity power factorload condition for both simulation and practical readings

Synchronizingcircuit

Matrixconverter

Three-phase induction motor

Digital signal processor

Interfacecircuit

IGBT coredriver circuit

Figure 16 Hardware realization of matrix converter system

Comparison between simulation and practical

SimulationPracticalVariation

050

100150200250

Line

to li

ne v

olta

ges (

V)

2 3 4 5 6 7 81Experimental reading samples

voltages (Vab)mdashunity Pf load

Figure 17 Comparison of simulation and practical line voltages

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Order of harmonics under simulation and

practical experimental conditions

020406080

100120

Har

mon

ic co

nten

t (

)

THD of matrix converter R-phasemdashunity Pf load

Figure 18 total harmonic distortion in the output voltage ofmatrix converter

Only odd harmonics are found to be present and the practicalTHD is slightly higher compared to the simulation valuesThis is obvious due to the presence of odd harmonics

7 Conclusion

Bidirectional switch based matrix converters are gettingmore popular due to their compact convenient and robustoperation State-of-the-art space vector PWM programmingand switching techniques are employed in the gate triggeringcontrol of the matrix converters The model was studiedunder different reference frequencies and modulation indexconditions The limitation of the proposed system is theunbalanced voltages produced due to odd harmonics pres-ence High harmonic contents are noticed which can be

10 Scientific Programming

eliminated by incorporating proper filter circuits Boostercircuits also can be used to obtain the desired output voltageThe modulation characteristics are studied in view of obtain-ing the balanced three-phase output voltages A significantbehavior is noticed when the SP2TP matrix converter isoperated above 150Hz with appropriate modulation indexthe output line to line voltages of the matrix converter arefound to be balanced and differ by 120∘ away from each otherand exactly resemble the three-phase system Adjustmenthas to be done at programming level to achieve the desiredoutcomes of the converter The magnitudes of the outputvoltages can be varied using booster circuits There are lotsof scopes for enhancing the system design through furtherresearch for more stable and quality outputs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J H H Alwash ldquoPredicting performance of three phaseinduction motors connected to single phase suppliesrdquo in IEEProceedings on Electric Power Applications vol 143 no 4 pp339ndash344 July 1996

[2] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics vol 2 pp547ndash550 Xian China May 1992

[3] V Agarwal and S Gupta ldquoAn efficient algorithm for generalisedsingle-phase converterrdquo IET Power Electronics vol 3 no 1 pp138ndash145 2010

[4] K Zhou and D Wang ldquoRelationship between space-vectormodulation and three-phase carrier-based PWM a compre-hensive analysis [three-phase inverters]rdquo IEEE Transactions onIndustrial Electronics vol 49 no 1 pp 186ndash196 2002

[5] S Kwak and H A Toliyat ldquoAn approach to fault-tolerant three-phase matrix converter drivesrdquo IEEE Transactions on EnergyConversion vol 22 no 4 pp 855ndash863 2007

[6] M-K Nguyen Y-G Jung Y-C Lim and Y-M Kim ldquoA single-phase Z-source buck-boost matrix converterrdquo IEEE Transac-tions on Power Electronics vol 25 no 2 pp 453ndash462 2010

[7] I K Shahidul D Z Phoivos and H R Muhammad ldquoNovelsingle- to three-phase static converterrdquo IEEE Transactions onIndustrial Applications vol 25 no 1 pp 143ndash152 1989

[8] M H El-Maghraby R H Thejel and M M Ibrahim ldquoNewapproach for the analysis of a three-phase induction motorof different ratings connected to a single-phase supplyrdquo IEEProceedings BmdashElectric Power Applications vol 139 no 3 pp145ndash154 1992

[9] J Xiao W Zhang H Omori and K Matsui ldquoA novel operationstrategy for single-to three-phase matrix converterrdquo in Proceed-ings of the 12th International Conference on Electrical Machinesand Systems (ICEMS rsquo09) pp 1ndash6 Tokyo Japan November2009

[10] J W Kolar F Schafmeister S D Round and H Ertl ldquoNovelthree-phase AC-AC sparse matrix convertersrdquo IEEE Transac-tions on Power Electronics vol 22 no 5 pp 1649ndash1661 2007

[11] K Iino K Kondo and Y Sato ldquoAn experimental study oninduction motor drive with a single phasemdashthree phase matrixconverterrdquo in Proceedings of the 13th European Conference onPower Electronics and Applications (EPE rsquo09) pp 1ndash9 BarcelonaSpain September 2009

[12] M ImayavarambanK Latha andGUma ldquoAnalysis of differentschemes ofmatrix converter withmaximum voltage conversionratiordquo inProceedings of the 12th IEEEMediterranean Electrotech-nical Conference (MELECON rsquo04) vol 3 pp 1137ndash1140 IEEEDubrovnik Croatia May 2004

[13] H Takahashi R Hisamichi and H Haga ldquoHigh power factorcontrol for current-source type single-phase to three-phasematrix converterrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo09) pp 3071ndash3076 San JoseCalif USA September 2009

[14] M Saito and N Matsui ldquoA single- to three-phase matrix con-verter for a vector-controlled induction motorrdquo in Proceedingsof the IEEE Industry Applications Society Annual Meeting (IASrsquo08) pp 1ndash6 IEEE Edmonton Canada October 2008

[15] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics (ISIE rsquo92)Xian China May 1992

[16] M Saito T Takeshita and N Matsui ldquoA single to threephase matrix converter with a power decupling capabilityrdquo inProceedings of the IEEE 35thAnnual Power Electronics SpecialistsConference (PESC rsquo04) pp 2400ndash2405 IEEEAachenGermanyJune 2004

[17] L A C Lopes and M F Naguib ldquoSpace vector modulationfor low switching frequency current source converters withreduced low-order noncharacteristic harmonicsrdquo IEEE Trans-actions on Power Electronics vol 24 no 4 pp 903ndash910 2009

Submit your manuscripts athttpwwwhindawicom

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

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Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Advances in

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International Journal of

Biomedical Imaging

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ArtificialNeural Systems

Advances in

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RoboticsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

2 Scientific Programming

Three-phase loadsSingle-phasealternating

sourceSP2TP matrix

converter system

Figure 1 SP2TP matrix converter system [9]

conversionsThe bidirectional switches are designed in such away that they should not short-circuit the voltage sources andopen-circuit the current sources [3] On the other hand theac-dc-ac converter adopts rectifier-inverter concepts wherethe single-phase ac voltage is converted to dc voltage in thefirst stage and in the second inverter stage the dc voltageis inverted back to three-phase voltages Despite the THDlosses of ac-dc-ac converter are much lesser compared todirect ac-ac converter other issues such as additional costdue to bulk storage devices are major drawbacks Thus thedirect ac-ac converters are more compact in size and costFor many years simple carrier based sinusoidal based PWMmodulation schemes are used inmany applications [4] How-ever advance switching algorithm such as space vector basedPWM modulation scheme can be employed to segregatethe input signal along with the bidirectional IGBT switchesbased matrix converter to produce the required three-phaseoutput waveforms Using scientific programming methodsadvanced modulation scheme can be implemented usingstate-of-the-art engineering simulation application and inter-facing with the digital signal processor and other controlcircuits in real time Space vector pulse widthmodulation is aunique technique that makes the switching complexity of ac-ac converters much easier Employing the space vector PWMtechnique for the single-phase-to-three-phase conversion isthe main contribution of the paper Adjustable speed drivesare considered matured due to advances in power semicon-ductor devices and lower cost Active devices continue toimprove whereas the passive devices such as energy storagecapacitor occupy huge system volume weight and reliability[5] Similar research initiative suggests that matrix convertercan be operated under buck-boost mode with variable fre-quencies but under Z-Source topology [6] Cycloconvertersbased static converters produced balanced output voltagesbut suffer from high low order harmonics [7] Anotherinitiative suggests having two capacitor converters for morebalanced operation of induction motor using single-phasesupply [8] which are tedious and unreliable However allthese drawbacks can be overcome by incorporating advanceprogramming techniques based on space vector PWM Thispaper provides the design details of the space vector PWMprogramming based simulation model of the single-phase-to-three-phase matrix converter system and its performanceunder different load conditions

2 SP2TP Matrix Converter System

Conventionally the four-quadrant matrix converter usesnine bidirectional switches which are constructed using 18unipolar turn-off IGBTs and 18 reverse blocking diodes [10]

However the proposed design only uses six bidirectionalswitches in the construction of the matrix converter Figure 1shows the block diagram of the single-phase-to-three-phase(SP2TP) matrix converter system The SP2TP system adoptsthe direct ac-ac conversion technique that converts the single-phase alternating source voltage to three-phase alternatingvoltages that differ by 120∘ from each otherThe SP2TP systemis designed using six bidirectional switches with two switchesbeing used for each phase

3 Design of Matric Converter andControl System

Space vector pulse width modulation technique can bedefined as the combined effect of the three-phase voltages orcurrents into an equivalent single space vector componentderived from all the three-phase quantities at that instantThe derived equivalent vector component is termed as spacevectorThere are a number of space vectormodulation (SVM)techniques available [11] The ultimate object of the SVM isto produce output voltage and currents nearing unity powerfactor However due to number of hardware limitationsattaining unity power factor becomes more difficult [12]This paper attempts to describe the most stable and simplestSVM technique for direct ac-ac conversions Space vectormodulation technique adopts the Rotating Magnetic Fieldtheory in which the instantaneous resultant flux of the threealternating fluxes that are 120∘ away produces the rotatingfield at synchronous speedThe theoretical background of thespace vector algorithm is given below

The three-phase sinusoidal currents are representedmathematically as follows

119894119886= 119868119898sin120596119905

119894119887= 119868119898sin (120596119905 minus 120)

119894119888= 119868119898sin (120596119905 minus 240)

(1)

In such three-phase system the three sinusoidal currentsproduce three sinusoidal alternating fluxes that are equal inmagnitude and 120∘ away from each other At the momentwhen the ldquo119886-phaserdquo current ldquo119894

119886rdquo carries amaximumvalue and

equals ldquo119868119898rdquo then the currents in other phases ldquo119894

119887rdquo and ldquo119894

119888rdquo are

negative with the magnitudes of

119894119887= 119868119898sin (minus30)

119894119888= 119868119898sin (minus150)

(2)

Thus the resultant flux produced by the varying fluxes at anyinstant is equal to 15 times the maximum flux (120601

119898) Con-

sidering all instants within a period will yield the condition

Scientific Programming 3

120601m 120601m2120601r = 32120601m

Figure 2 Resultant unit space vector

that the resultant unit vector always equals the value of 15120601119898

and traces a circle for every period of reference cycle Figure 2represents phasor diagram of the resultant flux

For any three-phase sinusoidal excitations the maximumflux density produces sinusoidal distribution of fluxes withthe maximum values that traces a circle A similar rotatingresultant flux can also be produced using two-phase systemwhere the two voltages are equal in magnitude and differby 90∘ [11] These fluxes can also be represented as 120572 and 120573components Superimposing on the three-phase fluxes theflux produced in the 120572 direction and the flux produced inthe 120573 direction can be estimated as follows The ampere-turnproduced by the 120572 and 120573 components of the resultant flux canbe expressed as

119873119894120572= 119873119894119886(119905) + 119873119894

119887(119905) cos 120 + 119873119894

119888cos 240

119873119894120573= 119873119894119887(119905) sin 120 + 119873119894

119888sin 240

(3)

The 120572 and120573 components of the resultant flux space vector canbe expressed in complex form as

119873119894120572(119905) + 119895119873119894

120573(119905) = 119873 [119894

120572(119905) + 119895119894

120573(119905)] = 119873119894

119877 (4)

where ldquo119894119904rdquo is the current reference space vector which can be

represented as

119894119877= [119894120572+ 119895119894120573] =

10038161003816100381610038161198941198771003816100381610038161003816 119890119895120596119905

(5)

Similarly the voltage reference space vector also can berepresented as

119881119877= [119881120572+ 119895119881120573] =

10038161003816100381610038161198811198771003816100381610038161003816 119890119895120596119905+120579

(6)

Thus the flux space vector is produced by the current spacevector However this current space vector is produced by anequivalent voltage space vector [13] In PWM operation theaverage variation is circular The PWM scheme should besuch that the tip of the space vector with the average variationshould trace a circle with uniform velocity equal to the inputfrequency For any sinusoidal three-phase excitations the tipof the average value of the space vector of the alternatingquantity traces a circle with uniform velocity

Figure 3 represents the circuit diagram of the single-phase-to-three-phase matrix converter circuit with the bidi-rectional switches Each pole will have two states say 1 and 0If the top switch is ON then it is represented as ldquo1rdquo whereasthe bottom switch is ON then it is represented as ldquo0rdquo Foreach pole there are two states so for the three phases thereare eight states (23states)

The operating conditions of the 8 states are represented as000 001 010 011 100 101 110 and 111 where 000 and 111 are

3-phaseinduction

motor load

VAC

Figure 3 Single-phase-to-three-phase matrix converter with bidi-rectional switches

100

110

010

011

001

101

111

000

Figure 4 Switching states in SVPWM

zero states 000 means that all the three bottom switches areON and the output terminals are shorted to bottom switchesOn the other hand 111 means that all the three top switchesare ON and the output terminals are shorted to the topswitches The states other than 000 and 111 are active statesThe condition of various active states is shown in Figure 4

Downward arrow represents that the upper switch isclosed and bottom switch is open in any particular pole andthe upward arrow represents that bottom switch is closed andtop switch is open in any particular pole Similarly three-phase voltages can be represented as a resultant voltage 119881

119877

that travels in a circle [14] The circular path is divided intosix sectors to represent the six active states 119881

0 1198811 1198812 119881

7

represent the voltages of the eight possible states betweeneach sector as shown in Figure 5

4 Scientific Programming

6

5

4

3

2

1

120573

120572

010 (V3) 110 (V2)

VR100 (V1)

001 (V5) 101 (V6)

000 (V0) and 111 (V7)

011 (V4)

Figure 5 Sector representation of space vector modulation

At any particular moment the resultant voltage vector119881119877

can be produced by appropriately firing the sector voltagesat the given proportional time that depends on the samplingfrequency Sampling time 119879

119904is the maximum time allocated

to complete the switching of states to produce the particularinstant resultant voltage vector In sector-1 the sequence oftriggering would be V

0V1V2V7V7V2V1V0 however the

sum of the time taken for this triggering sequence should beequal to twice the sampling time [15] The switching controlof the PWM should be programmed in such a way to producethe space vector of voltage which traces a circle with uniformvelocity

The radii of the hexagon are equal to the voltage spacevector For a two-level inverter all the six active voltagevectors lie along the radii of the hexagon It is also calledas six-step inverter [16] In order to generate switchingsequences 119881

119877should trace the circle with uniform velocity

If 119881119877is in sector-1 and rotating at uniform speed high

frequency sampling signals are used to sample the rotatingreference space voltage vector 119881

119877 Low sampling periods

will enhance the quality of the space vector PWM signalsThe average value is closest to the sinusoidal On the otherhand having high frequency will also increase the losses soan optimum sampling frequency has to be chosen Whilesampling until the next status is reached the amplitude andangle of 119881

119877are assumed to be constant During that period it

switches between the boundary active vectors of the sectorand with the zero vectors The sampling period should bedesigned such that volt-sec (119881

119877-119879119904) balances the required

amplitude of the voltage at that particular moment [17] Thecomponents of 119881

119877-119879119904along alpha and beta should be volt-

sec equal to the volt-sec of active vectors of the particularsection and to that of the zero vectors If 119881

119877in sector-

1 and the boundary voltage space vectors are 1198811and 119881

2

respectively then the sampling period 119879119904can be represented

by

119879119904= 1198791+ 1198792+ 1198790 (7)

where 1198791 1198792 and 119879

0are the sampling period for the active

vectors 1198811and 119881

2and the zero vectors respectively [11]

Generally the average value of the resultant voltage vector isrepresented as follows

int

119879119904

0

119881119877119889119905 = int

11987902

0

1198810119889119905 + int

11987902+119879119899

11987902

119881119899119889119905

+ int

11987902+119879119899+119879119899+1

11987902+119879119899

119881119899+1

119889119905

+ int

119879119904

11987902+119879119899+119879119899+1

1198817119889119905

(8)

and the sampling time 119879119904is

119879119904= (1198790+ 119879119899+ 119879119899+1) (9)

The average voltage of the zero vectors (1198810and 119881

7) is zero

Thus the fictitious time of the reference voltage vector can berepresented as follows

(119881119877119879119904) = [119881

120572+ 119895119881120573] 119879119904= (119881119899119879119899) + (119881

119899+1119879119899+1) (10)

By substituting the values of119881119899and119881119899+1

the reference voltagevector can be represented in the 120572120573 components as

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

119879119904

=2

3119881119878

[[[[

[

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

cos (119899 minus 1) 1205873

sin (119899 minus 1) 1205873

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119879119899+

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

cos (119899) 1205873

sin (119899) 1205873

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119879119899+1

]]]]

]

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

119879119904=2

3119881119878

[[[[

[

cos (119899 minus 1) 1205873

cos (119899) 1205873

sin (119899 minus 1) 1205873

sin (119899) 1205873

]]]]

]

1003816100381610038161003816100381610038161003816100381610038161003816

119879119899

119879119899+1

1003816100381610038161003816100381610038161003816100381610038161003816

(11)

where ldquo119881119878rdquo is the RMS value of the source input voltage of

the converter and 119899 = 1 2 3 represents the sector Thetriggering times for the various sectors can be expressed interms of 120572120573 components as

1003816100381610038161003816100381610038161003816100381610038161003816

119879119899

119879119899+1

1003816100381610038161003816100381610038161003816100381610038161003816

=radic3

2

119879119904

119881119878

[[[[

[

sin (119899) 1205873

minus cos (119899) 1205873

minus sin (119899 minus 1) 1205873

cos (119899 minus 1) 1205873

]]]]

]

sdot

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

(12)

For any given reference space vector 119881119877 corresponding

119881120572and 119881

120573components can be calculated from which the

duration of the active vectors in the respective sector canbe estimated The ultimate task of segregating the availablesingle-phase waveform into three different waveforms thatare 120∘ away from each other is achieved through the switch-ing timings estimated from (12) Scientific programming is

Scientific Programming 5

Figure 6 Segregation of input signal

used to produce the triggering pulse durations to turn on thesix bidirectional switches appropriately Figure 6 shows thestages of segregation that takes place at every 1205873 degrees forall the three phases At any instant any one of the phases has23rd of its maximum value and the other two phases have13rd of its maximum value in either direction

4 Simulation of SP2TP MatrixConverter System

MatlabSimulink application is used for the modelling andsimulation of the proposed algorithmThedesigned Simulinkmodel is then converted into C++ coding for hardwareimplementation using digital signal processor and IGBT coreand driver circuits Figure 7 shows the variousmodules of thespace vector pulse width modulation section of the converterin which the desired output magnitude frequency and theconverter input voltage are taken as reference

The reference three-phase sinusoidal signals are con-verted to two-dimensional 120572-120573 components with the sectorinformation A ramp signal is used for the sampling ofspace vector at high frequency According to the sector theswitching timing for each bidirectional switch is estimatedThere are six PWM signal outputs for the six bidirectional

switches of thematrix converter Table 1 shows the simulationspecification of the proposed model of the matrix convertersystem

In the Simulink model of the matrix converter circuitsix bidirectional switches are used to construct the matrixconverter module Each bidirectional switch is designedusing two IGBTs switched with reversing blocking diodesand the snubber circuits as shown in Figure 8 A three-phasebalanced resistive load is used to study the output signals

5 Simulation Results of Matrix Converter

The simulation results of the proposed design are studiedfor the suitability and implementation for the practicalapplications The standard 240V 50Hz single-phase supplyis applied as the input to the matrix converter systemBoth the space vector modules and the matrix convertermodules produce the expected outputs Figure 9 shows theoutput phase voltages of the matrix converter system andall the three-phase voltages are 120∘ away from each otherThe combined waveform resembles the three-phase systemwaveforms

Figure 10 shows the output line to line voltages of thematrix converter which are found to be sinusoidal and stable

6 Scientific Programming

Switching timecalculator

Trig

Sector Gate timing

Ramp generator

Ramp

Trig

Gates logic

Ramp

Gate_timing

L1a

L1b

L2a

L2b

L3a

L3bab vector

sector

Angle Sector

ab transform

Angle

ab_V

Sine wave

DSP

Scope8Scope1

Scope[s6]

[s5]

[s4]

[s3]

[s2]

[s1]

50

415

1

3-phase sin generatorFreq_com

Dir

Vcom Vabc Vabc

Vbus bus a_b_Vbus

Figure 7 Simulation of space vector PWM algorithm for SP2TP matrix converter

Table 1 Simulation parameters of the matrix converter system

Simulation parametersModulation scheme Space vector PWMCarrier wave Ramp signalCarrier amplitude (119881cm) 1 VCarrier frequency (119891

119888

) 4500HzCarrier wave ratio = (119891

119888

)(119891119903

) 90Modulation index = (119881rm)(119881cm) 10119881ref amplitude (119881rm) Sinusoidal 1 V119881ref frequency (119891119903) and angle 50Hz zero3-ph ref amplitude 415V3-ph ref frequency amp angle 50Hz zeroNumber of samples per cycle 90Sampling time period (119879

119904

) 2222 120583sSeconds per degree 0617120583sNumber of degrees per sample 4Sampling time per sector 333ms

The combined waveform exactly behaves like a three-phasesystem voltages

Figure 11 shows the input and output voltages of thematrix converter under unity power factor load A starconnected balanced resistive network is used as a unity powerfactor loadThe power factor of the input voltage and currentis found to be at unity No phase angle difference is observedbetween the input and 119877-phase output currents

Figure 12 shows the input and output voltages of thematrix converter under lagging power factor load A starconnected balanced119877-119871 load is used as a lagging power factorload The output currents are found to be 120 degrees awayfrom each other andmore smoother compared to the resistiveload

In order to determine the appropriate conditions in viewof obtaining the balanced output voltages the simulations

Table 2 Output voltages under the effect of varying modulationindex at 50Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 020 2319 1611 22201271 1797 040 1159 8052 1110847 1198 060 7719 5364 7394635 899 080 5789 4023 5546508 719 100 4627 3215 4433424 599 120 3852 2677 3692363 513 140 3297 2291 316318 449 160 2884 2004 2765282 399 180 2561 1779 2456254 359 200 2303 160 2209

were performed under different modulation indexes Thestudy on the modulation index characteristics is found tobe the vital factor that governs the magnitude of the outputvoltagesThemodulation index of the space vector pulse withmodulation can be defined as the ratio of the product ofsquare root times the space vector reference voltage to that ofthe input supply voltages The modulation index is expressedas

Modulation Index (Mi) = radic3119881ref119881119878

(13)

The RMS values of the output voltages under the effect ofvarying the modulation index are tabulated in Table 2 Itscorresponding modulation index characteristics are shownin Figure 13 The three output voltages are found to beunbalanced Two of the output voltages are at equal valueswhereas one of the phases is having relatively low voltageoutput

From the modulation index characteristics it is foundthat the output line to line voltages are inversely proportionalto the modulation index used in the space vector modulation

Scientific Programming 7

v

Scope9

Scope6

Scope4 Scope3

Scope2

s6s5

g

s4g

s3s2

g

s1

g

RMS5RMS

RMS4RMS

RMS2RMS

RMS1RMS

R3+

R2+

R1+

From5[s6]

From4[s5]

From3[s4]

From2[s3]

From1[s2]

From[s1]

Display3

Display2

Display1

Display

AC voltagesource

+

+ minus

+minus

++ +

+

minusminus minus

minus

i

g +minus

g +minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

+ minusi

+ minusi

+ minusi

Figure 8 Simulation of SP2TP matrix converter with unity power factor load

Table 3 Output voltages under the effect of varying modulationindex at 200Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 02 2090 2075 20561271 1797 04 1044 1037 1027847 1198 06 6958 6906 6843635 899 08 5217 5179 5131508 719 1 417 4139 4101424 599 12 3472 3446 3411363 513 14 2971 2949 2922318 449 16 2599 258 2556282 399 18 2308 2291 227254 359 2 2075 206 2041

algorithm The lower the modulation indexes the higherthe RMS values of the output voltages However the lowermodulation index means the higher input supply voltage Soto increase the input voltage additional step-up transformersare to be used

The model was studied under wide range of referencefrequencies of space vector algorithm In order to obtainbalanced output voltages the reference frequency of the spacevector algorithm has to be increased beyond 150Hz Whenthe reference frequency is varied the simulation model altersthe triggering pulses duration and corresponding controlsignals are produced in the digital signal processorsThus theoutput voltages of the converter are altered correspondinglyTable 3 shows the magnitude of the line to line outputvoltages of the matrix converter under 200Hz operation

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Output phase voltages

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

Time offset 0

minus500

0

500

minus500

0

500

minus500

0

500

minus500

0

500

Figure 9 Output phases voltages of SP2TP matrix converter withunity power factor load

and its corresponding modulation characteristics show morebalanced output voltages

The modulation index characteristics obtained with thereference frequency of the program as 200Hz are shown inFigure 14 The RMS values of the output voltages are foundto be balanced and proportional to each other at all values ofmodulation index

8 Scientific Programming

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

Output line to line voltages

Line voltage Vab

Line voltage Vbc

Line voltage Vca

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

Figure 10 Output line voltages of SP2TP matrix converter withunity power factor load

Single-phase input voltage

Three-phase output voltages

Input and output currents

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus400

minus200

0

200

400

minus400

minus200

0

200

400

minus5

0

5

Figure 11 Voltages and currents under unity power factor load

Scientific programming model provides more flexibilityto choose a wide range of reference frequencies so thatconverter can be tuned to generate range of voltages atdifferent frequencies However it is limited by the hardwarerealization issues The appropriate modulated index andreference frequency have to be selected for the desired outputvoltages of the matrix converter

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus505

minus5000

500

minus5000

500

minus2000

200

minus505

minus505

minus505

Three-phase output currents

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Line current Ia

Line current Ib

Line current Ic

Figure 12 Voltages and currents under lagging power factor load

05 1 15 2 250Modulation index

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

VabVbcVca

Figure 13 Modulation index characteristics at 50Hz referencefrequency

6 Hardware Experimentation of MatrixConverter System

The hardware realization of the proposed model is shownin Figure 15 The Code Composer Studio application is usedfor the real-time interface with the digital signal processor toproduce the space vector algorithm based IGBT gate signals

Scientific Programming 9

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

05 1 15 2 250Modulation index

VabVbcVca

Figure 14 Modulation index characteristics at 200Hz referencefrequency

MCB

DSP

Gate driver core and base board

3-phase squirrel cage induction

motor

IGBT bidirectionalswitches

Voltage transducer

Miniature circuit breaker

SP2TP matrix converter hardware implementation schematic

Figure 15 Hardware realization of matrix converter system

The gate drive circuits and base board circuits are used toprovide the appropriate gate voltages to the bidirectionalswitches The developed hardware model is tested underdifferent power factor loads

Figure 16 shows the actual hardware experimental setupof the single-phase-to-three-phase matrix converter systemIGBT based bidirectional switches are used to design thematrix converter system Texas Instrument DSP and theConcept IGBTCoreDrives are used for the control operationSynchronization circuit is used to synchronize the sinusoidalsupply voltage with the control signals

The RMS values of the practical hardware circuits areslightly lower than the simulation circuits Figure 17 showsthe practical line to line voltages compared with the simula-tion data The variation is mainly due to the presence of oddharmonics in the hardware circuits

Figure 18 shows the percentage total harmonic distortion(THD) of the 119877-phase voltage under unity power factorload condition for both simulation and practical readings

Synchronizingcircuit

Matrixconverter

Three-phase induction motor

Digital signal processor

Interfacecircuit

IGBT coredriver circuit

Figure 16 Hardware realization of matrix converter system

Comparison between simulation and practical

SimulationPracticalVariation

050

100150200250

Line

to li

ne v

olta

ges (

V)

2 3 4 5 6 7 81Experimental reading samples

voltages (Vab)mdashunity Pf load

Figure 17 Comparison of simulation and practical line voltages

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Order of harmonics under simulation and

practical experimental conditions

020406080

100120

Har

mon

ic co

nten

t (

)

THD of matrix converter R-phasemdashunity Pf load

Figure 18 total harmonic distortion in the output voltage ofmatrix converter

Only odd harmonics are found to be present and the practicalTHD is slightly higher compared to the simulation valuesThis is obvious due to the presence of odd harmonics

7 Conclusion

Bidirectional switch based matrix converters are gettingmore popular due to their compact convenient and robustoperation State-of-the-art space vector PWM programmingand switching techniques are employed in the gate triggeringcontrol of the matrix converters The model was studiedunder different reference frequencies and modulation indexconditions The limitation of the proposed system is theunbalanced voltages produced due to odd harmonics pres-ence High harmonic contents are noticed which can be

10 Scientific Programming

eliminated by incorporating proper filter circuits Boostercircuits also can be used to obtain the desired output voltageThe modulation characteristics are studied in view of obtain-ing the balanced three-phase output voltages A significantbehavior is noticed when the SP2TP matrix converter isoperated above 150Hz with appropriate modulation indexthe output line to line voltages of the matrix converter arefound to be balanced and differ by 120∘ away from each otherand exactly resemble the three-phase system Adjustmenthas to be done at programming level to achieve the desiredoutcomes of the converter The magnitudes of the outputvoltages can be varied using booster circuits There are lotsof scopes for enhancing the system design through furtherresearch for more stable and quality outputs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J H H Alwash ldquoPredicting performance of three phaseinduction motors connected to single phase suppliesrdquo in IEEProceedings on Electric Power Applications vol 143 no 4 pp339ndash344 July 1996

[2] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics vol 2 pp547ndash550 Xian China May 1992

[3] V Agarwal and S Gupta ldquoAn efficient algorithm for generalisedsingle-phase converterrdquo IET Power Electronics vol 3 no 1 pp138ndash145 2010

[4] K Zhou and D Wang ldquoRelationship between space-vectormodulation and three-phase carrier-based PWM a compre-hensive analysis [three-phase inverters]rdquo IEEE Transactions onIndustrial Electronics vol 49 no 1 pp 186ndash196 2002

[5] S Kwak and H A Toliyat ldquoAn approach to fault-tolerant three-phase matrix converter drivesrdquo IEEE Transactions on EnergyConversion vol 22 no 4 pp 855ndash863 2007

[6] M-K Nguyen Y-G Jung Y-C Lim and Y-M Kim ldquoA single-phase Z-source buck-boost matrix converterrdquo IEEE Transac-tions on Power Electronics vol 25 no 2 pp 453ndash462 2010

[7] I K Shahidul D Z Phoivos and H R Muhammad ldquoNovelsingle- to three-phase static converterrdquo IEEE Transactions onIndustrial Applications vol 25 no 1 pp 143ndash152 1989

[8] M H El-Maghraby R H Thejel and M M Ibrahim ldquoNewapproach for the analysis of a three-phase induction motorof different ratings connected to a single-phase supplyrdquo IEEProceedings BmdashElectric Power Applications vol 139 no 3 pp145ndash154 1992

[9] J Xiao W Zhang H Omori and K Matsui ldquoA novel operationstrategy for single-to three-phase matrix converterrdquo in Proceed-ings of the 12th International Conference on Electrical Machinesand Systems (ICEMS rsquo09) pp 1ndash6 Tokyo Japan November2009

[10] J W Kolar F Schafmeister S D Round and H Ertl ldquoNovelthree-phase AC-AC sparse matrix convertersrdquo IEEE Transac-tions on Power Electronics vol 22 no 5 pp 1649ndash1661 2007

[11] K Iino K Kondo and Y Sato ldquoAn experimental study oninduction motor drive with a single phasemdashthree phase matrixconverterrdquo in Proceedings of the 13th European Conference onPower Electronics and Applications (EPE rsquo09) pp 1ndash9 BarcelonaSpain September 2009

[12] M ImayavarambanK Latha andGUma ldquoAnalysis of differentschemes ofmatrix converter withmaximum voltage conversionratiordquo inProceedings of the 12th IEEEMediterranean Electrotech-nical Conference (MELECON rsquo04) vol 3 pp 1137ndash1140 IEEEDubrovnik Croatia May 2004

[13] H Takahashi R Hisamichi and H Haga ldquoHigh power factorcontrol for current-source type single-phase to three-phasematrix converterrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo09) pp 3071ndash3076 San JoseCalif USA September 2009

[14] M Saito and N Matsui ldquoA single- to three-phase matrix con-verter for a vector-controlled induction motorrdquo in Proceedingsof the IEEE Industry Applications Society Annual Meeting (IASrsquo08) pp 1ndash6 IEEE Edmonton Canada October 2008

[15] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics (ISIE rsquo92)Xian China May 1992

[16] M Saito T Takeshita and N Matsui ldquoA single to threephase matrix converter with a power decupling capabilityrdquo inProceedings of the IEEE 35thAnnual Power Electronics SpecialistsConference (PESC rsquo04) pp 2400ndash2405 IEEEAachenGermanyJune 2004

[17] L A C Lopes and M F Naguib ldquoSpace vector modulationfor low switching frequency current source converters withreduced low-order noncharacteristic harmonicsrdquo IEEE Trans-actions on Power Electronics vol 24 no 4 pp 903ndash910 2009

Submit your manuscripts athttpwwwhindawicom

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Scientific Programming 3

120601m 120601m2120601r = 32120601m

Figure 2 Resultant unit space vector

that the resultant unit vector always equals the value of 15120601119898

and traces a circle for every period of reference cycle Figure 2represents phasor diagram of the resultant flux

For any three-phase sinusoidal excitations the maximumflux density produces sinusoidal distribution of fluxes withthe maximum values that traces a circle A similar rotatingresultant flux can also be produced using two-phase systemwhere the two voltages are equal in magnitude and differby 90∘ [11] These fluxes can also be represented as 120572 and 120573components Superimposing on the three-phase fluxes theflux produced in the 120572 direction and the flux produced inthe 120573 direction can be estimated as follows The ampere-turnproduced by the 120572 and 120573 components of the resultant flux canbe expressed as

119873119894120572= 119873119894119886(119905) + 119873119894

119887(119905) cos 120 + 119873119894

119888cos 240

119873119894120573= 119873119894119887(119905) sin 120 + 119873119894

119888sin 240

(3)

The 120572 and120573 components of the resultant flux space vector canbe expressed in complex form as

119873119894120572(119905) + 119895119873119894

120573(119905) = 119873 [119894

120572(119905) + 119895119894

120573(119905)] = 119873119894

119877 (4)

where ldquo119894119904rdquo is the current reference space vector which can be

represented as

119894119877= [119894120572+ 119895119894120573] =

10038161003816100381610038161198941198771003816100381610038161003816 119890119895120596119905

(5)

Similarly the voltage reference space vector also can berepresented as

119881119877= [119881120572+ 119895119881120573] =

10038161003816100381610038161198811198771003816100381610038161003816 119890119895120596119905+120579

(6)

Thus the flux space vector is produced by the current spacevector However this current space vector is produced by anequivalent voltage space vector [13] In PWM operation theaverage variation is circular The PWM scheme should besuch that the tip of the space vector with the average variationshould trace a circle with uniform velocity equal to the inputfrequency For any sinusoidal three-phase excitations the tipof the average value of the space vector of the alternatingquantity traces a circle with uniform velocity

Figure 3 represents the circuit diagram of the single-phase-to-three-phase matrix converter circuit with the bidi-rectional switches Each pole will have two states say 1 and 0If the top switch is ON then it is represented as ldquo1rdquo whereasthe bottom switch is ON then it is represented as ldquo0rdquo Foreach pole there are two states so for the three phases thereare eight states (23states)

The operating conditions of the 8 states are represented as000 001 010 011 100 101 110 and 111 where 000 and 111 are

3-phaseinduction

motor load

VAC

Figure 3 Single-phase-to-three-phase matrix converter with bidi-rectional switches

100

110

010

011

001

101

111

000

Figure 4 Switching states in SVPWM

zero states 000 means that all the three bottom switches areON and the output terminals are shorted to bottom switchesOn the other hand 111 means that all the three top switchesare ON and the output terminals are shorted to the topswitches The states other than 000 and 111 are active statesThe condition of various active states is shown in Figure 4

Downward arrow represents that the upper switch isclosed and bottom switch is open in any particular pole andthe upward arrow represents that bottom switch is closed andtop switch is open in any particular pole Similarly three-phase voltages can be represented as a resultant voltage 119881

119877

that travels in a circle [14] The circular path is divided intosix sectors to represent the six active states 119881

0 1198811 1198812 119881

7

represent the voltages of the eight possible states betweeneach sector as shown in Figure 5

4 Scientific Programming

6

5

4

3

2

1

120573

120572

010 (V3) 110 (V2)

VR100 (V1)

001 (V5) 101 (V6)

000 (V0) and 111 (V7)

011 (V4)

Figure 5 Sector representation of space vector modulation

At any particular moment the resultant voltage vector119881119877

can be produced by appropriately firing the sector voltagesat the given proportional time that depends on the samplingfrequency Sampling time 119879

119904is the maximum time allocated

to complete the switching of states to produce the particularinstant resultant voltage vector In sector-1 the sequence oftriggering would be V

0V1V2V7V7V2V1V0 however the

sum of the time taken for this triggering sequence should beequal to twice the sampling time [15] The switching controlof the PWM should be programmed in such a way to producethe space vector of voltage which traces a circle with uniformvelocity

The radii of the hexagon are equal to the voltage spacevector For a two-level inverter all the six active voltagevectors lie along the radii of the hexagon It is also calledas six-step inverter [16] In order to generate switchingsequences 119881

119877should trace the circle with uniform velocity

If 119881119877is in sector-1 and rotating at uniform speed high

frequency sampling signals are used to sample the rotatingreference space voltage vector 119881

119877 Low sampling periods

will enhance the quality of the space vector PWM signalsThe average value is closest to the sinusoidal On the otherhand having high frequency will also increase the losses soan optimum sampling frequency has to be chosen Whilesampling until the next status is reached the amplitude andangle of 119881

119877are assumed to be constant During that period it

switches between the boundary active vectors of the sectorand with the zero vectors The sampling period should bedesigned such that volt-sec (119881

119877-119879119904) balances the required

amplitude of the voltage at that particular moment [17] Thecomponents of 119881

119877-119879119904along alpha and beta should be volt-

sec equal to the volt-sec of active vectors of the particularsection and to that of the zero vectors If 119881

119877in sector-

1 and the boundary voltage space vectors are 1198811and 119881

2

respectively then the sampling period 119879119904can be represented

by

119879119904= 1198791+ 1198792+ 1198790 (7)

where 1198791 1198792 and 119879

0are the sampling period for the active

vectors 1198811and 119881

2and the zero vectors respectively [11]

Generally the average value of the resultant voltage vector isrepresented as follows

int

119879119904

0

119881119877119889119905 = int

11987902

0

1198810119889119905 + int

11987902+119879119899

11987902

119881119899119889119905

+ int

11987902+119879119899+119879119899+1

11987902+119879119899

119881119899+1

119889119905

+ int

119879119904

11987902+119879119899+119879119899+1

1198817119889119905

(8)

and the sampling time 119879119904is

119879119904= (1198790+ 119879119899+ 119879119899+1) (9)

The average voltage of the zero vectors (1198810and 119881

7) is zero

Thus the fictitious time of the reference voltage vector can berepresented as follows

(119881119877119879119904) = [119881

120572+ 119895119881120573] 119879119904= (119881119899119879119899) + (119881

119899+1119879119899+1) (10)

By substituting the values of119881119899and119881119899+1

the reference voltagevector can be represented in the 120572120573 components as

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

119879119904

=2

3119881119878

[[[[

[

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

cos (119899 minus 1) 1205873

sin (119899 minus 1) 1205873

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119879119899+

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

cos (119899) 1205873

sin (119899) 1205873

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119879119899+1

]]]]

]

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

119879119904=2

3119881119878

[[[[

[

cos (119899 minus 1) 1205873

cos (119899) 1205873

sin (119899 minus 1) 1205873

sin (119899) 1205873

]]]]

]

1003816100381610038161003816100381610038161003816100381610038161003816

119879119899

119879119899+1

1003816100381610038161003816100381610038161003816100381610038161003816

(11)

where ldquo119881119878rdquo is the RMS value of the source input voltage of

the converter and 119899 = 1 2 3 represents the sector Thetriggering times for the various sectors can be expressed interms of 120572120573 components as

1003816100381610038161003816100381610038161003816100381610038161003816

119879119899

119879119899+1

1003816100381610038161003816100381610038161003816100381610038161003816

=radic3

2

119879119904

119881119878

[[[[

[

sin (119899) 1205873

minus cos (119899) 1205873

minus sin (119899 minus 1) 1205873

cos (119899 minus 1) 1205873

]]]]

]

sdot

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

(12)

For any given reference space vector 119881119877 corresponding

119881120572and 119881

120573components can be calculated from which the

duration of the active vectors in the respective sector canbe estimated The ultimate task of segregating the availablesingle-phase waveform into three different waveforms thatare 120∘ away from each other is achieved through the switch-ing timings estimated from (12) Scientific programming is

Scientific Programming 5

Figure 6 Segregation of input signal

used to produce the triggering pulse durations to turn on thesix bidirectional switches appropriately Figure 6 shows thestages of segregation that takes place at every 1205873 degrees forall the three phases At any instant any one of the phases has23rd of its maximum value and the other two phases have13rd of its maximum value in either direction

4 Simulation of SP2TP MatrixConverter System

MatlabSimulink application is used for the modelling andsimulation of the proposed algorithmThedesigned Simulinkmodel is then converted into C++ coding for hardwareimplementation using digital signal processor and IGBT coreand driver circuits Figure 7 shows the variousmodules of thespace vector pulse width modulation section of the converterin which the desired output magnitude frequency and theconverter input voltage are taken as reference

The reference three-phase sinusoidal signals are con-verted to two-dimensional 120572-120573 components with the sectorinformation A ramp signal is used for the sampling ofspace vector at high frequency According to the sector theswitching timing for each bidirectional switch is estimatedThere are six PWM signal outputs for the six bidirectional

switches of thematrix converter Table 1 shows the simulationspecification of the proposed model of the matrix convertersystem

In the Simulink model of the matrix converter circuitsix bidirectional switches are used to construct the matrixconverter module Each bidirectional switch is designedusing two IGBTs switched with reversing blocking diodesand the snubber circuits as shown in Figure 8 A three-phasebalanced resistive load is used to study the output signals

5 Simulation Results of Matrix Converter

The simulation results of the proposed design are studiedfor the suitability and implementation for the practicalapplications The standard 240V 50Hz single-phase supplyis applied as the input to the matrix converter systemBoth the space vector modules and the matrix convertermodules produce the expected outputs Figure 9 shows theoutput phase voltages of the matrix converter system andall the three-phase voltages are 120∘ away from each otherThe combined waveform resembles the three-phase systemwaveforms

Figure 10 shows the output line to line voltages of thematrix converter which are found to be sinusoidal and stable

6 Scientific Programming

Switching timecalculator

Trig

Sector Gate timing

Ramp generator

Ramp

Trig

Gates logic

Ramp

Gate_timing

L1a

L1b

L2a

L2b

L3a

L3bab vector

sector

Angle Sector

ab transform

Angle

ab_V

Sine wave

DSP

Scope8Scope1

Scope[s6]

[s5]

[s4]

[s3]

[s2]

[s1]

50

415

1

3-phase sin generatorFreq_com

Dir

Vcom Vabc Vabc

Vbus bus a_b_Vbus

Figure 7 Simulation of space vector PWM algorithm for SP2TP matrix converter

Table 1 Simulation parameters of the matrix converter system

Simulation parametersModulation scheme Space vector PWMCarrier wave Ramp signalCarrier amplitude (119881cm) 1 VCarrier frequency (119891

119888

) 4500HzCarrier wave ratio = (119891

119888

)(119891119903

) 90Modulation index = (119881rm)(119881cm) 10119881ref amplitude (119881rm) Sinusoidal 1 V119881ref frequency (119891119903) and angle 50Hz zero3-ph ref amplitude 415V3-ph ref frequency amp angle 50Hz zeroNumber of samples per cycle 90Sampling time period (119879

119904

) 2222 120583sSeconds per degree 0617120583sNumber of degrees per sample 4Sampling time per sector 333ms

The combined waveform exactly behaves like a three-phasesystem voltages

Figure 11 shows the input and output voltages of thematrix converter under unity power factor load A starconnected balanced resistive network is used as a unity powerfactor loadThe power factor of the input voltage and currentis found to be at unity No phase angle difference is observedbetween the input and 119877-phase output currents

Figure 12 shows the input and output voltages of thematrix converter under lagging power factor load A starconnected balanced119877-119871 load is used as a lagging power factorload The output currents are found to be 120 degrees awayfrom each other andmore smoother compared to the resistiveload

In order to determine the appropriate conditions in viewof obtaining the balanced output voltages the simulations

Table 2 Output voltages under the effect of varying modulationindex at 50Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 020 2319 1611 22201271 1797 040 1159 8052 1110847 1198 060 7719 5364 7394635 899 080 5789 4023 5546508 719 100 4627 3215 4433424 599 120 3852 2677 3692363 513 140 3297 2291 316318 449 160 2884 2004 2765282 399 180 2561 1779 2456254 359 200 2303 160 2209

were performed under different modulation indexes Thestudy on the modulation index characteristics is found tobe the vital factor that governs the magnitude of the outputvoltagesThemodulation index of the space vector pulse withmodulation can be defined as the ratio of the product ofsquare root times the space vector reference voltage to that ofthe input supply voltages The modulation index is expressedas

Modulation Index (Mi) = radic3119881ref119881119878

(13)

The RMS values of the output voltages under the effect ofvarying the modulation index are tabulated in Table 2 Itscorresponding modulation index characteristics are shownin Figure 13 The three output voltages are found to beunbalanced Two of the output voltages are at equal valueswhereas one of the phases is having relatively low voltageoutput

From the modulation index characteristics it is foundthat the output line to line voltages are inversely proportionalto the modulation index used in the space vector modulation

Scientific Programming 7

v

Scope9

Scope6

Scope4 Scope3

Scope2

s6s5

g

s4g

s3s2

g

s1

g

RMS5RMS

RMS4RMS

RMS2RMS

RMS1RMS

R3+

R2+

R1+

From5[s6]

From4[s5]

From3[s4]

From2[s3]

From1[s2]

From[s1]

Display3

Display2

Display1

Display

AC voltagesource

+

+ minus

+minus

++ +

+

minusminus minus

minus

i

g +minus

g +minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

+ minusi

+ minusi

+ minusi

Figure 8 Simulation of SP2TP matrix converter with unity power factor load

Table 3 Output voltages under the effect of varying modulationindex at 200Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 02 2090 2075 20561271 1797 04 1044 1037 1027847 1198 06 6958 6906 6843635 899 08 5217 5179 5131508 719 1 417 4139 4101424 599 12 3472 3446 3411363 513 14 2971 2949 2922318 449 16 2599 258 2556282 399 18 2308 2291 227254 359 2 2075 206 2041

algorithm The lower the modulation indexes the higherthe RMS values of the output voltages However the lowermodulation index means the higher input supply voltage Soto increase the input voltage additional step-up transformersare to be used

The model was studied under wide range of referencefrequencies of space vector algorithm In order to obtainbalanced output voltages the reference frequency of the spacevector algorithm has to be increased beyond 150Hz Whenthe reference frequency is varied the simulation model altersthe triggering pulses duration and corresponding controlsignals are produced in the digital signal processorsThus theoutput voltages of the converter are altered correspondinglyTable 3 shows the magnitude of the line to line outputvoltages of the matrix converter under 200Hz operation

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Output phase voltages

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

Time offset 0

minus500

0

500

minus500

0

500

minus500

0

500

minus500

0

500

Figure 9 Output phases voltages of SP2TP matrix converter withunity power factor load

and its corresponding modulation characteristics show morebalanced output voltages

The modulation index characteristics obtained with thereference frequency of the program as 200Hz are shown inFigure 14 The RMS values of the output voltages are foundto be balanced and proportional to each other at all values ofmodulation index

8 Scientific Programming

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

Output line to line voltages

Line voltage Vab

Line voltage Vbc

Line voltage Vca

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

Figure 10 Output line voltages of SP2TP matrix converter withunity power factor load

Single-phase input voltage

Three-phase output voltages

Input and output currents

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus400

minus200

0

200

400

minus400

minus200

0

200

400

minus5

0

5

Figure 11 Voltages and currents under unity power factor load

Scientific programming model provides more flexibilityto choose a wide range of reference frequencies so thatconverter can be tuned to generate range of voltages atdifferent frequencies However it is limited by the hardwarerealization issues The appropriate modulated index andreference frequency have to be selected for the desired outputvoltages of the matrix converter

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus505

minus5000

500

minus5000

500

minus2000

200

minus505

minus505

minus505

Three-phase output currents

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Line current Ia

Line current Ib

Line current Ic

Figure 12 Voltages and currents under lagging power factor load

05 1 15 2 250Modulation index

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

VabVbcVca

Figure 13 Modulation index characteristics at 50Hz referencefrequency

6 Hardware Experimentation of MatrixConverter System

The hardware realization of the proposed model is shownin Figure 15 The Code Composer Studio application is usedfor the real-time interface with the digital signal processor toproduce the space vector algorithm based IGBT gate signals

Scientific Programming 9

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

05 1 15 2 250Modulation index

VabVbcVca

Figure 14 Modulation index characteristics at 200Hz referencefrequency

MCB

DSP

Gate driver core and base board

3-phase squirrel cage induction

motor

IGBT bidirectionalswitches

Voltage transducer

Miniature circuit breaker

SP2TP matrix converter hardware implementation schematic

Figure 15 Hardware realization of matrix converter system

The gate drive circuits and base board circuits are used toprovide the appropriate gate voltages to the bidirectionalswitches The developed hardware model is tested underdifferent power factor loads

Figure 16 shows the actual hardware experimental setupof the single-phase-to-three-phase matrix converter systemIGBT based bidirectional switches are used to design thematrix converter system Texas Instrument DSP and theConcept IGBTCoreDrives are used for the control operationSynchronization circuit is used to synchronize the sinusoidalsupply voltage with the control signals

The RMS values of the practical hardware circuits areslightly lower than the simulation circuits Figure 17 showsthe practical line to line voltages compared with the simula-tion data The variation is mainly due to the presence of oddharmonics in the hardware circuits

Figure 18 shows the percentage total harmonic distortion(THD) of the 119877-phase voltage under unity power factorload condition for both simulation and practical readings

Synchronizingcircuit

Matrixconverter

Three-phase induction motor

Digital signal processor

Interfacecircuit

IGBT coredriver circuit

Figure 16 Hardware realization of matrix converter system

Comparison between simulation and practical

SimulationPracticalVariation

050

100150200250

Line

to li

ne v

olta

ges (

V)

2 3 4 5 6 7 81Experimental reading samples

voltages (Vab)mdashunity Pf load

Figure 17 Comparison of simulation and practical line voltages

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Order of harmonics under simulation and

practical experimental conditions

020406080

100120

Har

mon

ic co

nten

t (

)

THD of matrix converter R-phasemdashunity Pf load

Figure 18 total harmonic distortion in the output voltage ofmatrix converter

Only odd harmonics are found to be present and the practicalTHD is slightly higher compared to the simulation valuesThis is obvious due to the presence of odd harmonics

7 Conclusion

Bidirectional switch based matrix converters are gettingmore popular due to their compact convenient and robustoperation State-of-the-art space vector PWM programmingand switching techniques are employed in the gate triggeringcontrol of the matrix converters The model was studiedunder different reference frequencies and modulation indexconditions The limitation of the proposed system is theunbalanced voltages produced due to odd harmonics pres-ence High harmonic contents are noticed which can be

10 Scientific Programming

eliminated by incorporating proper filter circuits Boostercircuits also can be used to obtain the desired output voltageThe modulation characteristics are studied in view of obtain-ing the balanced three-phase output voltages A significantbehavior is noticed when the SP2TP matrix converter isoperated above 150Hz with appropriate modulation indexthe output line to line voltages of the matrix converter arefound to be balanced and differ by 120∘ away from each otherand exactly resemble the three-phase system Adjustmenthas to be done at programming level to achieve the desiredoutcomes of the converter The magnitudes of the outputvoltages can be varied using booster circuits There are lotsof scopes for enhancing the system design through furtherresearch for more stable and quality outputs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J H H Alwash ldquoPredicting performance of three phaseinduction motors connected to single phase suppliesrdquo in IEEProceedings on Electric Power Applications vol 143 no 4 pp339ndash344 July 1996

[2] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics vol 2 pp547ndash550 Xian China May 1992

[3] V Agarwal and S Gupta ldquoAn efficient algorithm for generalisedsingle-phase converterrdquo IET Power Electronics vol 3 no 1 pp138ndash145 2010

[4] K Zhou and D Wang ldquoRelationship between space-vectormodulation and three-phase carrier-based PWM a compre-hensive analysis [three-phase inverters]rdquo IEEE Transactions onIndustrial Electronics vol 49 no 1 pp 186ndash196 2002

[5] S Kwak and H A Toliyat ldquoAn approach to fault-tolerant three-phase matrix converter drivesrdquo IEEE Transactions on EnergyConversion vol 22 no 4 pp 855ndash863 2007

[6] M-K Nguyen Y-G Jung Y-C Lim and Y-M Kim ldquoA single-phase Z-source buck-boost matrix converterrdquo IEEE Transac-tions on Power Electronics vol 25 no 2 pp 453ndash462 2010

[7] I K Shahidul D Z Phoivos and H R Muhammad ldquoNovelsingle- to three-phase static converterrdquo IEEE Transactions onIndustrial Applications vol 25 no 1 pp 143ndash152 1989

[8] M H El-Maghraby R H Thejel and M M Ibrahim ldquoNewapproach for the analysis of a three-phase induction motorof different ratings connected to a single-phase supplyrdquo IEEProceedings BmdashElectric Power Applications vol 139 no 3 pp145ndash154 1992

[9] J Xiao W Zhang H Omori and K Matsui ldquoA novel operationstrategy for single-to three-phase matrix converterrdquo in Proceed-ings of the 12th International Conference on Electrical Machinesand Systems (ICEMS rsquo09) pp 1ndash6 Tokyo Japan November2009

[10] J W Kolar F Schafmeister S D Round and H Ertl ldquoNovelthree-phase AC-AC sparse matrix convertersrdquo IEEE Transac-tions on Power Electronics vol 22 no 5 pp 1649ndash1661 2007

[11] K Iino K Kondo and Y Sato ldquoAn experimental study oninduction motor drive with a single phasemdashthree phase matrixconverterrdquo in Proceedings of the 13th European Conference onPower Electronics and Applications (EPE rsquo09) pp 1ndash9 BarcelonaSpain September 2009

[12] M ImayavarambanK Latha andGUma ldquoAnalysis of differentschemes ofmatrix converter withmaximum voltage conversionratiordquo inProceedings of the 12th IEEEMediterranean Electrotech-nical Conference (MELECON rsquo04) vol 3 pp 1137ndash1140 IEEEDubrovnik Croatia May 2004

[13] H Takahashi R Hisamichi and H Haga ldquoHigh power factorcontrol for current-source type single-phase to three-phasematrix converterrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo09) pp 3071ndash3076 San JoseCalif USA September 2009

[14] M Saito and N Matsui ldquoA single- to three-phase matrix con-verter for a vector-controlled induction motorrdquo in Proceedingsof the IEEE Industry Applications Society Annual Meeting (IASrsquo08) pp 1ndash6 IEEE Edmonton Canada October 2008

[15] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics (ISIE rsquo92)Xian China May 1992

[16] M Saito T Takeshita and N Matsui ldquoA single to threephase matrix converter with a power decupling capabilityrdquo inProceedings of the IEEE 35thAnnual Power Electronics SpecialistsConference (PESC rsquo04) pp 2400ndash2405 IEEEAachenGermanyJune 2004

[17] L A C Lopes and M F Naguib ldquoSpace vector modulationfor low switching frequency current source converters withreduced low-order noncharacteristic harmonicsrdquo IEEE Trans-actions on Power Electronics vol 24 no 4 pp 903ndash910 2009

Submit your manuscripts athttpwwwhindawicom

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Applied Computational Intelligence and Soft Computing

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Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

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International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

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RoboticsJournal of

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Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

4 Scientific Programming

6

5

4

3

2

1

120573

120572

010 (V3) 110 (V2)

VR100 (V1)

001 (V5) 101 (V6)

000 (V0) and 111 (V7)

011 (V4)

Figure 5 Sector representation of space vector modulation

At any particular moment the resultant voltage vector119881119877

can be produced by appropriately firing the sector voltagesat the given proportional time that depends on the samplingfrequency Sampling time 119879

119904is the maximum time allocated

to complete the switching of states to produce the particularinstant resultant voltage vector In sector-1 the sequence oftriggering would be V

0V1V2V7V7V2V1V0 however the

sum of the time taken for this triggering sequence should beequal to twice the sampling time [15] The switching controlof the PWM should be programmed in such a way to producethe space vector of voltage which traces a circle with uniformvelocity

The radii of the hexagon are equal to the voltage spacevector For a two-level inverter all the six active voltagevectors lie along the radii of the hexagon It is also calledas six-step inverter [16] In order to generate switchingsequences 119881

119877should trace the circle with uniform velocity

If 119881119877is in sector-1 and rotating at uniform speed high

frequency sampling signals are used to sample the rotatingreference space voltage vector 119881

119877 Low sampling periods

will enhance the quality of the space vector PWM signalsThe average value is closest to the sinusoidal On the otherhand having high frequency will also increase the losses soan optimum sampling frequency has to be chosen Whilesampling until the next status is reached the amplitude andangle of 119881

119877are assumed to be constant During that period it

switches between the boundary active vectors of the sectorand with the zero vectors The sampling period should bedesigned such that volt-sec (119881

119877-119879119904) balances the required

amplitude of the voltage at that particular moment [17] Thecomponents of 119881

119877-119879119904along alpha and beta should be volt-

sec equal to the volt-sec of active vectors of the particularsection and to that of the zero vectors If 119881

119877in sector-

1 and the boundary voltage space vectors are 1198811and 119881

2

respectively then the sampling period 119879119904can be represented

by

119879119904= 1198791+ 1198792+ 1198790 (7)

where 1198791 1198792 and 119879

0are the sampling period for the active

vectors 1198811and 119881

2and the zero vectors respectively [11]

Generally the average value of the resultant voltage vector isrepresented as follows

int

119879119904

0

119881119877119889119905 = int

11987902

0

1198810119889119905 + int

11987902+119879119899

11987902

119881119899119889119905

+ int

11987902+119879119899+119879119899+1

11987902+119879119899

119881119899+1

119889119905

+ int

119879119904

11987902+119879119899+119879119899+1

1198817119889119905

(8)

and the sampling time 119879119904is

119879119904= (1198790+ 119879119899+ 119879119899+1) (9)

The average voltage of the zero vectors (1198810and 119881

7) is zero

Thus the fictitious time of the reference voltage vector can berepresented as follows

(119881119877119879119904) = [119881

120572+ 119895119881120573] 119879119904= (119881119899119879119899) + (119881

119899+1119879119899+1) (10)

By substituting the values of119881119899and119881119899+1

the reference voltagevector can be represented in the 120572120573 components as

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

119879119904

=2

3119881119878

[[[[

[

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

cos (119899 minus 1) 1205873

sin (119899 minus 1) 1205873

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119879119899+

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

cos (119899) 1205873

sin (119899) 1205873

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

119879119899+1

]]]]

]

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

119879119904=2

3119881119878

[[[[

[

cos (119899 minus 1) 1205873

cos (119899) 1205873

sin (119899 minus 1) 1205873

sin (119899) 1205873

]]]]

]

1003816100381610038161003816100381610038161003816100381610038161003816

119879119899

119879119899+1

1003816100381610038161003816100381610038161003816100381610038161003816

(11)

where ldquo119881119878rdquo is the RMS value of the source input voltage of

the converter and 119899 = 1 2 3 represents the sector Thetriggering times for the various sectors can be expressed interms of 120572120573 components as

1003816100381610038161003816100381610038161003816100381610038161003816

119879119899

119879119899+1

1003816100381610038161003816100381610038161003816100381610038161003816

=radic3

2

119879119904

119881119878

[[[[

[

sin (119899) 1205873

minus cos (119899) 1205873

minus sin (119899 minus 1) 1205873

cos (119899 minus 1) 1205873

]]]]

]

sdot

1003816100381610038161003816100381610038161003816100381610038161003816

119881120572

119881120573

1003816100381610038161003816100381610038161003816100381610038161003816

(12)

For any given reference space vector 119881119877 corresponding

119881120572and 119881

120573components can be calculated from which the

duration of the active vectors in the respective sector canbe estimated The ultimate task of segregating the availablesingle-phase waveform into three different waveforms thatare 120∘ away from each other is achieved through the switch-ing timings estimated from (12) Scientific programming is

Scientific Programming 5

Figure 6 Segregation of input signal

used to produce the triggering pulse durations to turn on thesix bidirectional switches appropriately Figure 6 shows thestages of segregation that takes place at every 1205873 degrees forall the three phases At any instant any one of the phases has23rd of its maximum value and the other two phases have13rd of its maximum value in either direction

4 Simulation of SP2TP MatrixConverter System

MatlabSimulink application is used for the modelling andsimulation of the proposed algorithmThedesigned Simulinkmodel is then converted into C++ coding for hardwareimplementation using digital signal processor and IGBT coreand driver circuits Figure 7 shows the variousmodules of thespace vector pulse width modulation section of the converterin which the desired output magnitude frequency and theconverter input voltage are taken as reference

The reference three-phase sinusoidal signals are con-verted to two-dimensional 120572-120573 components with the sectorinformation A ramp signal is used for the sampling ofspace vector at high frequency According to the sector theswitching timing for each bidirectional switch is estimatedThere are six PWM signal outputs for the six bidirectional

switches of thematrix converter Table 1 shows the simulationspecification of the proposed model of the matrix convertersystem

In the Simulink model of the matrix converter circuitsix bidirectional switches are used to construct the matrixconverter module Each bidirectional switch is designedusing two IGBTs switched with reversing blocking diodesand the snubber circuits as shown in Figure 8 A three-phasebalanced resistive load is used to study the output signals

5 Simulation Results of Matrix Converter

The simulation results of the proposed design are studiedfor the suitability and implementation for the practicalapplications The standard 240V 50Hz single-phase supplyis applied as the input to the matrix converter systemBoth the space vector modules and the matrix convertermodules produce the expected outputs Figure 9 shows theoutput phase voltages of the matrix converter system andall the three-phase voltages are 120∘ away from each otherThe combined waveform resembles the three-phase systemwaveforms

Figure 10 shows the output line to line voltages of thematrix converter which are found to be sinusoidal and stable

6 Scientific Programming

Switching timecalculator

Trig

Sector Gate timing

Ramp generator

Ramp

Trig

Gates logic

Ramp

Gate_timing

L1a

L1b

L2a

L2b

L3a

L3bab vector

sector

Angle Sector

ab transform

Angle

ab_V

Sine wave

DSP

Scope8Scope1

Scope[s6]

[s5]

[s4]

[s3]

[s2]

[s1]

50

415

1

3-phase sin generatorFreq_com

Dir

Vcom Vabc Vabc

Vbus bus a_b_Vbus

Figure 7 Simulation of space vector PWM algorithm for SP2TP matrix converter

Table 1 Simulation parameters of the matrix converter system

Simulation parametersModulation scheme Space vector PWMCarrier wave Ramp signalCarrier amplitude (119881cm) 1 VCarrier frequency (119891

119888

) 4500HzCarrier wave ratio = (119891

119888

)(119891119903

) 90Modulation index = (119881rm)(119881cm) 10119881ref amplitude (119881rm) Sinusoidal 1 V119881ref frequency (119891119903) and angle 50Hz zero3-ph ref amplitude 415V3-ph ref frequency amp angle 50Hz zeroNumber of samples per cycle 90Sampling time period (119879

119904

) 2222 120583sSeconds per degree 0617120583sNumber of degrees per sample 4Sampling time per sector 333ms

The combined waveform exactly behaves like a three-phasesystem voltages

Figure 11 shows the input and output voltages of thematrix converter under unity power factor load A starconnected balanced resistive network is used as a unity powerfactor loadThe power factor of the input voltage and currentis found to be at unity No phase angle difference is observedbetween the input and 119877-phase output currents

Figure 12 shows the input and output voltages of thematrix converter under lagging power factor load A starconnected balanced119877-119871 load is used as a lagging power factorload The output currents are found to be 120 degrees awayfrom each other andmore smoother compared to the resistiveload

In order to determine the appropriate conditions in viewof obtaining the balanced output voltages the simulations

Table 2 Output voltages under the effect of varying modulationindex at 50Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 020 2319 1611 22201271 1797 040 1159 8052 1110847 1198 060 7719 5364 7394635 899 080 5789 4023 5546508 719 100 4627 3215 4433424 599 120 3852 2677 3692363 513 140 3297 2291 316318 449 160 2884 2004 2765282 399 180 2561 1779 2456254 359 200 2303 160 2209

were performed under different modulation indexes Thestudy on the modulation index characteristics is found tobe the vital factor that governs the magnitude of the outputvoltagesThemodulation index of the space vector pulse withmodulation can be defined as the ratio of the product ofsquare root times the space vector reference voltage to that ofthe input supply voltages The modulation index is expressedas

Modulation Index (Mi) = radic3119881ref119881119878

(13)

The RMS values of the output voltages under the effect ofvarying the modulation index are tabulated in Table 2 Itscorresponding modulation index characteristics are shownin Figure 13 The three output voltages are found to beunbalanced Two of the output voltages are at equal valueswhereas one of the phases is having relatively low voltageoutput

From the modulation index characteristics it is foundthat the output line to line voltages are inversely proportionalto the modulation index used in the space vector modulation

Scientific Programming 7

v

Scope9

Scope6

Scope4 Scope3

Scope2

s6s5

g

s4g

s3s2

g

s1

g

RMS5RMS

RMS4RMS

RMS2RMS

RMS1RMS

R3+

R2+

R1+

From5[s6]

From4[s5]

From3[s4]

From2[s3]

From1[s2]

From[s1]

Display3

Display2

Display1

Display

AC voltagesource

+

+ minus

+minus

++ +

+

minusminus minus

minus

i

g +minus

g +minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

+ minusi

+ minusi

+ minusi

Figure 8 Simulation of SP2TP matrix converter with unity power factor load

Table 3 Output voltages under the effect of varying modulationindex at 200Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 02 2090 2075 20561271 1797 04 1044 1037 1027847 1198 06 6958 6906 6843635 899 08 5217 5179 5131508 719 1 417 4139 4101424 599 12 3472 3446 3411363 513 14 2971 2949 2922318 449 16 2599 258 2556282 399 18 2308 2291 227254 359 2 2075 206 2041

algorithm The lower the modulation indexes the higherthe RMS values of the output voltages However the lowermodulation index means the higher input supply voltage Soto increase the input voltage additional step-up transformersare to be used

The model was studied under wide range of referencefrequencies of space vector algorithm In order to obtainbalanced output voltages the reference frequency of the spacevector algorithm has to be increased beyond 150Hz Whenthe reference frequency is varied the simulation model altersthe triggering pulses duration and corresponding controlsignals are produced in the digital signal processorsThus theoutput voltages of the converter are altered correspondinglyTable 3 shows the magnitude of the line to line outputvoltages of the matrix converter under 200Hz operation

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Output phase voltages

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

Time offset 0

minus500

0

500

minus500

0

500

minus500

0

500

minus500

0

500

Figure 9 Output phases voltages of SP2TP matrix converter withunity power factor load

and its corresponding modulation characteristics show morebalanced output voltages

The modulation index characteristics obtained with thereference frequency of the program as 200Hz are shown inFigure 14 The RMS values of the output voltages are foundto be balanced and proportional to each other at all values ofmodulation index

8 Scientific Programming

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

Output line to line voltages

Line voltage Vab

Line voltage Vbc

Line voltage Vca

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

Figure 10 Output line voltages of SP2TP matrix converter withunity power factor load

Single-phase input voltage

Three-phase output voltages

Input and output currents

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus400

minus200

0

200

400

minus400

minus200

0

200

400

minus5

0

5

Figure 11 Voltages and currents under unity power factor load

Scientific programming model provides more flexibilityto choose a wide range of reference frequencies so thatconverter can be tuned to generate range of voltages atdifferent frequencies However it is limited by the hardwarerealization issues The appropriate modulated index andreference frequency have to be selected for the desired outputvoltages of the matrix converter

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus505

minus5000

500

minus5000

500

minus2000

200

minus505

minus505

minus505

Three-phase output currents

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Line current Ia

Line current Ib

Line current Ic

Figure 12 Voltages and currents under lagging power factor load

05 1 15 2 250Modulation index

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

VabVbcVca

Figure 13 Modulation index characteristics at 50Hz referencefrequency

6 Hardware Experimentation of MatrixConverter System

The hardware realization of the proposed model is shownin Figure 15 The Code Composer Studio application is usedfor the real-time interface with the digital signal processor toproduce the space vector algorithm based IGBT gate signals

Scientific Programming 9

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

05 1 15 2 250Modulation index

VabVbcVca

Figure 14 Modulation index characteristics at 200Hz referencefrequency

MCB

DSP

Gate driver core and base board

3-phase squirrel cage induction

motor

IGBT bidirectionalswitches

Voltage transducer

Miniature circuit breaker

SP2TP matrix converter hardware implementation schematic

Figure 15 Hardware realization of matrix converter system

The gate drive circuits and base board circuits are used toprovide the appropriate gate voltages to the bidirectionalswitches The developed hardware model is tested underdifferent power factor loads

Figure 16 shows the actual hardware experimental setupof the single-phase-to-three-phase matrix converter systemIGBT based bidirectional switches are used to design thematrix converter system Texas Instrument DSP and theConcept IGBTCoreDrives are used for the control operationSynchronization circuit is used to synchronize the sinusoidalsupply voltage with the control signals

The RMS values of the practical hardware circuits areslightly lower than the simulation circuits Figure 17 showsthe practical line to line voltages compared with the simula-tion data The variation is mainly due to the presence of oddharmonics in the hardware circuits

Figure 18 shows the percentage total harmonic distortion(THD) of the 119877-phase voltage under unity power factorload condition for both simulation and practical readings

Synchronizingcircuit

Matrixconverter

Three-phase induction motor

Digital signal processor

Interfacecircuit

IGBT coredriver circuit

Figure 16 Hardware realization of matrix converter system

Comparison between simulation and practical

SimulationPracticalVariation

050

100150200250

Line

to li

ne v

olta

ges (

V)

2 3 4 5 6 7 81Experimental reading samples

voltages (Vab)mdashunity Pf load

Figure 17 Comparison of simulation and practical line voltages

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Order of harmonics under simulation and

practical experimental conditions

020406080

100120

Har

mon

ic co

nten

t (

)

THD of matrix converter R-phasemdashunity Pf load

Figure 18 total harmonic distortion in the output voltage ofmatrix converter

Only odd harmonics are found to be present and the practicalTHD is slightly higher compared to the simulation valuesThis is obvious due to the presence of odd harmonics

7 Conclusion

Bidirectional switch based matrix converters are gettingmore popular due to their compact convenient and robustoperation State-of-the-art space vector PWM programmingand switching techniques are employed in the gate triggeringcontrol of the matrix converters The model was studiedunder different reference frequencies and modulation indexconditions The limitation of the proposed system is theunbalanced voltages produced due to odd harmonics pres-ence High harmonic contents are noticed which can be

10 Scientific Programming

eliminated by incorporating proper filter circuits Boostercircuits also can be used to obtain the desired output voltageThe modulation characteristics are studied in view of obtain-ing the balanced three-phase output voltages A significantbehavior is noticed when the SP2TP matrix converter isoperated above 150Hz with appropriate modulation indexthe output line to line voltages of the matrix converter arefound to be balanced and differ by 120∘ away from each otherand exactly resemble the three-phase system Adjustmenthas to be done at programming level to achieve the desiredoutcomes of the converter The magnitudes of the outputvoltages can be varied using booster circuits There are lotsof scopes for enhancing the system design through furtherresearch for more stable and quality outputs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J H H Alwash ldquoPredicting performance of three phaseinduction motors connected to single phase suppliesrdquo in IEEProceedings on Electric Power Applications vol 143 no 4 pp339ndash344 July 1996

[2] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics vol 2 pp547ndash550 Xian China May 1992

[3] V Agarwal and S Gupta ldquoAn efficient algorithm for generalisedsingle-phase converterrdquo IET Power Electronics vol 3 no 1 pp138ndash145 2010

[4] K Zhou and D Wang ldquoRelationship between space-vectormodulation and three-phase carrier-based PWM a compre-hensive analysis [three-phase inverters]rdquo IEEE Transactions onIndustrial Electronics vol 49 no 1 pp 186ndash196 2002

[5] S Kwak and H A Toliyat ldquoAn approach to fault-tolerant three-phase matrix converter drivesrdquo IEEE Transactions on EnergyConversion vol 22 no 4 pp 855ndash863 2007

[6] M-K Nguyen Y-G Jung Y-C Lim and Y-M Kim ldquoA single-phase Z-source buck-boost matrix converterrdquo IEEE Transac-tions on Power Electronics vol 25 no 2 pp 453ndash462 2010

[7] I K Shahidul D Z Phoivos and H R Muhammad ldquoNovelsingle- to three-phase static converterrdquo IEEE Transactions onIndustrial Applications vol 25 no 1 pp 143ndash152 1989

[8] M H El-Maghraby R H Thejel and M M Ibrahim ldquoNewapproach for the analysis of a three-phase induction motorof different ratings connected to a single-phase supplyrdquo IEEProceedings BmdashElectric Power Applications vol 139 no 3 pp145ndash154 1992

[9] J Xiao W Zhang H Omori and K Matsui ldquoA novel operationstrategy for single-to three-phase matrix converterrdquo in Proceed-ings of the 12th International Conference on Electrical Machinesand Systems (ICEMS rsquo09) pp 1ndash6 Tokyo Japan November2009

[10] J W Kolar F Schafmeister S D Round and H Ertl ldquoNovelthree-phase AC-AC sparse matrix convertersrdquo IEEE Transac-tions on Power Electronics vol 22 no 5 pp 1649ndash1661 2007

[11] K Iino K Kondo and Y Sato ldquoAn experimental study oninduction motor drive with a single phasemdashthree phase matrixconverterrdquo in Proceedings of the 13th European Conference onPower Electronics and Applications (EPE rsquo09) pp 1ndash9 BarcelonaSpain September 2009

[12] M ImayavarambanK Latha andGUma ldquoAnalysis of differentschemes ofmatrix converter withmaximum voltage conversionratiordquo inProceedings of the 12th IEEEMediterranean Electrotech-nical Conference (MELECON rsquo04) vol 3 pp 1137ndash1140 IEEEDubrovnik Croatia May 2004

[13] H Takahashi R Hisamichi and H Haga ldquoHigh power factorcontrol for current-source type single-phase to three-phasematrix converterrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo09) pp 3071ndash3076 San JoseCalif USA September 2009

[14] M Saito and N Matsui ldquoA single- to three-phase matrix con-verter for a vector-controlled induction motorrdquo in Proceedingsof the IEEE Industry Applications Society Annual Meeting (IASrsquo08) pp 1ndash6 IEEE Edmonton Canada October 2008

[15] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics (ISIE rsquo92)Xian China May 1992

[16] M Saito T Takeshita and N Matsui ldquoA single to threephase matrix converter with a power decupling capabilityrdquo inProceedings of the IEEE 35thAnnual Power Electronics SpecialistsConference (PESC rsquo04) pp 2400ndash2405 IEEEAachenGermanyJune 2004

[17] L A C Lopes and M F Naguib ldquoSpace vector modulationfor low switching frequency current source converters withreduced low-order noncharacteristic harmonicsrdquo IEEE Trans-actions on Power Electronics vol 24 no 4 pp 903ndash910 2009

Submit your manuscripts athttpwwwhindawicom

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Applied Computational Intelligence and Soft Computing

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Artificial Intelligence

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

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International Journal of

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Industrial EngineeringJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 5

Figure 6 Segregation of input signal

used to produce the triggering pulse durations to turn on thesix bidirectional switches appropriately Figure 6 shows thestages of segregation that takes place at every 1205873 degrees forall the three phases At any instant any one of the phases has23rd of its maximum value and the other two phases have13rd of its maximum value in either direction

4 Simulation of SP2TP MatrixConverter System

MatlabSimulink application is used for the modelling andsimulation of the proposed algorithmThedesigned Simulinkmodel is then converted into C++ coding for hardwareimplementation using digital signal processor and IGBT coreand driver circuits Figure 7 shows the variousmodules of thespace vector pulse width modulation section of the converterin which the desired output magnitude frequency and theconverter input voltage are taken as reference

The reference three-phase sinusoidal signals are con-verted to two-dimensional 120572-120573 components with the sectorinformation A ramp signal is used for the sampling ofspace vector at high frequency According to the sector theswitching timing for each bidirectional switch is estimatedThere are six PWM signal outputs for the six bidirectional

switches of thematrix converter Table 1 shows the simulationspecification of the proposed model of the matrix convertersystem

In the Simulink model of the matrix converter circuitsix bidirectional switches are used to construct the matrixconverter module Each bidirectional switch is designedusing two IGBTs switched with reversing blocking diodesand the snubber circuits as shown in Figure 8 A three-phasebalanced resistive load is used to study the output signals

5 Simulation Results of Matrix Converter

The simulation results of the proposed design are studiedfor the suitability and implementation for the practicalapplications The standard 240V 50Hz single-phase supplyis applied as the input to the matrix converter systemBoth the space vector modules and the matrix convertermodules produce the expected outputs Figure 9 shows theoutput phase voltages of the matrix converter system andall the three-phase voltages are 120∘ away from each otherThe combined waveform resembles the three-phase systemwaveforms

Figure 10 shows the output line to line voltages of thematrix converter which are found to be sinusoidal and stable

6 Scientific Programming

Switching timecalculator

Trig

Sector Gate timing

Ramp generator

Ramp

Trig

Gates logic

Ramp

Gate_timing

L1a

L1b

L2a

L2b

L3a

L3bab vector

sector

Angle Sector

ab transform

Angle

ab_V

Sine wave

DSP

Scope8Scope1

Scope[s6]

[s5]

[s4]

[s3]

[s2]

[s1]

50

415

1

3-phase sin generatorFreq_com

Dir

Vcom Vabc Vabc

Vbus bus a_b_Vbus

Figure 7 Simulation of space vector PWM algorithm for SP2TP matrix converter

Table 1 Simulation parameters of the matrix converter system

Simulation parametersModulation scheme Space vector PWMCarrier wave Ramp signalCarrier amplitude (119881cm) 1 VCarrier frequency (119891

119888

) 4500HzCarrier wave ratio = (119891

119888

)(119891119903

) 90Modulation index = (119881rm)(119881cm) 10119881ref amplitude (119881rm) Sinusoidal 1 V119881ref frequency (119891119903) and angle 50Hz zero3-ph ref amplitude 415V3-ph ref frequency amp angle 50Hz zeroNumber of samples per cycle 90Sampling time period (119879

119904

) 2222 120583sSeconds per degree 0617120583sNumber of degrees per sample 4Sampling time per sector 333ms

The combined waveform exactly behaves like a three-phasesystem voltages

Figure 11 shows the input and output voltages of thematrix converter under unity power factor load A starconnected balanced resistive network is used as a unity powerfactor loadThe power factor of the input voltage and currentis found to be at unity No phase angle difference is observedbetween the input and 119877-phase output currents

Figure 12 shows the input and output voltages of thematrix converter under lagging power factor load A starconnected balanced119877-119871 load is used as a lagging power factorload The output currents are found to be 120 degrees awayfrom each other andmore smoother compared to the resistiveload

In order to determine the appropriate conditions in viewof obtaining the balanced output voltages the simulations

Table 2 Output voltages under the effect of varying modulationindex at 50Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 020 2319 1611 22201271 1797 040 1159 8052 1110847 1198 060 7719 5364 7394635 899 080 5789 4023 5546508 719 100 4627 3215 4433424 599 120 3852 2677 3692363 513 140 3297 2291 316318 449 160 2884 2004 2765282 399 180 2561 1779 2456254 359 200 2303 160 2209

were performed under different modulation indexes Thestudy on the modulation index characteristics is found tobe the vital factor that governs the magnitude of the outputvoltagesThemodulation index of the space vector pulse withmodulation can be defined as the ratio of the product ofsquare root times the space vector reference voltage to that ofthe input supply voltages The modulation index is expressedas

Modulation Index (Mi) = radic3119881ref119881119878

(13)

The RMS values of the output voltages under the effect ofvarying the modulation index are tabulated in Table 2 Itscorresponding modulation index characteristics are shownin Figure 13 The three output voltages are found to beunbalanced Two of the output voltages are at equal valueswhereas one of the phases is having relatively low voltageoutput

From the modulation index characteristics it is foundthat the output line to line voltages are inversely proportionalto the modulation index used in the space vector modulation

Scientific Programming 7

v

Scope9

Scope6

Scope4 Scope3

Scope2

s6s5

g

s4g

s3s2

g

s1

g

RMS5RMS

RMS4RMS

RMS2RMS

RMS1RMS

R3+

R2+

R1+

From5[s6]

From4[s5]

From3[s4]

From2[s3]

From1[s2]

From[s1]

Display3

Display2

Display1

Display

AC voltagesource

+

+ minus

+minus

++ +

+

minusminus minus

minus

i

g +minus

g +minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

+ minusi

+ minusi

+ minusi

Figure 8 Simulation of SP2TP matrix converter with unity power factor load

Table 3 Output voltages under the effect of varying modulationindex at 200Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 02 2090 2075 20561271 1797 04 1044 1037 1027847 1198 06 6958 6906 6843635 899 08 5217 5179 5131508 719 1 417 4139 4101424 599 12 3472 3446 3411363 513 14 2971 2949 2922318 449 16 2599 258 2556282 399 18 2308 2291 227254 359 2 2075 206 2041

algorithm The lower the modulation indexes the higherthe RMS values of the output voltages However the lowermodulation index means the higher input supply voltage Soto increase the input voltage additional step-up transformersare to be used

The model was studied under wide range of referencefrequencies of space vector algorithm In order to obtainbalanced output voltages the reference frequency of the spacevector algorithm has to be increased beyond 150Hz Whenthe reference frequency is varied the simulation model altersthe triggering pulses duration and corresponding controlsignals are produced in the digital signal processorsThus theoutput voltages of the converter are altered correspondinglyTable 3 shows the magnitude of the line to line outputvoltages of the matrix converter under 200Hz operation

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Output phase voltages

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

Time offset 0

minus500

0

500

minus500

0

500

minus500

0

500

minus500

0

500

Figure 9 Output phases voltages of SP2TP matrix converter withunity power factor load

and its corresponding modulation characteristics show morebalanced output voltages

The modulation index characteristics obtained with thereference frequency of the program as 200Hz are shown inFigure 14 The RMS values of the output voltages are foundto be balanced and proportional to each other at all values ofmodulation index

8 Scientific Programming

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

Output line to line voltages

Line voltage Vab

Line voltage Vbc

Line voltage Vca

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

Figure 10 Output line voltages of SP2TP matrix converter withunity power factor load

Single-phase input voltage

Three-phase output voltages

Input and output currents

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus400

minus200

0

200

400

minus400

minus200

0

200

400

minus5

0

5

Figure 11 Voltages and currents under unity power factor load

Scientific programming model provides more flexibilityto choose a wide range of reference frequencies so thatconverter can be tuned to generate range of voltages atdifferent frequencies However it is limited by the hardwarerealization issues The appropriate modulated index andreference frequency have to be selected for the desired outputvoltages of the matrix converter

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus505

minus5000

500

minus5000

500

minus2000

200

minus505

minus505

minus505

Three-phase output currents

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Line current Ia

Line current Ib

Line current Ic

Figure 12 Voltages and currents under lagging power factor load

05 1 15 2 250Modulation index

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

VabVbcVca

Figure 13 Modulation index characteristics at 50Hz referencefrequency

6 Hardware Experimentation of MatrixConverter System

The hardware realization of the proposed model is shownin Figure 15 The Code Composer Studio application is usedfor the real-time interface with the digital signal processor toproduce the space vector algorithm based IGBT gate signals

Scientific Programming 9

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

05 1 15 2 250Modulation index

VabVbcVca

Figure 14 Modulation index characteristics at 200Hz referencefrequency

MCB

DSP

Gate driver core and base board

3-phase squirrel cage induction

motor

IGBT bidirectionalswitches

Voltage transducer

Miniature circuit breaker

SP2TP matrix converter hardware implementation schematic

Figure 15 Hardware realization of matrix converter system

The gate drive circuits and base board circuits are used toprovide the appropriate gate voltages to the bidirectionalswitches The developed hardware model is tested underdifferent power factor loads

Figure 16 shows the actual hardware experimental setupof the single-phase-to-three-phase matrix converter systemIGBT based bidirectional switches are used to design thematrix converter system Texas Instrument DSP and theConcept IGBTCoreDrives are used for the control operationSynchronization circuit is used to synchronize the sinusoidalsupply voltage with the control signals

The RMS values of the practical hardware circuits areslightly lower than the simulation circuits Figure 17 showsthe practical line to line voltages compared with the simula-tion data The variation is mainly due to the presence of oddharmonics in the hardware circuits

Figure 18 shows the percentage total harmonic distortion(THD) of the 119877-phase voltage under unity power factorload condition for both simulation and practical readings

Synchronizingcircuit

Matrixconverter

Three-phase induction motor

Digital signal processor

Interfacecircuit

IGBT coredriver circuit

Figure 16 Hardware realization of matrix converter system

Comparison between simulation and practical

SimulationPracticalVariation

050

100150200250

Line

to li

ne v

olta

ges (

V)

2 3 4 5 6 7 81Experimental reading samples

voltages (Vab)mdashunity Pf load

Figure 17 Comparison of simulation and practical line voltages

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Order of harmonics under simulation and

practical experimental conditions

020406080

100120

Har

mon

ic co

nten

t (

)

THD of matrix converter R-phasemdashunity Pf load

Figure 18 total harmonic distortion in the output voltage ofmatrix converter

Only odd harmonics are found to be present and the practicalTHD is slightly higher compared to the simulation valuesThis is obvious due to the presence of odd harmonics

7 Conclusion

Bidirectional switch based matrix converters are gettingmore popular due to their compact convenient and robustoperation State-of-the-art space vector PWM programmingand switching techniques are employed in the gate triggeringcontrol of the matrix converters The model was studiedunder different reference frequencies and modulation indexconditions The limitation of the proposed system is theunbalanced voltages produced due to odd harmonics pres-ence High harmonic contents are noticed which can be

10 Scientific Programming

eliminated by incorporating proper filter circuits Boostercircuits also can be used to obtain the desired output voltageThe modulation characteristics are studied in view of obtain-ing the balanced three-phase output voltages A significantbehavior is noticed when the SP2TP matrix converter isoperated above 150Hz with appropriate modulation indexthe output line to line voltages of the matrix converter arefound to be balanced and differ by 120∘ away from each otherand exactly resemble the three-phase system Adjustmenthas to be done at programming level to achieve the desiredoutcomes of the converter The magnitudes of the outputvoltages can be varied using booster circuits There are lotsof scopes for enhancing the system design through furtherresearch for more stable and quality outputs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J H H Alwash ldquoPredicting performance of three phaseinduction motors connected to single phase suppliesrdquo in IEEProceedings on Electric Power Applications vol 143 no 4 pp339ndash344 July 1996

[2] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics vol 2 pp547ndash550 Xian China May 1992

[3] V Agarwal and S Gupta ldquoAn efficient algorithm for generalisedsingle-phase converterrdquo IET Power Electronics vol 3 no 1 pp138ndash145 2010

[4] K Zhou and D Wang ldquoRelationship between space-vectormodulation and three-phase carrier-based PWM a compre-hensive analysis [three-phase inverters]rdquo IEEE Transactions onIndustrial Electronics vol 49 no 1 pp 186ndash196 2002

[5] S Kwak and H A Toliyat ldquoAn approach to fault-tolerant three-phase matrix converter drivesrdquo IEEE Transactions on EnergyConversion vol 22 no 4 pp 855ndash863 2007

[6] M-K Nguyen Y-G Jung Y-C Lim and Y-M Kim ldquoA single-phase Z-source buck-boost matrix converterrdquo IEEE Transac-tions on Power Electronics vol 25 no 2 pp 453ndash462 2010

[7] I K Shahidul D Z Phoivos and H R Muhammad ldquoNovelsingle- to three-phase static converterrdquo IEEE Transactions onIndustrial Applications vol 25 no 1 pp 143ndash152 1989

[8] M H El-Maghraby R H Thejel and M M Ibrahim ldquoNewapproach for the analysis of a three-phase induction motorof different ratings connected to a single-phase supplyrdquo IEEProceedings BmdashElectric Power Applications vol 139 no 3 pp145ndash154 1992

[9] J Xiao W Zhang H Omori and K Matsui ldquoA novel operationstrategy for single-to three-phase matrix converterrdquo in Proceed-ings of the 12th International Conference on Electrical Machinesand Systems (ICEMS rsquo09) pp 1ndash6 Tokyo Japan November2009

[10] J W Kolar F Schafmeister S D Round and H Ertl ldquoNovelthree-phase AC-AC sparse matrix convertersrdquo IEEE Transac-tions on Power Electronics vol 22 no 5 pp 1649ndash1661 2007

[11] K Iino K Kondo and Y Sato ldquoAn experimental study oninduction motor drive with a single phasemdashthree phase matrixconverterrdquo in Proceedings of the 13th European Conference onPower Electronics and Applications (EPE rsquo09) pp 1ndash9 BarcelonaSpain September 2009

[12] M ImayavarambanK Latha andGUma ldquoAnalysis of differentschemes ofmatrix converter withmaximum voltage conversionratiordquo inProceedings of the 12th IEEEMediterranean Electrotech-nical Conference (MELECON rsquo04) vol 3 pp 1137ndash1140 IEEEDubrovnik Croatia May 2004

[13] H Takahashi R Hisamichi and H Haga ldquoHigh power factorcontrol for current-source type single-phase to three-phasematrix converterrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo09) pp 3071ndash3076 San JoseCalif USA September 2009

[14] M Saito and N Matsui ldquoA single- to three-phase matrix con-verter for a vector-controlled induction motorrdquo in Proceedingsof the IEEE Industry Applications Society Annual Meeting (IASrsquo08) pp 1ndash6 IEEE Edmonton Canada October 2008

[15] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics (ISIE rsquo92)Xian China May 1992

[16] M Saito T Takeshita and N Matsui ldquoA single to threephase matrix converter with a power decupling capabilityrdquo inProceedings of the IEEE 35thAnnual Power Electronics SpecialistsConference (PESC rsquo04) pp 2400ndash2405 IEEEAachenGermanyJune 2004

[17] L A C Lopes and M F Naguib ldquoSpace vector modulationfor low switching frequency current source converters withreduced low-order noncharacteristic harmonicsrdquo IEEE Trans-actions on Power Electronics vol 24 no 4 pp 903ndash910 2009

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

6 Scientific Programming

Switching timecalculator

Trig

Sector Gate timing

Ramp generator

Ramp

Trig

Gates logic

Ramp

Gate_timing

L1a

L1b

L2a

L2b

L3a

L3bab vector

sector

Angle Sector

ab transform

Angle

ab_V

Sine wave

DSP

Scope8Scope1

Scope[s6]

[s5]

[s4]

[s3]

[s2]

[s1]

50

415

1

3-phase sin generatorFreq_com

Dir

Vcom Vabc Vabc

Vbus bus a_b_Vbus

Figure 7 Simulation of space vector PWM algorithm for SP2TP matrix converter

Table 1 Simulation parameters of the matrix converter system

Simulation parametersModulation scheme Space vector PWMCarrier wave Ramp signalCarrier amplitude (119881cm) 1 VCarrier frequency (119891

119888

) 4500HzCarrier wave ratio = (119891

119888

)(119891119903

) 90Modulation index = (119881rm)(119881cm) 10119881ref amplitude (119881rm) Sinusoidal 1 V119881ref frequency (119891119903) and angle 50Hz zero3-ph ref amplitude 415V3-ph ref frequency amp angle 50Hz zeroNumber of samples per cycle 90Sampling time period (119879

119904

) 2222 120583sSeconds per degree 0617120583sNumber of degrees per sample 4Sampling time per sector 333ms

The combined waveform exactly behaves like a three-phasesystem voltages

Figure 11 shows the input and output voltages of thematrix converter under unity power factor load A starconnected balanced resistive network is used as a unity powerfactor loadThe power factor of the input voltage and currentis found to be at unity No phase angle difference is observedbetween the input and 119877-phase output currents

Figure 12 shows the input and output voltages of thematrix converter under lagging power factor load A starconnected balanced119877-119871 load is used as a lagging power factorload The output currents are found to be 120 degrees awayfrom each other andmore smoother compared to the resistiveload

In order to determine the appropriate conditions in viewof obtaining the balanced output voltages the simulations

Table 2 Output voltages under the effect of varying modulationindex at 50Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 020 2319 1611 22201271 1797 040 1159 8052 1110847 1198 060 7719 5364 7394635 899 080 5789 4023 5546508 719 100 4627 3215 4433424 599 120 3852 2677 3692363 513 140 3297 2291 316318 449 160 2884 2004 2765282 399 180 2561 1779 2456254 359 200 2303 160 2209

were performed under different modulation indexes Thestudy on the modulation index characteristics is found tobe the vital factor that governs the magnitude of the outputvoltagesThemodulation index of the space vector pulse withmodulation can be defined as the ratio of the product ofsquare root times the space vector reference voltage to that ofthe input supply voltages The modulation index is expressedas

Modulation Index (Mi) = radic3119881ref119881119878

(13)

The RMS values of the output voltages under the effect ofvarying the modulation index are tabulated in Table 2 Itscorresponding modulation index characteristics are shownin Figure 13 The three output voltages are found to beunbalanced Two of the output voltages are at equal valueswhereas one of the phases is having relatively low voltageoutput

From the modulation index characteristics it is foundthat the output line to line voltages are inversely proportionalto the modulation index used in the space vector modulation

Scientific Programming 7

v

Scope9

Scope6

Scope4 Scope3

Scope2

s6s5

g

s4g

s3s2

g

s1

g

RMS5RMS

RMS4RMS

RMS2RMS

RMS1RMS

R3+

R2+

R1+

From5[s6]

From4[s5]

From3[s4]

From2[s3]

From1[s2]

From[s1]

Display3

Display2

Display1

Display

AC voltagesource

+

+ minus

+minus

++ +

+

minusminus minus

minus

i

g +minus

g +minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

+ minusi

+ minusi

+ minusi

Figure 8 Simulation of SP2TP matrix converter with unity power factor load

Table 3 Output voltages under the effect of varying modulationindex at 200Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 02 2090 2075 20561271 1797 04 1044 1037 1027847 1198 06 6958 6906 6843635 899 08 5217 5179 5131508 719 1 417 4139 4101424 599 12 3472 3446 3411363 513 14 2971 2949 2922318 449 16 2599 258 2556282 399 18 2308 2291 227254 359 2 2075 206 2041

algorithm The lower the modulation indexes the higherthe RMS values of the output voltages However the lowermodulation index means the higher input supply voltage Soto increase the input voltage additional step-up transformersare to be used

The model was studied under wide range of referencefrequencies of space vector algorithm In order to obtainbalanced output voltages the reference frequency of the spacevector algorithm has to be increased beyond 150Hz Whenthe reference frequency is varied the simulation model altersthe triggering pulses duration and corresponding controlsignals are produced in the digital signal processorsThus theoutput voltages of the converter are altered correspondinglyTable 3 shows the magnitude of the line to line outputvoltages of the matrix converter under 200Hz operation

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Output phase voltages

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

Time offset 0

minus500

0

500

minus500

0

500

minus500

0

500

minus500

0

500

Figure 9 Output phases voltages of SP2TP matrix converter withunity power factor load

and its corresponding modulation characteristics show morebalanced output voltages

The modulation index characteristics obtained with thereference frequency of the program as 200Hz are shown inFigure 14 The RMS values of the output voltages are foundto be balanced and proportional to each other at all values ofmodulation index

8 Scientific Programming

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

Output line to line voltages

Line voltage Vab

Line voltage Vbc

Line voltage Vca

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

Figure 10 Output line voltages of SP2TP matrix converter withunity power factor load

Single-phase input voltage

Three-phase output voltages

Input and output currents

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus400

minus200

0

200

400

minus400

minus200

0

200

400

minus5

0

5

Figure 11 Voltages and currents under unity power factor load

Scientific programming model provides more flexibilityto choose a wide range of reference frequencies so thatconverter can be tuned to generate range of voltages atdifferent frequencies However it is limited by the hardwarerealization issues The appropriate modulated index andreference frequency have to be selected for the desired outputvoltages of the matrix converter

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus505

minus5000

500

minus5000

500

minus2000

200

minus505

minus505

minus505

Three-phase output currents

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Line current Ia

Line current Ib

Line current Ic

Figure 12 Voltages and currents under lagging power factor load

05 1 15 2 250Modulation index

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

VabVbcVca

Figure 13 Modulation index characteristics at 50Hz referencefrequency

6 Hardware Experimentation of MatrixConverter System

The hardware realization of the proposed model is shownin Figure 15 The Code Composer Studio application is usedfor the real-time interface with the digital signal processor toproduce the space vector algorithm based IGBT gate signals

Scientific Programming 9

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

05 1 15 2 250Modulation index

VabVbcVca

Figure 14 Modulation index characteristics at 200Hz referencefrequency

MCB

DSP

Gate driver core and base board

3-phase squirrel cage induction

motor

IGBT bidirectionalswitches

Voltage transducer

Miniature circuit breaker

SP2TP matrix converter hardware implementation schematic

Figure 15 Hardware realization of matrix converter system

The gate drive circuits and base board circuits are used toprovide the appropriate gate voltages to the bidirectionalswitches The developed hardware model is tested underdifferent power factor loads

Figure 16 shows the actual hardware experimental setupof the single-phase-to-three-phase matrix converter systemIGBT based bidirectional switches are used to design thematrix converter system Texas Instrument DSP and theConcept IGBTCoreDrives are used for the control operationSynchronization circuit is used to synchronize the sinusoidalsupply voltage with the control signals

The RMS values of the practical hardware circuits areslightly lower than the simulation circuits Figure 17 showsthe practical line to line voltages compared with the simula-tion data The variation is mainly due to the presence of oddharmonics in the hardware circuits

Figure 18 shows the percentage total harmonic distortion(THD) of the 119877-phase voltage under unity power factorload condition for both simulation and practical readings

Synchronizingcircuit

Matrixconverter

Three-phase induction motor

Digital signal processor

Interfacecircuit

IGBT coredriver circuit

Figure 16 Hardware realization of matrix converter system

Comparison between simulation and practical

SimulationPracticalVariation

050

100150200250

Line

to li

ne v

olta

ges (

V)

2 3 4 5 6 7 81Experimental reading samples

voltages (Vab)mdashunity Pf load

Figure 17 Comparison of simulation and practical line voltages

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Order of harmonics under simulation and

practical experimental conditions

020406080

100120

Har

mon

ic co

nten

t (

)

THD of matrix converter R-phasemdashunity Pf load

Figure 18 total harmonic distortion in the output voltage ofmatrix converter

Only odd harmonics are found to be present and the practicalTHD is slightly higher compared to the simulation valuesThis is obvious due to the presence of odd harmonics

7 Conclusion

Bidirectional switch based matrix converters are gettingmore popular due to their compact convenient and robustoperation State-of-the-art space vector PWM programmingand switching techniques are employed in the gate triggeringcontrol of the matrix converters The model was studiedunder different reference frequencies and modulation indexconditions The limitation of the proposed system is theunbalanced voltages produced due to odd harmonics pres-ence High harmonic contents are noticed which can be

10 Scientific Programming

eliminated by incorporating proper filter circuits Boostercircuits also can be used to obtain the desired output voltageThe modulation characteristics are studied in view of obtain-ing the balanced three-phase output voltages A significantbehavior is noticed when the SP2TP matrix converter isoperated above 150Hz with appropriate modulation indexthe output line to line voltages of the matrix converter arefound to be balanced and differ by 120∘ away from each otherand exactly resemble the three-phase system Adjustmenthas to be done at programming level to achieve the desiredoutcomes of the converter The magnitudes of the outputvoltages can be varied using booster circuits There are lotsof scopes for enhancing the system design through furtherresearch for more stable and quality outputs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J H H Alwash ldquoPredicting performance of three phaseinduction motors connected to single phase suppliesrdquo in IEEProceedings on Electric Power Applications vol 143 no 4 pp339ndash344 July 1996

[2] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics vol 2 pp547ndash550 Xian China May 1992

[3] V Agarwal and S Gupta ldquoAn efficient algorithm for generalisedsingle-phase converterrdquo IET Power Electronics vol 3 no 1 pp138ndash145 2010

[4] K Zhou and D Wang ldquoRelationship between space-vectormodulation and three-phase carrier-based PWM a compre-hensive analysis [three-phase inverters]rdquo IEEE Transactions onIndustrial Electronics vol 49 no 1 pp 186ndash196 2002

[5] S Kwak and H A Toliyat ldquoAn approach to fault-tolerant three-phase matrix converter drivesrdquo IEEE Transactions on EnergyConversion vol 22 no 4 pp 855ndash863 2007

[6] M-K Nguyen Y-G Jung Y-C Lim and Y-M Kim ldquoA single-phase Z-source buck-boost matrix converterrdquo IEEE Transac-tions on Power Electronics vol 25 no 2 pp 453ndash462 2010

[7] I K Shahidul D Z Phoivos and H R Muhammad ldquoNovelsingle- to three-phase static converterrdquo IEEE Transactions onIndustrial Applications vol 25 no 1 pp 143ndash152 1989

[8] M H El-Maghraby R H Thejel and M M Ibrahim ldquoNewapproach for the analysis of a three-phase induction motorof different ratings connected to a single-phase supplyrdquo IEEProceedings BmdashElectric Power Applications vol 139 no 3 pp145ndash154 1992

[9] J Xiao W Zhang H Omori and K Matsui ldquoA novel operationstrategy for single-to three-phase matrix converterrdquo in Proceed-ings of the 12th International Conference on Electrical Machinesand Systems (ICEMS rsquo09) pp 1ndash6 Tokyo Japan November2009

[10] J W Kolar F Schafmeister S D Round and H Ertl ldquoNovelthree-phase AC-AC sparse matrix convertersrdquo IEEE Transac-tions on Power Electronics vol 22 no 5 pp 1649ndash1661 2007

[11] K Iino K Kondo and Y Sato ldquoAn experimental study oninduction motor drive with a single phasemdashthree phase matrixconverterrdquo in Proceedings of the 13th European Conference onPower Electronics and Applications (EPE rsquo09) pp 1ndash9 BarcelonaSpain September 2009

[12] M ImayavarambanK Latha andGUma ldquoAnalysis of differentschemes ofmatrix converter withmaximum voltage conversionratiordquo inProceedings of the 12th IEEEMediterranean Electrotech-nical Conference (MELECON rsquo04) vol 3 pp 1137ndash1140 IEEEDubrovnik Croatia May 2004

[13] H Takahashi R Hisamichi and H Haga ldquoHigh power factorcontrol for current-source type single-phase to three-phasematrix converterrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo09) pp 3071ndash3076 San JoseCalif USA September 2009

[14] M Saito and N Matsui ldquoA single- to three-phase matrix con-verter for a vector-controlled induction motorrdquo in Proceedingsof the IEEE Industry Applications Society Annual Meeting (IASrsquo08) pp 1ndash6 IEEE Edmonton Canada October 2008

[15] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics (ISIE rsquo92)Xian China May 1992

[16] M Saito T Takeshita and N Matsui ldquoA single to threephase matrix converter with a power decupling capabilityrdquo inProceedings of the IEEE 35thAnnual Power Electronics SpecialistsConference (PESC rsquo04) pp 2400ndash2405 IEEEAachenGermanyJune 2004

[17] L A C Lopes and M F Naguib ldquoSpace vector modulationfor low switching frequency current source converters withreduced low-order noncharacteristic harmonicsrdquo IEEE Trans-actions on Power Electronics vol 24 no 4 pp 903ndash910 2009

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 7

v

Scope9

Scope6

Scope4 Scope3

Scope2

s6s5

g

s4g

s3s2

g

s1

g

RMS5RMS

RMS4RMS

RMS2RMS

RMS1RMS

R3+

R2+

R1+

From5[s6]

From4[s5]

From3[s4]

From2[s3]

From1[s2]

From[s1]

Display3

Display2

Display1

Display

AC voltagesource

+

+ minus

+minus

++ +

+

minusminus minus

minus

i

g +minus

g +minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

v+ minus

+ minusi

+ minusi

+ minusi

Figure 8 Simulation of SP2TP matrix converter with unity power factor load

Table 3 Output voltages under the effect of varying modulationindex at 200Hz reference frequency

1-ph 119881119878

1-ph max Mi 119881119886119887

119881119887119888

119881119888119886

2541 3594 02 2090 2075 20561271 1797 04 1044 1037 1027847 1198 06 6958 6906 6843635 899 08 5217 5179 5131508 719 1 417 4139 4101424 599 12 3472 3446 3411363 513 14 2971 2949 2922318 449 16 2599 258 2556282 399 18 2308 2291 227254 359 2 2075 206 2041

algorithm The lower the modulation indexes the higherthe RMS values of the output voltages However the lowermodulation index means the higher input supply voltage Soto increase the input voltage additional step-up transformersare to be used

The model was studied under wide range of referencefrequencies of space vector algorithm In order to obtainbalanced output voltages the reference frequency of the spacevector algorithm has to be increased beyond 150Hz Whenthe reference frequency is varied the simulation model altersthe triggering pulses duration and corresponding controlsignals are produced in the digital signal processorsThus theoutput voltages of the converter are altered correspondinglyTable 3 shows the magnitude of the line to line outputvoltages of the matrix converter under 200Hz operation

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Output phase voltages

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

0 01003 004 005 006 007 008 009002001

Time offset 0

minus500

0

500

minus500

0

500

minus500

0

500

minus500

0

500

Figure 9 Output phases voltages of SP2TP matrix converter withunity power factor load

and its corresponding modulation characteristics show morebalanced output voltages

The modulation index characteristics obtained with thereference frequency of the program as 200Hz are shown inFigure 14 The RMS values of the output voltages are foundto be balanced and proportional to each other at all values ofmodulation index

8 Scientific Programming

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

Output line to line voltages

Line voltage Vab

Line voltage Vbc

Line voltage Vca

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

Figure 10 Output line voltages of SP2TP matrix converter withunity power factor load

Single-phase input voltage

Three-phase output voltages

Input and output currents

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus400

minus200

0

200

400

minus400

minus200

0

200

400

minus5

0

5

Figure 11 Voltages and currents under unity power factor load

Scientific programming model provides more flexibilityto choose a wide range of reference frequencies so thatconverter can be tuned to generate range of voltages atdifferent frequencies However it is limited by the hardwarerealization issues The appropriate modulated index andreference frequency have to be selected for the desired outputvoltages of the matrix converter

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus505

minus5000

500

minus5000

500

minus2000

200

minus505

minus505

minus505

Three-phase output currents

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Line current Ia

Line current Ib

Line current Ic

Figure 12 Voltages and currents under lagging power factor load

05 1 15 2 250Modulation index

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

VabVbcVca

Figure 13 Modulation index characteristics at 50Hz referencefrequency

6 Hardware Experimentation of MatrixConverter System

The hardware realization of the proposed model is shownin Figure 15 The Code Composer Studio application is usedfor the real-time interface with the digital signal processor toproduce the space vector algorithm based IGBT gate signals

Scientific Programming 9

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

05 1 15 2 250Modulation index

VabVbcVca

Figure 14 Modulation index characteristics at 200Hz referencefrequency

MCB

DSP

Gate driver core and base board

3-phase squirrel cage induction

motor

IGBT bidirectionalswitches

Voltage transducer

Miniature circuit breaker

SP2TP matrix converter hardware implementation schematic

Figure 15 Hardware realization of matrix converter system

The gate drive circuits and base board circuits are used toprovide the appropriate gate voltages to the bidirectionalswitches The developed hardware model is tested underdifferent power factor loads

Figure 16 shows the actual hardware experimental setupof the single-phase-to-three-phase matrix converter systemIGBT based bidirectional switches are used to design thematrix converter system Texas Instrument DSP and theConcept IGBTCoreDrives are used for the control operationSynchronization circuit is used to synchronize the sinusoidalsupply voltage with the control signals

The RMS values of the practical hardware circuits areslightly lower than the simulation circuits Figure 17 showsthe practical line to line voltages compared with the simula-tion data The variation is mainly due to the presence of oddharmonics in the hardware circuits

Figure 18 shows the percentage total harmonic distortion(THD) of the 119877-phase voltage under unity power factorload condition for both simulation and practical readings

Synchronizingcircuit

Matrixconverter

Three-phase induction motor

Digital signal processor

Interfacecircuit

IGBT coredriver circuit

Figure 16 Hardware realization of matrix converter system

Comparison between simulation and practical

SimulationPracticalVariation

050

100150200250

Line

to li

ne v

olta

ges (

V)

2 3 4 5 6 7 81Experimental reading samples

voltages (Vab)mdashunity Pf load

Figure 17 Comparison of simulation and practical line voltages

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Order of harmonics under simulation and

practical experimental conditions

020406080

100120

Har

mon

ic co

nten

t (

)

THD of matrix converter R-phasemdashunity Pf load

Figure 18 total harmonic distortion in the output voltage ofmatrix converter

Only odd harmonics are found to be present and the practicalTHD is slightly higher compared to the simulation valuesThis is obvious due to the presence of odd harmonics

7 Conclusion

Bidirectional switch based matrix converters are gettingmore popular due to their compact convenient and robustoperation State-of-the-art space vector PWM programmingand switching techniques are employed in the gate triggeringcontrol of the matrix converters The model was studiedunder different reference frequencies and modulation indexconditions The limitation of the proposed system is theunbalanced voltages produced due to odd harmonics pres-ence High harmonic contents are noticed which can be

10 Scientific Programming

eliminated by incorporating proper filter circuits Boostercircuits also can be used to obtain the desired output voltageThe modulation characteristics are studied in view of obtain-ing the balanced three-phase output voltages A significantbehavior is noticed when the SP2TP matrix converter isoperated above 150Hz with appropriate modulation indexthe output line to line voltages of the matrix converter arefound to be balanced and differ by 120∘ away from each otherand exactly resemble the three-phase system Adjustmenthas to be done at programming level to achieve the desiredoutcomes of the converter The magnitudes of the outputvoltages can be varied using booster circuits There are lotsof scopes for enhancing the system design through furtherresearch for more stable and quality outputs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J H H Alwash ldquoPredicting performance of three phaseinduction motors connected to single phase suppliesrdquo in IEEProceedings on Electric Power Applications vol 143 no 4 pp339ndash344 July 1996

[2] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics vol 2 pp547ndash550 Xian China May 1992

[3] V Agarwal and S Gupta ldquoAn efficient algorithm for generalisedsingle-phase converterrdquo IET Power Electronics vol 3 no 1 pp138ndash145 2010

[4] K Zhou and D Wang ldquoRelationship between space-vectormodulation and three-phase carrier-based PWM a compre-hensive analysis [three-phase inverters]rdquo IEEE Transactions onIndustrial Electronics vol 49 no 1 pp 186ndash196 2002

[5] S Kwak and H A Toliyat ldquoAn approach to fault-tolerant three-phase matrix converter drivesrdquo IEEE Transactions on EnergyConversion vol 22 no 4 pp 855ndash863 2007

[6] M-K Nguyen Y-G Jung Y-C Lim and Y-M Kim ldquoA single-phase Z-source buck-boost matrix converterrdquo IEEE Transac-tions on Power Electronics vol 25 no 2 pp 453ndash462 2010

[7] I K Shahidul D Z Phoivos and H R Muhammad ldquoNovelsingle- to three-phase static converterrdquo IEEE Transactions onIndustrial Applications vol 25 no 1 pp 143ndash152 1989

[8] M H El-Maghraby R H Thejel and M M Ibrahim ldquoNewapproach for the analysis of a three-phase induction motorof different ratings connected to a single-phase supplyrdquo IEEProceedings BmdashElectric Power Applications vol 139 no 3 pp145ndash154 1992

[9] J Xiao W Zhang H Omori and K Matsui ldquoA novel operationstrategy for single-to three-phase matrix converterrdquo in Proceed-ings of the 12th International Conference on Electrical Machinesand Systems (ICEMS rsquo09) pp 1ndash6 Tokyo Japan November2009

[10] J W Kolar F Schafmeister S D Round and H Ertl ldquoNovelthree-phase AC-AC sparse matrix convertersrdquo IEEE Transac-tions on Power Electronics vol 22 no 5 pp 1649ndash1661 2007

[11] K Iino K Kondo and Y Sato ldquoAn experimental study oninduction motor drive with a single phasemdashthree phase matrixconverterrdquo in Proceedings of the 13th European Conference onPower Electronics and Applications (EPE rsquo09) pp 1ndash9 BarcelonaSpain September 2009

[12] M ImayavarambanK Latha andGUma ldquoAnalysis of differentschemes ofmatrix converter withmaximum voltage conversionratiordquo inProceedings of the 12th IEEEMediterranean Electrotech-nical Conference (MELECON rsquo04) vol 3 pp 1137ndash1140 IEEEDubrovnik Croatia May 2004

[13] H Takahashi R Hisamichi and H Haga ldquoHigh power factorcontrol for current-source type single-phase to three-phasematrix converterrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo09) pp 3071ndash3076 San JoseCalif USA September 2009

[14] M Saito and N Matsui ldquoA single- to three-phase matrix con-verter for a vector-controlled induction motorrdquo in Proceedingsof the IEEE Industry Applications Society Annual Meeting (IASrsquo08) pp 1ndash6 IEEE Edmonton Canada October 2008

[15] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics (ISIE rsquo92)Xian China May 1992

[16] M Saito T Takeshita and N Matsui ldquoA single to threephase matrix converter with a power decupling capabilityrdquo inProceedings of the IEEE 35thAnnual Power Electronics SpecialistsConference (PESC rsquo04) pp 2400ndash2405 IEEEAachenGermanyJune 2004

[17] L A C Lopes and M F Naguib ldquoSpace vector modulationfor low switching frequency current source converters withreduced low-order noncharacteristic harmonicsrdquo IEEE Trans-actions on Power Electronics vol 24 no 4 pp 903ndash910 2009

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

8 Scientific Programming

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

Output line to line voltages

Line voltage Vab

Line voltage Vbc

Line voltage Vca

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

minus400minus200

0200400

Figure 10 Output line voltages of SP2TP matrix converter withunity power factor load

Single-phase input voltage

Three-phase output voltages

Input and output currents

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus400

minus200

0

200

400

minus400

minus200

0

200

400

minus5

0

5

Figure 11 Voltages and currents under unity power factor load

Scientific programming model provides more flexibilityto choose a wide range of reference frequencies so thatconverter can be tuned to generate range of voltages atdifferent frequencies However it is limited by the hardwarerealization issues The appropriate modulated index andreference frequency have to be selected for the desired outputvoltages of the matrix converter

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

001 002 003 004 005 006 007 008 009 010

Time offset 0

minus505

minus5000

500

minus5000

500

minus2000

200

minus505

minus505

minus505

Three-phase output currents

Phase voltage Va

Phase voltage Vb

Phase voltage Vc

Line current Ia

Line current Ib

Line current Ic

Figure 12 Voltages and currents under lagging power factor load

05 1 15 2 250Modulation index

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

VabVbcVca

Figure 13 Modulation index characteristics at 50Hz referencefrequency

6 Hardware Experimentation of MatrixConverter System

The hardware realization of the proposed model is shownin Figure 15 The Code Composer Studio application is usedfor the real-time interface with the digital signal processor toproduce the space vector algorithm based IGBT gate signals

Scientific Programming 9

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

05 1 15 2 250Modulation index

VabVbcVca

Figure 14 Modulation index characteristics at 200Hz referencefrequency

MCB

DSP

Gate driver core and base board

3-phase squirrel cage induction

motor

IGBT bidirectionalswitches

Voltage transducer

Miniature circuit breaker

SP2TP matrix converter hardware implementation schematic

Figure 15 Hardware realization of matrix converter system

The gate drive circuits and base board circuits are used toprovide the appropriate gate voltages to the bidirectionalswitches The developed hardware model is tested underdifferent power factor loads

Figure 16 shows the actual hardware experimental setupof the single-phase-to-three-phase matrix converter systemIGBT based bidirectional switches are used to design thematrix converter system Texas Instrument DSP and theConcept IGBTCoreDrives are used for the control operationSynchronization circuit is used to synchronize the sinusoidalsupply voltage with the control signals

The RMS values of the practical hardware circuits areslightly lower than the simulation circuits Figure 17 showsthe practical line to line voltages compared with the simula-tion data The variation is mainly due to the presence of oddharmonics in the hardware circuits

Figure 18 shows the percentage total harmonic distortion(THD) of the 119877-phase voltage under unity power factorload condition for both simulation and practical readings

Synchronizingcircuit

Matrixconverter

Three-phase induction motor

Digital signal processor

Interfacecircuit

IGBT coredriver circuit

Figure 16 Hardware realization of matrix converter system

Comparison between simulation and practical

SimulationPracticalVariation

050

100150200250

Line

to li

ne v

olta

ges (

V)

2 3 4 5 6 7 81Experimental reading samples

voltages (Vab)mdashunity Pf load

Figure 17 Comparison of simulation and practical line voltages

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Order of harmonics under simulation and

practical experimental conditions

020406080

100120

Har

mon

ic co

nten

t (

)

THD of matrix converter R-phasemdashunity Pf load

Figure 18 total harmonic distortion in the output voltage ofmatrix converter

Only odd harmonics are found to be present and the practicalTHD is slightly higher compared to the simulation valuesThis is obvious due to the presence of odd harmonics

7 Conclusion

Bidirectional switch based matrix converters are gettingmore popular due to their compact convenient and robustoperation State-of-the-art space vector PWM programmingand switching techniques are employed in the gate triggeringcontrol of the matrix converters The model was studiedunder different reference frequencies and modulation indexconditions The limitation of the proposed system is theunbalanced voltages produced due to odd harmonics pres-ence High harmonic contents are noticed which can be

10 Scientific Programming

eliminated by incorporating proper filter circuits Boostercircuits also can be used to obtain the desired output voltageThe modulation characteristics are studied in view of obtain-ing the balanced three-phase output voltages A significantbehavior is noticed when the SP2TP matrix converter isoperated above 150Hz with appropriate modulation indexthe output line to line voltages of the matrix converter arefound to be balanced and differ by 120∘ away from each otherand exactly resemble the three-phase system Adjustmenthas to be done at programming level to achieve the desiredoutcomes of the converter The magnitudes of the outputvoltages can be varied using booster circuits There are lotsof scopes for enhancing the system design through furtherresearch for more stable and quality outputs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J H H Alwash ldquoPredicting performance of three phaseinduction motors connected to single phase suppliesrdquo in IEEProceedings on Electric Power Applications vol 143 no 4 pp339ndash344 July 1996

[2] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics vol 2 pp547ndash550 Xian China May 1992

[3] V Agarwal and S Gupta ldquoAn efficient algorithm for generalisedsingle-phase converterrdquo IET Power Electronics vol 3 no 1 pp138ndash145 2010

[4] K Zhou and D Wang ldquoRelationship between space-vectormodulation and three-phase carrier-based PWM a compre-hensive analysis [three-phase inverters]rdquo IEEE Transactions onIndustrial Electronics vol 49 no 1 pp 186ndash196 2002

[5] S Kwak and H A Toliyat ldquoAn approach to fault-tolerant three-phase matrix converter drivesrdquo IEEE Transactions on EnergyConversion vol 22 no 4 pp 855ndash863 2007

[6] M-K Nguyen Y-G Jung Y-C Lim and Y-M Kim ldquoA single-phase Z-source buck-boost matrix converterrdquo IEEE Transac-tions on Power Electronics vol 25 no 2 pp 453ndash462 2010

[7] I K Shahidul D Z Phoivos and H R Muhammad ldquoNovelsingle- to three-phase static converterrdquo IEEE Transactions onIndustrial Applications vol 25 no 1 pp 143ndash152 1989

[8] M H El-Maghraby R H Thejel and M M Ibrahim ldquoNewapproach for the analysis of a three-phase induction motorof different ratings connected to a single-phase supplyrdquo IEEProceedings BmdashElectric Power Applications vol 139 no 3 pp145ndash154 1992

[9] J Xiao W Zhang H Omori and K Matsui ldquoA novel operationstrategy for single-to three-phase matrix converterrdquo in Proceed-ings of the 12th International Conference on Electrical Machinesand Systems (ICEMS rsquo09) pp 1ndash6 Tokyo Japan November2009

[10] J W Kolar F Schafmeister S D Round and H Ertl ldquoNovelthree-phase AC-AC sparse matrix convertersrdquo IEEE Transac-tions on Power Electronics vol 22 no 5 pp 1649ndash1661 2007

[11] K Iino K Kondo and Y Sato ldquoAn experimental study oninduction motor drive with a single phasemdashthree phase matrixconverterrdquo in Proceedings of the 13th European Conference onPower Electronics and Applications (EPE rsquo09) pp 1ndash9 BarcelonaSpain September 2009

[12] M ImayavarambanK Latha andGUma ldquoAnalysis of differentschemes ofmatrix converter withmaximum voltage conversionratiordquo inProceedings of the 12th IEEEMediterranean Electrotech-nical Conference (MELECON rsquo04) vol 3 pp 1137ndash1140 IEEEDubrovnik Croatia May 2004

[13] H Takahashi R Hisamichi and H Haga ldquoHigh power factorcontrol for current-source type single-phase to three-phasematrix converterrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo09) pp 3071ndash3076 San JoseCalif USA September 2009

[14] M Saito and N Matsui ldquoA single- to three-phase matrix con-verter for a vector-controlled induction motorrdquo in Proceedingsof the IEEE Industry Applications Society Annual Meeting (IASrsquo08) pp 1ndash6 IEEE Edmonton Canada October 2008

[15] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics (ISIE rsquo92)Xian China May 1992

[16] M Saito T Takeshita and N Matsui ldquoA single to threephase matrix converter with a power decupling capabilityrdquo inProceedings of the IEEE 35thAnnual Power Electronics SpecialistsConference (PESC rsquo04) pp 2400ndash2405 IEEEAachenGermanyJune 2004

[17] L A C Lopes and M F Naguib ldquoSpace vector modulationfor low switching frequency current source converters withreduced low-order noncharacteristic harmonicsrdquo IEEE Trans-actions on Power Electronics vol 24 no 4 pp 903ndash910 2009

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Scientific Programming 9

0

500

1000

1500

2000

2500

Out

put l

ine t

o lin

e vol

tage

s (V

)

05 1 15 2 250Modulation index

VabVbcVca

Figure 14 Modulation index characteristics at 200Hz referencefrequency

MCB

DSP

Gate driver core and base board

3-phase squirrel cage induction

motor

IGBT bidirectionalswitches

Voltage transducer

Miniature circuit breaker

SP2TP matrix converter hardware implementation schematic

Figure 15 Hardware realization of matrix converter system

The gate drive circuits and base board circuits are used toprovide the appropriate gate voltages to the bidirectionalswitches The developed hardware model is tested underdifferent power factor loads

Figure 16 shows the actual hardware experimental setupof the single-phase-to-three-phase matrix converter systemIGBT based bidirectional switches are used to design thematrix converter system Texas Instrument DSP and theConcept IGBTCoreDrives are used for the control operationSynchronization circuit is used to synchronize the sinusoidalsupply voltage with the control signals

The RMS values of the practical hardware circuits areslightly lower than the simulation circuits Figure 17 showsthe practical line to line voltages compared with the simula-tion data The variation is mainly due to the presence of oddharmonics in the hardware circuits

Figure 18 shows the percentage total harmonic distortion(THD) of the 119877-phase voltage under unity power factorload condition for both simulation and practical readings

Synchronizingcircuit

Matrixconverter

Three-phase induction motor

Digital signal processor

Interfacecircuit

IGBT coredriver circuit

Figure 16 Hardware realization of matrix converter system

Comparison between simulation and practical

SimulationPracticalVariation

050

100150200250

Line

to li

ne v

olta

ges (

V)

2 3 4 5 6 7 81Experimental reading samples

voltages (Vab)mdashunity Pf load

Figure 17 Comparison of simulation and practical line voltages

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Order of harmonics under simulation and

practical experimental conditions

020406080

100120

Har

mon

ic co

nten

t (

)

THD of matrix converter R-phasemdashunity Pf load

Figure 18 total harmonic distortion in the output voltage ofmatrix converter

Only odd harmonics are found to be present and the practicalTHD is slightly higher compared to the simulation valuesThis is obvious due to the presence of odd harmonics

7 Conclusion

Bidirectional switch based matrix converters are gettingmore popular due to their compact convenient and robustoperation State-of-the-art space vector PWM programmingand switching techniques are employed in the gate triggeringcontrol of the matrix converters The model was studiedunder different reference frequencies and modulation indexconditions The limitation of the proposed system is theunbalanced voltages produced due to odd harmonics pres-ence High harmonic contents are noticed which can be

10 Scientific Programming

eliminated by incorporating proper filter circuits Boostercircuits also can be used to obtain the desired output voltageThe modulation characteristics are studied in view of obtain-ing the balanced three-phase output voltages A significantbehavior is noticed when the SP2TP matrix converter isoperated above 150Hz with appropriate modulation indexthe output line to line voltages of the matrix converter arefound to be balanced and differ by 120∘ away from each otherand exactly resemble the three-phase system Adjustmenthas to be done at programming level to achieve the desiredoutcomes of the converter The magnitudes of the outputvoltages can be varied using booster circuits There are lotsof scopes for enhancing the system design through furtherresearch for more stable and quality outputs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J H H Alwash ldquoPredicting performance of three phaseinduction motors connected to single phase suppliesrdquo in IEEProceedings on Electric Power Applications vol 143 no 4 pp339ndash344 July 1996

[2] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics vol 2 pp547ndash550 Xian China May 1992

[3] V Agarwal and S Gupta ldquoAn efficient algorithm for generalisedsingle-phase converterrdquo IET Power Electronics vol 3 no 1 pp138ndash145 2010

[4] K Zhou and D Wang ldquoRelationship between space-vectormodulation and three-phase carrier-based PWM a compre-hensive analysis [three-phase inverters]rdquo IEEE Transactions onIndustrial Electronics vol 49 no 1 pp 186ndash196 2002

[5] S Kwak and H A Toliyat ldquoAn approach to fault-tolerant three-phase matrix converter drivesrdquo IEEE Transactions on EnergyConversion vol 22 no 4 pp 855ndash863 2007

[6] M-K Nguyen Y-G Jung Y-C Lim and Y-M Kim ldquoA single-phase Z-source buck-boost matrix converterrdquo IEEE Transac-tions on Power Electronics vol 25 no 2 pp 453ndash462 2010

[7] I K Shahidul D Z Phoivos and H R Muhammad ldquoNovelsingle- to three-phase static converterrdquo IEEE Transactions onIndustrial Applications vol 25 no 1 pp 143ndash152 1989

[8] M H El-Maghraby R H Thejel and M M Ibrahim ldquoNewapproach for the analysis of a three-phase induction motorof different ratings connected to a single-phase supplyrdquo IEEProceedings BmdashElectric Power Applications vol 139 no 3 pp145ndash154 1992

[9] J Xiao W Zhang H Omori and K Matsui ldquoA novel operationstrategy for single-to three-phase matrix converterrdquo in Proceed-ings of the 12th International Conference on Electrical Machinesand Systems (ICEMS rsquo09) pp 1ndash6 Tokyo Japan November2009

[10] J W Kolar F Schafmeister S D Round and H Ertl ldquoNovelthree-phase AC-AC sparse matrix convertersrdquo IEEE Transac-tions on Power Electronics vol 22 no 5 pp 1649ndash1661 2007

[11] K Iino K Kondo and Y Sato ldquoAn experimental study oninduction motor drive with a single phasemdashthree phase matrixconverterrdquo in Proceedings of the 13th European Conference onPower Electronics and Applications (EPE rsquo09) pp 1ndash9 BarcelonaSpain September 2009

[12] M ImayavarambanK Latha andGUma ldquoAnalysis of differentschemes ofmatrix converter withmaximum voltage conversionratiordquo inProceedings of the 12th IEEEMediterranean Electrotech-nical Conference (MELECON rsquo04) vol 3 pp 1137ndash1140 IEEEDubrovnik Croatia May 2004

[13] H Takahashi R Hisamichi and H Haga ldquoHigh power factorcontrol for current-source type single-phase to three-phasematrix converterrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo09) pp 3071ndash3076 San JoseCalif USA September 2009

[14] M Saito and N Matsui ldquoA single- to three-phase matrix con-verter for a vector-controlled induction motorrdquo in Proceedingsof the IEEE Industry Applications Society Annual Meeting (IASrsquo08) pp 1ndash6 IEEE Edmonton Canada October 2008

[15] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics (ISIE rsquo92)Xian China May 1992

[16] M Saito T Takeshita and N Matsui ldquoA single to threephase matrix converter with a power decupling capabilityrdquo inProceedings of the IEEE 35thAnnual Power Electronics SpecialistsConference (PESC rsquo04) pp 2400ndash2405 IEEEAachenGermanyJune 2004

[17] L A C Lopes and M F Naguib ldquoSpace vector modulationfor low switching frequency current source converters withreduced low-order noncharacteristic harmonicsrdquo IEEE Trans-actions on Power Electronics vol 24 no 4 pp 903ndash910 2009

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

10 Scientific Programming

eliminated by incorporating proper filter circuits Boostercircuits also can be used to obtain the desired output voltageThe modulation characteristics are studied in view of obtain-ing the balanced three-phase output voltages A significantbehavior is noticed when the SP2TP matrix converter isoperated above 150Hz with appropriate modulation indexthe output line to line voltages of the matrix converter arefound to be balanced and differ by 120∘ away from each otherand exactly resemble the three-phase system Adjustmenthas to be done at programming level to achieve the desiredoutcomes of the converter The magnitudes of the outputvoltages can be varied using booster circuits There are lotsof scopes for enhancing the system design through furtherresearch for more stable and quality outputs

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J H H Alwash ldquoPredicting performance of three phaseinduction motors connected to single phase suppliesrdquo in IEEProceedings on Electric Power Applications vol 143 no 4 pp339ndash344 July 1996

[2] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics vol 2 pp547ndash550 Xian China May 1992

[3] V Agarwal and S Gupta ldquoAn efficient algorithm for generalisedsingle-phase converterrdquo IET Power Electronics vol 3 no 1 pp138ndash145 2010

[4] K Zhou and D Wang ldquoRelationship between space-vectormodulation and three-phase carrier-based PWM a compre-hensive analysis [three-phase inverters]rdquo IEEE Transactions onIndustrial Electronics vol 49 no 1 pp 186ndash196 2002

[5] S Kwak and H A Toliyat ldquoAn approach to fault-tolerant three-phase matrix converter drivesrdquo IEEE Transactions on EnergyConversion vol 22 no 4 pp 855ndash863 2007

[6] M-K Nguyen Y-G Jung Y-C Lim and Y-M Kim ldquoA single-phase Z-source buck-boost matrix converterrdquo IEEE Transac-tions on Power Electronics vol 25 no 2 pp 453ndash462 2010

[7] I K Shahidul D Z Phoivos and H R Muhammad ldquoNovelsingle- to three-phase static converterrdquo IEEE Transactions onIndustrial Applications vol 25 no 1 pp 143ndash152 1989

[8] M H El-Maghraby R H Thejel and M M Ibrahim ldquoNewapproach for the analysis of a three-phase induction motorof different ratings connected to a single-phase supplyrdquo IEEProceedings BmdashElectric Power Applications vol 139 no 3 pp145ndash154 1992

[9] J Xiao W Zhang H Omori and K Matsui ldquoA novel operationstrategy for single-to three-phase matrix converterrdquo in Proceed-ings of the 12th International Conference on Electrical Machinesand Systems (ICEMS rsquo09) pp 1ndash6 Tokyo Japan November2009

[10] J W Kolar F Schafmeister S D Round and H Ertl ldquoNovelthree-phase AC-AC sparse matrix convertersrdquo IEEE Transac-tions on Power Electronics vol 22 no 5 pp 1649ndash1661 2007

[11] K Iino K Kondo and Y Sato ldquoAn experimental study oninduction motor drive with a single phasemdashthree phase matrixconverterrdquo in Proceedings of the 13th European Conference onPower Electronics and Applications (EPE rsquo09) pp 1ndash9 BarcelonaSpain September 2009

[12] M ImayavarambanK Latha andGUma ldquoAnalysis of differentschemes ofmatrix converter withmaximum voltage conversionratiordquo inProceedings of the 12th IEEEMediterranean Electrotech-nical Conference (MELECON rsquo04) vol 3 pp 1137ndash1140 IEEEDubrovnik Croatia May 2004

[13] H Takahashi R Hisamichi and H Haga ldquoHigh power factorcontrol for current-source type single-phase to three-phasematrix converterrdquo in Proceedings of the IEEE Energy ConversionCongress and Exposition (ECCE rsquo09) pp 3071ndash3076 San JoseCalif USA September 2009

[14] M Saito and N Matsui ldquoA single- to three-phase matrix con-verter for a vector-controlled induction motorrdquo in Proceedingsof the IEEE Industry Applications Society Annual Meeting (IASrsquo08) pp 1ndash6 IEEE Edmonton Canada October 2008

[15] M R Udayagiri and V S S Sarma ldquoSingle phase to threephase conversion without DC filterrdquo in Proceedings of the IEEEInternational Symposium on Industrial Electronics (ISIE rsquo92)Xian China May 1992

[16] M Saito T Takeshita and N Matsui ldquoA single to threephase matrix converter with a power decupling capabilityrdquo inProceedings of the IEEE 35thAnnual Power Electronics SpecialistsConference (PESC rsquo04) pp 2400ndash2405 IEEEAachenGermanyJune 2004

[17] L A C Lopes and M F Naguib ldquoSpace vector modulationfor low switching frequency current source converters withreduced low-order noncharacteristic harmonicsrdquo IEEE Trans-actions on Power Electronics vol 24 no 4 pp 903ndash910 2009

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Distributed Sensor Networks

International Journal of

Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014

International Journal of

ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia

International Journal of

Biomedical Imaging

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

ArtificialNeural Systems

Advances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Computational Intelligence and Neuroscience

Industrial EngineeringJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014