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Abstract - In this paper; simulation, design, and

implementation of three-phase to three-phase matrix

converter using Venturini modulation algorithm have been

presented. Furthermore, effects of input filter on stability of

matrix converter have been examined. A Simulink model

has been developed in such a way that it supports real time

work with the use of DSP control card supported by

Simulink. Simulation and experimental results for the input

and output waveforms of the matrix converter using R-L

load are given at various operating conditions. Goodagreement was obtained between the simulation results and

the results obtained from the prototype.

Index Terms- Matrix converter, Venturini modulation

algorithm

I. I NTRODUCTION

Matrix converter is a static circuit which consists of an array of bidirectional switches connected betweensupply and load in matrix form. It provides single or three-phase variable voltage and frequency source at its

output from 3-phase fixed input supply without requiringany intermediate dc link. Hence, the power/volume ratioof the converter is higher then that of the other type of converters such as diode-bridge rectifier fed inverters. The converter is capable of operating at lagging, unity or even leading fundamental input displacement factor,regardless of the load displacement factor. The converter offers the advantages of four quadrant operation,sinusoidal input and output waveforms, minimum energystorage components and controllable displacement factor [1]. Because of these advantages, matrix converters

become an important alternative to voltage sourceinverters.

There are many researches carrying on matrixconverters about the modulation techniques and power circuit improvements. The main idea of the modulationalgorithms for controlling the output voltage is to chopthree-phase input voltages at the proper instant and for atime to construct single or three-phase output voltagewaveforms which have a desired amplitude andfrequency with low harmonic distortion. Since there are anumber of switches in the power circuit the controlalgorithms should be able to perform all the processesmentioned above with a minimum switching frequency.This is important from the point of switching losses [2,3].

One of the modulation algorithms which is mostly

used in matrix converters is Venturini control algorithm. In this algorithm, the output voltage amplitude is

restricted to the half of input voltage amplitude.However, this rate can be increased up to 0.866 by addingthe third harmonics of the input and output voltages to thedesired output voltage waveform [3,4].

In order to calculate the target output voltages it isnecessary to know the instantaneous input voltages.Therefore, from the point of the correct calculations the

process of measuring the instantaneous input voltages

becomes crucial because of both the possible noises onthe input voltage waveforms and filtering process.

There would be notching and spikes on the inputvoltage waveforms in case of high power applications or voltage supplies with having high impedance and strayinductances. In this case, the instantaneous value of theinput voltage might be inaccurately measured and as aresult the target voltages would be incorrectly calculated.Filtering the input voltages of the matrix converter willresult in phase shift, which will affect the calculations [1].

Fig.1. Schematic representation of matrix converter

In this work, simulation and implementation of athree-phase matrix converter fed by a three-phase supplyhaving high impedance has been performed and particular attention was paid to the input filter. First, importanceand design of the input filter will be discussed. Then,simulation and experimental results from a three-phase

matrix converter with and without having input filter will be given and discussed.

II. I NPUT FILTER

Matrix converters produce reactive harmonic currentsto the ac supply because of their discontinuous inputcurrents. These harmonic currents cause voltagedistortions which affect the operation of the matrixconverter. At the switching process of the converter voltage spikes will be produced in both input and outputof the converter because of high di/dt and dv/dt rates bythe presence of stray inductance.

Spikes on the input voltage waveforms cause wrong

detection of the input voltages and instantaneous inputvector position which is required to be used by Venturini

Effects of Input Filter on Stability of MatrixConverter Using Venturini Modulation Algorithm

Ebubekir ERDEM1, Yetkin TATAR 2, Sedat SÜNTER 3 1, 2Department of Computer Engineering, Faculty of Engineering, Firat University, 23119, Elazıg, Turkey

3Department of Electrical and Electronic Engineering, Faculty of Engineering, Firat University, 23119, Elazıg, Turkey1e-mail: [email protected] 2 e-mail: [email protected] 3 e-mail: [email protected]

978-1-4244-7919-1/10/$25.00 ©2010 IEEE

SPEEDAM 2010

International Symposium on Power Electronics,

Electrical Drives, Automation and Motion

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control algorithm. Fig.2 shows the input voltagewaveform of the matrix converter without using filter.Here, we can see the voltage spikes with maximuminstantaneous value of 150V feeding the matrixconverter. For instance, let’s consider the situation wherethe real instantaneous input voltage is about 140V.

Because of the spikes this instantaneous value would beincorrectly measured as 120V or 174V. Therefore, thiswould cause wrong calculations in Venturini algorithm.

Figure 2. Unfiltered input voltage waveform.

In order to prevent this undesired situation a secondorder L-C filter is usually used at the input of the matrixconverter [5,6].

Fig.3 shows filter topologies used in the matrixconverter input where C components are usually used todecrease the voltage disturbances occurred on the inputvoltages and they should be placed as close as to the

bidirectional switches. In order to limit slope of thecirculating currents, filter inductances are used since no-active protection exists during circulation instants [1,5].

Fig.3. Basic input filter configurations used in matrix converter a) Capacitors star or delta connected b) Second order LC filter

c) LC filter with parallel damping resistors.

According to various national and internationalagencies (such as IEEE), magnitudes of harmoniccurrents and harmonic voltage distortion of a power electronic equipment connected to the utility have to belimited below specified limits. Input filters are a solutionto limit THD. In this work, an L-C filter which is mostly

preferred in the matrix converters has been used as shownin Fig.3(c).

By considering Eq(1), the filter inductance iscalculated as L=2.93 mH for C=12.5 Fμ . Switching

frequency (f s) and cutting frequency (f c) are taken as 2

kHz and 830 Hz, respectively.

LC f c

π 2

1= (1)

III. VENTURINI CONTROL ALGORITHM

Schematic representation of three-phase to three-

phase matrix converter used in this work is illustrated inFig.4. Venturini algorithm has been used for modulation.

Fig.4. Schematic representation of 3x3 phase matrix converter

Venturini control algorithm provides variable voltagefrequency source to the load by controlling bidirectionalswitches which are connected between the input supplyand load. As can be seen in Fig.4, the subscripts, a,b,crepresent the input of the converter whereas A,B,Crepresent the output. In this algorithm the maximumoutput voltage rate of the converter is restricted to thehalf of the input (q≤ 0.5). However, this can be increasedup to 0.866 by adding third harmonics of the input and

output voltage waveforms. For unity input displacementfactor, duty cycle for the switch connected between theinput phase, β and output phase, γ can be defined as [3,4];

⎥⎥⎦

⎤

⎢⎢⎣

⎡Ψ+++= )3sin()sin(

9

2

3

2

3

12

t t q

q

V

V V TsT ii

mim

ioω ω β

β γ γβ (2)

Where; ψ β: 0, 2π/3, 4π/3 corresponds to the input phasesa, b and c, respectively, qm is the maximum voltage ratio(0.866), q is the desired voltage ratio, Vim is the inputvoltage vector magnitude and Voγ is given by;

)3cos(4

)3cos(6

)cos(

t V q

q

t V q

t qV V

iimm

oimoimo

ω

ω ω γ γ

+

−Ψ+=

(3)

Where; ψ γ :0, 2π/3, 4π/3 corresponds to the output phasesA, B and C, respectively and ω o is angular outputfrequency.

IV. SIMULATION AND IMPLEMENTATION OF THE

SYSTEM

The modified Venturini algorithm (Eq(2-3)) has beenused to calculate the duty cycle of the bidirectional

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switches [3]. Fig.5 shows Simulink model of the three- phase matrix converter with Venturini modulationalgorithm. This model consists of three parts. First partcontains the supply voltage blocks. Generation of theduty cycles of the devices are placed in the second partand finally third part consists of nine bidirectional

switches. Ideal switches are used in the Matlab/Simulink model [7].Equations (2) and (3) are evaluated every sampling

period with updated values to calculate the duty cyclesfor the switches. As can be seen from Fig.5, the algorithmonly requires the instantaneous three phase input voltagesto be measured from which the input vector position iscalculated as follows;

))

3

1

3

2(3

arctan(

bcab

bci

V V

V t

+

−=ω (4)

)(

9

4 222bcabbcabim V V V V V ++= (5)

Hence, the duty periods of the switches whichconnect each input phase to one output phase during oneswitching period can be calculated by using Eq(2) and (3)(for instance these times will be tAa, tAb, tAc for output

phase, A). The duty cycle generation block for one

output phase of the matrix converter is given in Fig.6 indetail (0≤ q≤ 0.866) where modified Venturini algorithmis used. The related input phase is connected to therelated output phase during a period, which is calculatedin this generation block.

For the real time application of Venturini algorithm,

the switching blocks forming the input and outputvoltages in the simulation model shown in Fig.5 has beenremoved and instead voltage transducers (Model:LV25-P) and MUX-ADC which is required to convert thismeasured voltages for DSP environment are placed. I/O

blocks are placed instead of the switches. Hence,experimental models have been obtained by thesemodifications. These models are converted to the real-time codes by “Real-Time Workshop” in Simulink and“Real-Time Interface” software of DSPACE. “Real-TimeInterface” software is added to Simulink block library. Alink is constructed between Simulink and real-timehardware by these additional blocks. In addition, real-

time control signals and voltage and current data takenfrom ADC can be measured by “Control Desk Developer” software and are saved in a computer environment to be analyzed later. DS1103 dSPACEGmbH control board has been used for controlling theconverter [8].

Figure 5. Simulink model of the matrix converter with Venturini control algorithm ( 866.00 ≤≤ q )

Aat

tAb

tAc

Figure 6. Simulink model of duty cycle generation for one output phase of the matrix

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The matrix converter induction motor drive has beendesigned by using 1200V, 35A three-phase matrixconverter module produced by EUPEC Company. Themodule consists of nine-bidirectional switch (common-collector) composed by IGBTs. The block scheme and a

photograph of the drive system constructed in the

laboratory are shown in Fig.7.

(a)

(b)

Fig. 7. 3x3 phase matrix converter experimental prototype a) Block diagram b) A view of the experimental setup.

V. SIMULATION AND EXPERIMENTAL RESULTS

The simulation and experimental results of thematrix converter feeding a passive RL load have beenobtained with and without using input filters. The

bidirectional switches are controlled by using Venturinicontrol algorithm where the voltage ratio, q is taken as0.8. The converter is fed by a three- phase supply whichhas line voltage and frequency of 100V and 50Hz,respectively. The load parameters are 50Ω and 0.15H.Simulation and experimental results for various outputfrequencies are given in Figs.8-11. The switchingfrequency was taken as 1500Hz.

Fig.8(a) illustrates the input phase voltage andcurrent of the matrix converter using input filter for 10Hz output frequency. Results shown in Fig.8 (b)illustrate the matrix converter operation with the absenceof the input filter. Similar operating conditions are

repeated for 50Hz output frequency and results are givenin Fig.9. It can be clearly seen that the converter operates

with unity displacement factor so that the input voltageand current are in phase.

(a)

(b)Fig. 8. Experimental waveforms of input line voltage and current

for f 0=10Hz a) With input filter b) Without input filter

(a)

(b) Fig. 9. Experimental waveforms of input line voltage and current for

f 0=50Hz a) With input filter b) Without input filter

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Fig.10 shows experimental and simulationwaveforms of the output line voltage, spectrum andoutput phase currents of the matrix converter for 10Hzoutput frequency. In Fig.10 (a) and (b), the experimentalresults were taken without input filter and with inputfilter, respectively. Fig.10(c) shows the corresponding

simulation results using three-phase ideal supply. Similar results are given in Fig.11 for 50Hz output frequency.If the impedance of the supply feeding the converter

is high, voltage spikes will be seen on the input voltages.

Since Venturini control algorithm requires the inputvoltages to be measured there will be wrong calculation

process of the duty cycles because of the false detectionof ω it. This will directly affect the output voltage andcurrent waveforms. This effect is seen in Fig.10 andFig.11. For instance, the peak line voltage in Fig.10 (a)

and Fig.11 (a) were incorrectly measured as 130,8V and172,5V, respectively in which its value would be 195V.

Fig. 10. Output line voltage, harmonic spectrum and phase currents of the matrix converter (f 0=10Hz)a) Experimental (without input filter) b) Experimental (with input filter) c) Simulation (with input filter)

VI. CONCLUSIONS

In this paper, three-phase to three-phase matrixconverter using Venturini modulation algorithm has

been modeled, simulated and implemented.Furthermore, effects of input filter on stability of thematrix converter have been examined. Simulation has

been performed in Matlab 6.5 and then it has beenconverted into real time codes for DS1103 control card.

The current and voltage waveforms and harmonic

spectrum for the input and output of the converter have been examined with and without using input filter for various output frequencies using simulation model andexperimental setup. Good agreements were observed

between the simulation and experimental results. It has been also demonstrated that the converter operates withunity displacement factor regardless of the load power factor (in our case the load has inductivecharacteristic).

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(a) (b) (c)

Fig. 11. line voltage, harmonic spectrum and phase currents of the matrix converter (f 0=50Hz)a) Experimental (without input filter) b) Experimental (with input filter) c) Simulation (with input filter)

The matrix converter which is fed by a supplyhaving high impedance will face high voltage spikes onthe input voltage at high switching frequencies. Thiswill cause both harmonics at the output voltages andfalse detection of the input voltage signals required bymatrix converter modulation algorithms such asVenturini algorithm. This problem can be eliminated

by using a well designed input L-C filter. In this paper,

an input filter with the parameters of L=2.93mH andC=12.5 F μ has been used and it has been observed that

it has eliminated both the spikes on the input voltagesand errors on the detection of input voltage vector. Inaddition, this filter is also filter harmonics in the inputcurrents.

R EFERENCES

[1] Andreu, J., de Alegria, I.M., Kortabarria, I., Martin, J.,L., Ceballos, S., Improvement of the Matrix Converter Start-up Process, IECON, Taipei, Taiwan, 5-8 Nov.,2007, pp. 1811-1816

[2] Wheeler, P., Rodriguez, J., Clare, J, Empringham L.,

Weinstein A., Matrix converter: A technology review, inIEEE Transactions on industrial electronics, Vol. 49, No:2, 2002, pp. 276-288

[3] Sunter, S., Clare, J.C., A true four quadrant matrixconverter induction motor drive with servo performance, Power Electronics Specialists Conference, PESC '96Record., 27th Annual IEEE, 1996, pp. 146–151

[4] Erdem, E., Design of an induction motor drive fed by amatrix converter and a novel approach in application of

control algorithms. (in Turkish), PhD Thesis 2008; FiratUniversity, Elaziğ -Turkey.

[5] Matteini, Marco, Control techniques for matrix

converter adjustable speed drives, PhD Thesis, 2001,University of Bologna, Italy.

[6] Wheeler, P., Grant, D.A., Optimised Input Fitler Designand Low-Loss Switching Techniques for a Practical Matrix Converter, lEE Proceedings, Electrical Power Applications, 144(1), 1997, pp. 53-60

[7] MATLAB for Microsoft Windows, The Math WorksInc., 1999.

[8] Erdem, E., Tatar, Y., Sunter, S., Implementation of DSP-

based matrix converter using space vector modulationalgorithm, ACEMP’07, Bodrum-Turkey, 10-13September, 2007, pp. 474-479.

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