modiﬁed space vector modulated matrix converter with

Modified Space Vector Modulated MatrixConverter with Supply Current Quality

Improvement under Unbalanced Supply ConditionsPayal Patel, and Mahmadasraf A. Mulla, Senior Member, IEEE,

Abstract—In this work, a new input current modulationtechnique is presented for the matrix converter (MC) workingin the conditions of unbalanced supply. The proposed techniqueimproves the quality of the supply currents when the outputperformance of the MC is improved by considering the actualsupply voltage characteristics in the SVM technique. Whilethe balanced output voltages are produced by SVM techniqueunder unbalanced supply voltage condition, the MC inputperformance is degraded due to the injection of harmonics withthe low frequencies in the supply currents. In this condition,the supply current quality is upgraded by modifying the inputmodulation vector based on the positive/negative sequencecomponents of the supply voltages. The approaches adopted bythe existing input current modulation techniques to decomposethe positive/negative sequence components are complex andrequire large storage space. This drawback is overcome inthe presented technique by using the instantaneous powertheory to derive the input current modulation vector basedon the positive sequence components of the supply voltages.The presented technique of deriving input modulation vectordoes not require the complex and memory consuming sequencedecomposition methods and therefore can be realized easily ascompared to existing input modulation techniques of the MC.The effectuality of the new technique is confirmed by the resultsof simulation performed in PSIM software and real time resultsin OPAL-RT. Comparison of the presented technique is carriedout with two other techniques to show the effectiveness.

Index Terms—Harmonics, input current modulation, matrixconverter, space vector modulation, THD.

I. INTRODUCTION

THE matrix converter (MC) is a single stage AC-ACpower conversion device which is able to produce the

variable voltage with the variable frequency. Some distinctfeatures of the MC are sinusoidal input/output waveforms,four quadrant operation, adjustable power factor, long lifewith compact size due to the absence of energy storingelement [1][2][3][4]. Despite of having many advantages, theMC suffers from the several limitations which hinder its fullacceptance by the industry. The limitations of the MC arecomplexity of controlling nine bidirectional switches, limitedvoltage transfer ratio, sensitivity to the input disturbances,complicated commutation and protection etc.

Practically, the input voltages to the MC become unbal-anced and/or distorted due to the large number of asymmetricand nonlinear loads connected to the supply grid. Therefore,

Manuscript received July 1, 2020; revised November 6, 2020.Mahmadasraf A. Mulla is with the Department of Electrical Engineer-

ing, S. V. National Institute of Technology, Surat, India, (e-mail: [email protected]).

Payal Patel is with the Department of Electrical Engineering, S.V. National Institute of Technology, Surat, India, (e-mail: [email protected]).

it becomes necessary to examine the MC performance undersuch an abnormal input voltage conditions. In the MC, dueto the absence of energy storing element, the output per-formance is highly degraded in the presence of unbalancedand/or distorted power supplies [5]. In the literature, severalmodified modulation techniques for the MC are suggestedto eliminate the effects of unbalance/distortion present in theinput voltages on the MC output voltages[6], [7], [8], [9],[10], [11], [12], [13]. In [6] [7], the conventional Alesina-Venturini modulation technique of the MC is modified toproduce the required output voltages by calculating the dutyratios using the actual supply voltages. The MC outputperformance is enhanced by close loop control of the outputcurrents in [8]. Most widely used space vector modulation(SVM) strategy for the MC is modified in [9], [10], [11],[12], [13] for producing the balanced load voltages fromthe abnormal supply. The output performance of the MCis improved in [9] by modifying the modulation vector ofthe fictitious rectifier stage of the MC based on the nega-tive sequence components of the supply voltages. Feedbackand Feed-forward modulation techniques are presented in[10][11] to refine the output performance of the MC withthe unbalance present in the supply voltages. In [12][13],the required output performances of the MC are obtainedby considering the real supply voltages for the calculationsof the input modulation angle and modulation index of theSVM technique.

However, the above modulation techniques which upgradethe MC output performance in the presence of unbalancedinput voltages, degrades the input performance. Considerableamount of lower order harmonics are injected into the supplycurrents whilst balanced output voltages are generated bythe MC with the unbalanced supply [14]. With the purposeof improving the supply current quality in the presence ofsupply voltage unbalance, several input current modulationtechniques are suggested in the literature [15], [16], [17],[18], [19].

The dynamic modulation technique presented in [14], [15],[16], [17] modifies the input modulation vector of the MCbased on the positive and negative sequence components ofthe supply voltages. The input current modulation techniquesuggested in [18], modifies the input modulation vector usingthe positive sequence components of the supply voltages. Anotch filter based simplified technique is proposed in [20]which overcomes the realization difficulties associated withthe above input current modulation methods. The supplycurrents in [21] are improved by using the feedback controlloops on the input side of the MC. The method uses theresonant controllers to regulate the input active power and

Engineering Letters, 29:1, EL_29_1_15

Volume 29, Issue 1: March 2021

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a

b

c

A B C

SaA

SbA

ScA

SaB

SbB

ScB

SaC

SbC

ScC

Inp

ut

filt

er

DMC topology

Vdc

Sa

Saa

Sb

Sbb

Sc

Scc

SA

SAA

SB SC

SBB SCC

3-Ф

load

Idc

IdcVirtual CSR Virtual VSI

(a) (b)

3-Ф

su

pp

ly

3-Ф

su

pp

ly

3-Ф

load

Fig. 1. (a) Matrix converter topology and (b) Indirect equivalent circuit of matrix converter

V1(100)

V2(110)V3(010)

V5(001) V6(101)

0

1

2

3

4

5

V4(011)

vref

I1(ab)

I2(ac)

I3(bc)

I4(ba)

I5(ca)

I6(cb)

12

3

4 5

0

Iref

(a)

(b)

θi

θo

Fig. 2. Active switching vectors of (a) Rectifier and (b) Inverter stages

currents. Almost all above modulation techniques require thedecomposition the positive/negative sequence components toenhance the supply current quality. However, the realizationof decomposing positive/negative sequence components bythe conventional methods suffers from the large storagerequirements and/or high complexity.

This work proposes a new input current modulation tech-nique for the MC to refine the quality of the supply cur-rents under the conditions of unbalanced supply. The SVMtechnique upgrades the output performance of the MC byconsidering the actual input voltages as presented in [12][13].The degraded quality of the supply currents in the aboveconditions is refined by the new input current modulationtechnique developed based on the principle of instantaneous

power theory. The proposed technique modulates the inputvector in the direction of the positive sequence vector ofthe supply voltages. Unlike the existing input modulationtechniques, the presented technique realizes the above targetby using the principle of dual p-q theory. The instantaneousoscillating powers are used to calculate the voltage com-ponents corresponding to negative sequence and harmoniccomponents present in the supply voltages. The conventionalapproaches of decomposing sequence components for theexisting input modulation techniques require large memoryspace and therefore difficult to realize in the practice. Inthis work, the performances of the MC are compared forthe three different cases of input current modulations. Thecomparisons among the three cases are carried out basedon the amount of harmonics present in the supply currentsto prove the ability of new technique to upgrade the inputperformance of the MC. The results obtained by PSIM andOPAL-RT are presented to verify the effectiveness of theproposed input modulation technique.

This paper is organized in five sections. The modifiedSVM technique of the MC with the unbalanced supplyvoltages is explained in the section II. Section III explainsthe proposed input modulation technique. Simulation and realtime simulation results are presented and discussed in sectionIV. Section V includes the conclusion of the work.

II. SPACE VECTOR MODULATION OF MC WITHUNBALANCED SUPPLY VOLTAGES

In this section, the indirect SVM technique of the MC isexplained. The SVM technique provides the required outputperformance under the unbalanced supply voltage conditions[13]. Fig. 1 (a) shows the topology of the MC consistingof nine bidirectional switches. The indirect SVM techniqueis derived using the indirect equivalent circuit of the MCas represented in Fig. 1 (b). The SVM techniques of theconventional rectifier and the inverter are applied to the inputand output stages of the equivalent circuit of MC to calculatethe duty cycles. The duty cycles of both stages are combinedto obtain the duty cycles required to produce the switchingpulses for the nine bidirectional switches of the MC topology[22].



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Gate pulses

Clarke

Transformation

Clarke

Transformation

Space vector

Modulation

Input vector

& angle:

Eq.(3), (17)

Output vector

& angle:

Eq. (7), (18)

i

m

oInput

references

Matrix converterAv

Bv

Cv

ai

bi

ci Ci3 -

Ф s

up

ply

3 - Ф loadav

bv

cv

fC

fR

fLAi

Bi

Modulation indexiv iv

oAv oBv oCv

ov ov

Output

references

ivo

i

vm

v

ov

Fig. 3. MC modulation with the SVM technique

The modulations of the input and output stages of the MCusing the SVM technique require the input angle θi, outputangle θo and modulation index m. The conventional SVMtechnique of the MC does not incorporate the actual inputvoltage characteristics in the calculations of θi and m. As aresult, the conventional SVM technique fails to produce thebalanced output voltages in the presence of unbalanced anddistorted power supply.

The modified SVM technique presented in [13] overcomesthe above mentioned limitation of the conventional SVMtechnique by considering the actual characteristics of thesupply voltages in the calculations of θi and m. As aresult, the disturbances present in the supply voltages arecompensated and balanced voltages are obtained at the outputof the MC. The reference currents and voltages requiredto modulate the input and output stages of the indirectequivalent circuit are represented by Eq. (1) and Eq. (2)respectively. The reference currents are directly derived fromthe actual supply voltages va, vb and vc.

Iia = sinωit

Iib = sin

(ωit−

2π

3

)Iic = sin

(ωit+

2π

3

) (1)

where ωi represents the angular frequency of the supplyvoltages. Here it is shown that the input reference currentsfollow the supply voltages as directly derived from it.

voA = sinωot

voB = sin

(ωot−

2π

3

)voC = sin

(ωot+

2π

3

) (2)

where ωo represents the required output angular frequency.The six input and six output sectors associated with the

modulations of the virtual input and output stages of the MCare shown in Fig. 2 (a) and (b), respectively. Figure 2 (a)represents the six active current vectors I1-I6 and three nullvectors I0 associated with the modulation of input rectifierstage in form of hexagon. Similarly, the hexagon formed bythe six active voltage vectors V1-V6 and two zero vectors V0of the virtual output inverter stage of the MC are shown inFig. 2 (b).

Fig. 3 shows the block diagram of the MC operation withthe modified SVM technique considering the actual inputvoltages va, vb and vc. The input modulation angle θi iscalculated using the αβ components of these input voltagesrepresented as viα and viβ as given by Eq. (3). The inputangle θi decides the position of the input reference vector Iref

among the six input sectors. Let, Iref is in sector-1 as shownin Fig. 2 (a). Based on this, the input vector Iref is consideredto be synthesized by impressing the adjoining active vectorsI1 and I2 with duty cycles dγ and dδ respectively ascalculated by Eq. (4)-(6).

θi = tan−1viβviα

(3)

Iref = I1 · dγ + I2 · dδ (4)

dγ = mc · sin(π3− θr

)(5)

dδ = mc · sin (θr) (6)

where mc is the modulation index. θr = θi−(Sr−1)· π3 is theangle which represents the position of Iref in the respectiveinput sector. Sr represents the input sector number.

Similarly, the output modulation angle θo is calculatedusing the αβ components voα and voβ of the output referencevoltages voA, voB and voC as given by Eq. (7). Let, the output



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reference vector is in sector-1 as shown in Fig. 2 (b). Thecorresponding equations of the output reference vector Vrefand duty cycles are given by Eq. (8)-(10).

θo = tan−1voβvoα

(7)

Vref = V1 · dα + V2 · dβ (8)

dα = mv · sin(π3− θv

)(9)

dβ = mv · sin (θv) (10)

where mv is the modulation index. θv = θo−(Sv−1)·π3 is theangle which represents the position of Vref in the respectiveoutput sector. Sv represents the output sector number.

The combined duty cycles of the MC are calculated byEq. (11)-(15).

dαγ = dα · dγ = m · sin(π3− θv

)· sin

(π3− θi

)(11)

dαδ = dα · dδ = m · sin(π3− θv

)· sin (θi) (12)

dβγ = dβ · dγ = m · sin (θv) · sin(π3− θi

)(13)

dβδ = dβ · dδ = m · sin (θv) · sin (θi) (14)

d0 = 1− dαγ − dαδ − dβγ − dβδ (15)

where m is the overall modulation index of the MC ascalculated by Eq. (16).

m = mc.mv =|vo||vi|

(16)

where |vi| and |vo| are obtained by the αβ components of theactual input and the output reference voltages as representedby Eq. (17) and Eq. (18), respectively. The modulationindex m in Eq. (16) assumes the variable amplitude forthe abnormal supply voltage conditions. The m adjusts itselfaccording to the actual characteristics of the supply voltages.

|vi| =√v2iα + v2iβ (17)

|vo| =√v2oα + v2oβ (18)

Thus, the modifications incorporated in the calculations ofθi, θo and m according to the actual input voltages ensure thesinusoidal and balanced output waveforms in the unbalancedsupply voltage conditions.

Nevertheless, the above condition introduces the largeamount of lower order harmonics, esp. 3rd and 5th, intothe supply currents degrading the quality of the supply asdiscussed previously [14]. This necessitates the use of any ofthe input modulation techniques suggested in[16], [15], [17]to use with the SVM technique to upgrade the supply currentquality. These techniques make use of positive/negative se-quence components of the supply voltages to derive the inputreferences for the SVM technique. This helps in reducingthe supply current harmonics when balanced voltages aregenerated at the output of the MC.

III. PROPOSED INPUT MODULATION TECHNIQUE

In this section, the new technique of deriving the inputreference currents for the MC is developed to improve thesupply current quality. This new technique is derived basedon the dual p-q theory explained in [23] for 3-phase, 3-wire system. Section III-A explains the distribution of theharmonics in the MC supply currents due to the modifiedSVM technique. In Section III-B, the proposed technique ofderiving the input modulation vector is explained in detail.

Consider the MC operation in the unbalanced supplyvoltage conditions. The MC produces the balanced outputvoltages using the modified SVM technique [12][13]. Thesupply voltages and currents to the MC in abc and αβreference frames are represented as follows:

vabc =

vavbvc

abc−αβ−→ viαβ =

[viαviβ

](19)

iabc =

iaibic

abc−αβ−→ iiαβ =

[iiαiiβ

](20)

where vabc and iabc are the supply voltage and current vectorsin abc reference frame. viα and viβ are components ofvabc in αβ reference frame. Similarly, iiα and iiβ are αβcomponents of iabc. The components viα and viβ can berepresented as follows due to the unbalanced nature of thesupply voltages.

viα = viα++ viα− (21)

viβ = viβ+ + viβ− (22)

where viα+and viβ+

represent the αβ components ofpositive sequence supply voltages. Similarly, viα− and viβ−

represent the αβ components of negative sequence voltagespresent in the supply.

A. MC supply currents with the modified SVM techniqueunder unbalanced supply voltage conditions

The MC performance is already examined in [12], [13],[14] for the unbalanced supply voltage conditions. The oddharmonics are introduced into the supply currents when thebalanced load voltages are produced by the MC from theunbalanced supply [12]. Therefore, iiα and iiβ componentsof the supply currents can be represented in terms of positivesequence, negative sequence and harmonic components asfollows:

iiα = iiα++ iiα− + iiαh

(23)

iiβ = iiβ+ + iiβ− + iiβh(24)

where iiα+and iiβ+

represent the αβ components of thepositive sequence supply currents. Similarly iiα− , iiβ− andiiαh

, iiβhrepresent the αβ components of the negative

sequence and harmonic components present in the supplycurrents respectively.



______________________________________________________________________________________

Fig. 4. Control diagram of deriving input modulation signals using proposed technique

Fig. 5. Extraction of oscillating power components from the instantaneousactive and reactive powers using low pass filter

B. Derivation of MC input modulation vector

The instantaneous p-q theory decomposes the currentcomponents corresponding to the various active and reactivepower components. On the other hand, the voltage compo-nents corresponding to the various active and reactive powercomponents are derived using the dual p-q theory [23]. Boththese instantaneous theories are dual of each other. Recently,Farnaz et. al. presented the enhanced instantaneous powertheory (EIPT) with the new approach of decomposing thevarious current components in the unbalanced and distortedsupply conditions [24]. It is shown in [24] that, by using thisoscillating power component and the voltage components,the unbalance and distorted components of the currents canbe calculated. Using the similar approach and the duality,the present work develops the new technique of derivingthe input reference vector for the MC under the unbalancedsupply voltage condition. In this work, the unbalanced anddistorted components of the voltages are calculated by usingthe supply current components and the instantaneous oscil-lating components of the power. Figure 4 shows the controldiagram of the MC including the proposed input modulationtechnique.

The αβ components of the supply voltages measured afterthe input filter are represented as follows:

viα = viα+ + viα− + viαh(25)

viβ = viβ++ viβ− + viβh

(26)

where viαhand viβh

represent the harmonic components in-jected into the supply voltages as a result of the voltage dropacross the source and filter impedance by the distortion inthe supply currents. However, the amount of these harmoniccomponents is very small.

According to the instantaneous power theory, the activeand reactive powers are calculated using the αβ componentsof the supply voltages and currents as given below:

piαβ = viαiiα + viβiiβ (27)

qiαβ = viβiiα − viαiiβ (28)

where piαβ and qiαβ represent the instantaneous active andreactive powers.

The instantaneous active and reactive powers are repre-sented in terms of average and oscillating components asgiven by Eq. (29) and (30). The presence of the oscillatingterm in the power is due to the unbalance present in thepower supply.

piαβ = piαβ + piαβ (29)

qiαβ = qiαβ + qiαβ (30)

where piαβ and qiαβ represent the average active and reactivepower components, respectively. The oscillating componentsof the active and reactive powers are represented by piαβand qiαβ , respectively.

The oscillating power components are extracted from theinstantaneous active and reactive powers using the low passfilter as shown in the Fig. 5. The oscillating power termspiαβ and qiαβ are separated by subtracting the averagepower components piαβ and qiαβ obtained at the output ofthe low pass filter from piαβ and qiαβ , respectively. Basedon the principle of dual p-q theory and the formulationsof the current components in EIPT presented in [24], thevoltage components corresponding to the oscillating powercomponents piαβ and qiαβ are calculated using the Eq. (31)and Eq. (32).

˜viα =iiα

i2iα + i2iβpiαβ +

iiβi2iα + i2iβ

qiαβ (31)

viβ =iiβ

i2iα + i2iβpiαβ −

iiαi2iα + i2iβ

qiαβ (32)

where ˜viα and viβ represent the unbalanced and distortedvoltage components of the supply voltages. As the amountof harmonics is small in the supply voltages, these oscillatingvoltage components ˜viα and viβ dominated with the negativesequence components of the supply voltages. ˜viα and viβ arerepresented by Eq. (33) and (34).

˜viα = viα− + viαh(33)

viβ = viβ− + viβh(34)

Now, the input modulation vector components v∗iα and v∗iβare derived by subtracting the oscillating voltage components˜viα and viβ from the supply voltage components viα and viβ

as represented by following expressions:

v∗iα = viα − ˜viα = viα+(35)

v∗iβ = viβ − viβ = viβ+(36)



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Gate pulses

Matrix converter

Av

Bv

Cv

ai

bi

ci Ci

iv

Clarke Transformation

ii

iv

Space vector Modulation

i

o

i

vm

v

m

o

ov

3 - Ф supply 3 - Ф load

Input vector: Eq. (17)

Proposed technique:

Eq. (27)-(36)

iv

ii

av

bv

cv

fC

fR

fL

Modulation indexInput angle:

Clarke Transformation

Output reference: Eq. (2)

Output vector & angle: Eq. (7), (18)

Ai

Bi

iv

iv

oAv oBv oCv

of

ov ov

ai cibi av bv cv

1 *tan i iv v

Input filter

Input modulation technique Output modulation technique

Fig. 6. Block diagram of MSVM modulated MC with proposed input modulation technique

It is shown that the αβ components of the input modulationvector contain only the positive sequence components of thesupply voltages. This is similar to the well established inputmodulation technique presented in [17][18] which utilizesthe positive sequence components of the supply voltages forthe input modulation of the MC. Therefore, the proposedtechnique is expected to provide the performance similar tothat obtained with the input modulation scheme of [17][18].The presented approach of deriving the input modulationvector does not need complex and memory consumingsequence decomposition methods which leads to the easyimplementation. Now, v∗iα and v∗iβ are used in Eq. (3) and(17) instead of viα and viβ to calculate the input referencevector and input angle, respectively as represented by Eq.(37) and (38), respectively.

|vi| =√v∗2iα + v∗2iβ (37)

θi = tan−1v∗iβv∗iα

(38)

Figure 6 shows the modified SVM scheme to control theMC with the proposed input modulation technique in theunbalanced supply voltage conditions.

IV. RESULTS AND DISCUSSION

In this section, the performance of the MC modulatedwith the SVM technique is evaluated by applying newinput modulation technique in the presence of unbalancedsupply voltages. The MC performances for the three differentcases are compared in order to verify the effectiveness ofthe new input current modulation technique. The supply

TABLE ISIMULATION PARAMETERS

System parameter Description ValueSource parameters Frequency (fi) 50 HzFilter parameters Inductor (Lf ) 2 mH

Capacitor (Cf ) 18 µFResistance (Rf ) 58 Ω

Load parameters Resistance (RL) 10 ΩInductance (LL) 10 mH

Control parameters Carrier frequency (fc) 5 kHz

current qualities of the MC for the three cases are com-pared based on the amount of harmonics. Case-1 includesthe operation of the MC with the SVM technique withoutmodifying the input modulation vector [13]. In case-2, theinput reference vector is modulated in the same directionto that of positive sequence vector of the supply voltages[17]. In this case, the positive sequence components aredecomposed using the Fortescue theorem. In Case-3, theinput reference vector is derived using the proposed inputcurrent modulation technique. The simulations are performedin the PSIM environment. The system parameters in thesimulation are chosen according to the Table I. The real timeresults for the MC are obtained by the OPAL-RT integratedwith MATLAB/Simulink. The setup of OPAL-RT integratedwith MATLAB/Simulink is shown in Fig. 7. The real timesimulation parameters are shown in Table II.

The comparison of the MC performance for the abovethree cases is carried out in the presence of unbalanced



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Fig. 7. Real time simulation set up using OPAL-RT

Fig. 8. Simulation results of supply currents: (a) Case-1 (b) Case-2 and(c) Case-3 TABLE II

REAL TIME SIMULATION PARAMETERS

System parameter Description ValueSource parameters Frequency (fi) 50 HzFilter parameters Inductor (Lf ) 5 mH

Capacitor (Cf ) 15 µFResistance (Rf ) 48 Ω

Load parameters Resistance (RL) 15 ΩInductance (LL) 15 mH

Control parameters Carrier frequency (fc) 3.7 kHz

supply voltages as given in Eq. (39).

va = vm sin(ωit)

vb = 0.7vm sin(ωit− 2π/3)

vc = 1.4vm sin(ωit+ 2π/3)

(39)

where the values of vm and f are chosen to be 255√2 V

and 50 Hz respectively.As the MC is controlled by SVM technique by considering

the actual supply voltages, the balanced output currents

Fig. 9. Harmonic spectrums of simulated supply currents for the threecases: (a) Phase-a (b) Phase-b and (c) Phase-c

are expected in all three cases. The input performances ofthe MC are evaluated based on the amount of harmonicspresent in the supply currents. The index terms used toanalyze the presence of the harmonics in the supply currentsare: harmonic distortion (HD), frequency weighted harmonicdistortion (FHD) and total harmonic distortion (THD). Theexpressions of HD, FHD and THD are given below [17],

HD =

√∑∞h=3,5.. ih

i1

(40)

FHD =

√∑∞h=3,5..(ih/h)

i1

(41)

THD =

√∑∞h=3,5.. i

2h

i1

(42)

where h, ih and i1 represent the order of the harmonic,magnitude of the harmonic and fundamental supply currentcomponents respectively.

The simulation results of the supply currents for the case-1, 2 and 3 are shown in the Fig. 8. It is observed thatthe supply currents in case-1 are much more distorted ascompared to case-2 and case-3. Fig. 12 includes the harmonicspectrums of the supply currents obtained in the three cases.Fig. 10 compares the supply currents of the MC for thethree cases on the basis of %HD, %FHD and %THD. Thecomparison carried out in terms of %HD is shown in Fig. 10(a). The %HD of the supply currents in case-1 are highest



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Fig. 10. Comparison of simulated supply currents based on: (a)%HD,(b)%FHD and (c)%THD

Fig. 11. Experimental results of the supply currents: (a) case-1 (b) case-2and (c) case-3

whereas lowest in case-3. In Fig. 10 (b), the supply currentsare compared based on the %FHD. The %FHD are highestfor the supply currents in case-1 and lowest for the supplycurrents of case-3. However, there is no major differencebetween the performances of the supply currents in case-2

Fig. 12. Harmonic spectrums of experimental supply currents for the threecases: (a) Phase-a (b) Phase-b and (c) Phase-c

and case-3. Fig. 10 (c) represents the comparison of MCsupply currents for the three cases based on %THD. Case-1 provides the highest %THD of the supply currents. Thesupply current %THDs are nearly equal in case-2 and 3and are remarkably lower than case-1. Comparison of theMC input performances in the above three cases prove thepotential of the new technique to upgrade the supply currentquality. The real time results of the MC supply currentsobtained for the three above cases are shown in Fig. 11. Theharmonic spectrums of these experimental supply currentsare compared in Fig. 12. Fig. 13 shows the comparison ofthese currents based on%HD, %FHD and %THD. Theseresults also prove the ability of the proposed techniqueto reduce the harmonics from the supply currents in thepresence of unbalance supply. The performance exhibited bythis new technique is approximately similar to that of theperformance obtained in case-2.

Fig. 14 shows the load current waveforms of the MCobtained in the three cases. It is observed that the outputcurrents are balanced and nearly sinusoidal in the nature.The comparisons of the load currents for the three cases arepresented in Fig. 15 (a) and (b) based on %THD and peakamplitude of the fundamental components, respectively. Thevalue of %THD is approximately 5% for the load currentsin all the three cases. Also, the peak amplitudes of the loadcurrents in three cases are approximately same. This provesthe effectuality of SVM technique to yield the balanced and



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Fig. 13. Comparison of experimental supply currents based on: (a)%HD,(b)%FHD and (c)%THD

Fig. 14. Simulation results of load currents: (a) case-1 (b) case-2 and (c)case-3

Fig. 15. Comparison of simulated load currents based on: (a) %THD and(b) peak amplitude of fundamental component

Fig. 16. Experimental results of the load currents: (a) case-1 (b) case-2and (c) case-3

sinusoidal output currents in the presence of unbalancedsupply voltages. The real time results of load currents forthe three considered cases are represented in Fig. 16 whichare approximately similar to the simulation results. Fig. 17(a) and (b) represent the %THD and peak amplitudes of thefundamental components of the experimentally obtained loadcurrents, respectively. Approximately 6.5 %THD and 5 Vpeak amplitudes are obtained for the load currents in all thethree cases.

The simulation and the real time results of the outputline voltages obtained in case-3 are shown in Fig. 18 and



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Fig. 17. Comparison of experimental load currents based on: (a) %THDand (b) peak amplitude of fundamental component

Fig. 18. Simulation results of balanced load voltages (line) produced bySVM technique

Fig. 19. Experimental results of load voltages (line) produced by MSVMtechnique

Fig. 19, respectively. Figure 20 shows the comparison ofthe fundamental components of the output line voltagesobtained by the simulation and the experiment. It is shownthat the peak amplitudes of all output line voltages areapproximately 140 V. This shows that the improvement inthe supply currents by the proposed technique does not affectthe generation of the ability of the SVM technique to provide

Fig. 20. Comparison of the fundamental amplitudes of the output linevoltages obtained by the simulation and experiment.

the balanced output voltages for the MC.The comparison of the MC input performance under

the unbalanced supply conditions proves the ability of thepresented new input modulation technique to reduce thesupply current harmonics. It is observed that the harmonicsin the supply currents are reduced up to the considerableamount in case-2 and case-3 in comparison with the case-1.The output performance of the MC in case-3 is not affectedby the new input modulation technique similar to case-1 andcase-2.

V. CONCLUSION

This work introduces the new input current modulationtechnique for the MC. The new technique improves thesupply current quality of the MC when the supply voltagesare unbalanced. The new technique developed on the conceptof dual p-q theory modulates the input reference vector ofthe MC in the same direction to that of positive sequencecomponents of the supply. The presented technique calculatesthe voltage components corresponding to the oscillatingpower components of the total instantaneous power to derivethe input modulation vector of the MC. These voltage com-ponents correspond to the negative sequence and harmoniccomponents present in the supply voltages. This is differentfrom most of the existing input modulation techniques whichare highly dependent on the sequence decomposition algo-rithms requiring the large storage space for the realization.The harmonics present in the supply currents are successfullyreduced by the new input modulation technique withoutaffecting the output performance of the MC. The presentedwork is validated by the simulation results obtained in PSIMand test results of real-time simulations performed in OPAL-RT.

REFERENCES

[1] L. Empringham, J. W. Kolar, J. Rodriguez, P. W. Wheeler, andJ. C. Clare, “Technological issues and industrial application of matrixconverters: A review,” IEEE Transactions on Industrial Electronics,vol. 60, no. 10, pp. 4260–4271, 2013.

[2] L. Huber and D. Borojevic, “Space vector modulated three-phase tothree-phase matrix converter with input power factor correction,” IEEEtransactions on industry applications, vol. 31, no. 6, pp. 1234–1246,1995.

[3] Sirichai and Tammaruckwattana, “Modeling and simulation of windpower generation system using ac to ac converter,” International Mul-tiConference of Engineers and Computer Scientists (IMECS), vol. 2,pp. 593–597, March 16-18, 2016.

[4] H. Karaca and R. Akkaya, “Control of venturini method based matrixconverter in input voltage variations,” International MultiConferenceof Engineers and Computer Scientists (IMECS), vol. 2, March 18-20,2009.



______________________________________________________________________________________

[5] P. Enjeti and X. Wang, “A critical evaluation of harmonics generatedby forced commutated cycloconverters (fcc’s) under unbalance,” in[Proceedings] IECON’90: 16th Annual Conference of IEEE IndustrialElectronics Society. IEEE, 1990, pp. 1162–1168.

[6] A. Dastfan and M. Haghshenas, “Design and simulation of a powersupply based on a matrix converter under unbalanced input voltage,”in Universities Power Engineering Conference, 2006. UPEC’06. Pro-ceedings of the 41st International, vol. 2. IEEE, 2006, pp. 569–573.

[7] L. Zhang, C. Watthanasarn, and W. Shepherd, “Control of ac-ac matrixconverters for unbalanced and/or distorted supply voltage,” in 2001IEEE 32nd Annual Power Electronics Specialists Conference (IEEECat. No. 01CH37230), vol. 2. IEEE, 2001, pp. 1108–1113.

[8] H. Karaca, R. Akkaya, and H. Dogan, “A novel compensation methodbased on fuzzy logic control for matrix converter under distortedinput voltage conditions,” in 2008 18th International Conference onElectrical Machines. IEEE, 2008, pp. 1–5.

[9] C. Xiyou, C. Xueyun, and W. Qi, “The improvement of space vectormodulation strategy for matrix converter under unbalanced inputvoltages,” Transactions of China Electrotechnical Society, vol. 15,no. 2, pp. 78–82, 2000.

[10] M. Jussila and H. Tuusa, “Comparison of simple control strategiesof space-vector modulated indirect matrix converter under distortedsupply voltage,” IEEE Transactions on Power Electronics, vol. 22,no. 1, pp. 139–148, 2007.

[11] P. Nielsen, F. Blaabjerg, and J. K. Pedersen, “Space vector modulatedmatrix converter with minimized number of switchings and a feedfor-ward compensation of input voltage unbalance,” in Power Electronics,Drives and Energy Systems for Industrial Growth, 1996., Proceedingsof the 1996 International Conference on, vol. 2. IEEE, 1996, pp.833–839.

[12] X. Wang, H. Lin, H. She, and B. Feng, “A research on space vectormodulation strategy for matrix converter under abnormal input-voltageconditions,” IEEE Transactions on Industrial Electronics, vol. 59,no. 1, pp. 93–104, 2012.

[13] P. Patel and M. A. Mulla, “Modified space vector modulated three-phase to three-phase matrix converter under unbalanced supply con-ditions,” in 2018 8th IEEE India International Conference on PowerElectronics (IICPE). IEEE, 2018, pp. 1–6.

[14] D. Casadei, G. Serra, and A. Tani, “A general approach for the analysisof the input power quality in matrix converters,” IEEE Transactions

on Power Electronics, vol. 13, no. 5, pp. 882–891, 1998.[15] F. Blaabjerg, D. Casadei, C. Klumpner, and M. Matteini, “Comparison

of two current modulation strategies for matrix converters underunbalanced input voltage conditions,” IEEE Transactions on IndustrialElectronics, vol. 49, no. 2, pp. 289–296, 2002.

[16] D. Casadei, G. Serra, and A. Tani, “Reduction of the input currentharmonic content in matrix converters under input/output unbalance,”IEEE Transactions on Industrial Electronics, vol. 45, no. 3, pp. 401–411, 1998.

[17] P. Patel and M. A. Mulla, “Supply current quality improvement forthree-phase matrix converter under unbalanced supply voltage condi-tions,” in 2018 IEEE International Conference on Power Electronics,Drives and Energy Systems (PEDES). IEEE, 2018, pp. 1–6.

[18] X. Li, M. Su, Y. Sun, H. Dan, and W. Xiong, “Modulation strategiesbased on mathematical construction method for matrix converter underunbalanced input voltages,” IET Power Electronics, vol. 6, no. 3, pp.434–445, 2013.

[19] Y. Yan, H. An, T. Shi, and C. Xia, “Improved double line voltagesynthesis of matrix converter for input current enhancement underunbalanced power supply,” IET Power Electronics, vol. 6, no. 4, pp.798–808, 2013.

[20] J. Lei, B. Zhou, J. Bian, X. Qin, and J. Wei, “A simple method forsinusoidal input currents of matrix converter under unbalanced inputvoltages,” IEEE Transactions on Power Electronics, vol. 31, no. 1, pp.21–25, 2015.

[21] J. Lei, B. Zhou, J. Bian, J. Wei, Y. Zhu, J. Yu, and Y. Yang, “Feedbackcontrol strategy to eliminate the input current harmonics of matrixconverter under unbalanced input voltages,” IEEE Transactions onPower Electronics, vol. 32, no. 1, pp. 878–888, 2016.

[22] P. Patel and M. A. Mulla, “Space vector modulated three-phase tothree-phase direct matrix converter,” in 2016 IEEE 16th InternationalConference on Environment and Electrical Engineering (EEEIC).IEEE, 2016, pp. 1–6.

[23] H. Akagi, E. H. Watanabe, and M. Aredes, Instantaneous power theoryand applications to power conditioning. John Wiley & Sons, 2017.

[24] F. Harirchi and M. G. Simoes, “Enhanced instantaneous power theorydecomposition for power quality smart converter applications,” IEEETransactions on Power Electronics, vol. 33, no. 11, pp. 9344–9359,2018.



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modiﬁed space vector modulated matrix converter with

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