# THE development of new methods and circuits for electrical energy conversion

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1 FACTA UNIERSITATIS (NIŠ) SER.: ELEC. ENERG. vol. 22, no. 2, August 29, Investigation of ThreePhase to SinglePhase Matrix Converter Mihail Antchev and Georgi Kunov Abstract: A threephase to singlephase matrix converter is investigated in the present paper. Based on the state matrix vector, a mathematical analysis of the converter is performed giving the relation between the sinusoidal line voltage (current) and the output voltage (current). The results of the investigation are confirmed using computer simulation of the converter by the program product Cadence PSpice Keywords: Power Electronics, matrix converter, PSpice simulation. Introduction THE development of new methods and circuits for electrical energy conversion with improved characteristics is a basic way for increasing of the energy efficiency of power electronic converters with respect to mains network. The matrix converters realize a direct conversion of alternating current to alternating current [,2]. Investigations exist for the electrical motor control, where the frequency of the output voltage is lower than the frequency of the mains network voltage [,4]. The singlephase matrix converter is investigated in [5]. The aim of the present paper is the investigation of the threephase to singlephase matrix converter. The frequency of the singlephase output voltage is higher than the frequency of the threephase line input voltage. Based on the state matrix vector, a mathematical analysis of the converter is performed giving the relation between the sinusoidal line voltage (current) and the output voltage (current). The results of the investigation are confirmed using computer simulation of the converter by the program product Cadence PSpice. Manuscript received on June 4, 29 The authors are with Technical University of Sofia, Department of Power Electronics, 56 Sofia, Bulgaria ( [antchev, 245

2 246 M. Antchev and G. Kunov: 2 Mathematical Description The circuit for mathematical analysis is presented in Fig. a. Bidirectional switches are used, realized as shown in Fig. b and controlled by a corresponding algorithm. R SW4 SW S SW6 SW T SW2 SW5 out D T2 SW N T D2 (a) (b) Fig.. Circuit for investigation. (a) Equivalent circuit. (b) Bidirectional power switch. The converter is supplied directly by the mains network. The threephase line input voltages are described by the following equations: v R (t) = m sinω t () v S (t) = m sin(ω t 2π ) (2) v T (t) = m sin(ω t 2π ) () The state of the bidirectional switches open or closed, can be described in matrix form in the following way: [ SW SW SW 5 [SW] = SW 4 SW 6 SW 2 ] (4) The following dependencies are valid for the elements in (4):

3 Investigation of ThreePhase to SinglePhase Matrix Converter 247 SW = SW 4 SW = SW 6 SW 5 = SW 2 (5) The state of the power devices can be described in matrix form in the following way: [ ] v (t) = v (t) [ SW SW SW5 SW4 SW6 SW2 ] R (t) v v S (t) (6) v T (t) The singlephase output voltage v out (t) = v (t) v (t) has the form: where: v out (t) = (SW SW4)v R (t)(sw SW6)v S (t)(sw 5 SW2)v T (t) (7) SW SW4 = A sin(ω S t) SW SW6 = A sin(ω S t 2π ) SW5 SW2 = A sin(ω S t 2π ) n=,5... n=,5... n=,5... A n sin(nω S t) (8) A n sin(nω S t 2π ) (9) A n sin(nω S t 2π ) () The parameter ω S in (8), (9) and () is the commutation frequency of the bidirectional switches. The coefficient A is the magnitude of the commutation function. The first harmonic of the Fourier expansion of A is of the value 4 π. The higher harmonics A n have significantly lower magnitudes and can be neglected. Replacing (8), (9) and () in (7), the following dependence is obtained for v out (t): v out (t) = 4 π m sinω t sinω S t 4 π m sin(ω t 2π )sin(ω St 2π ) 4 π m sin(ωt 2π )sin(ω St 2π ) () The program product CadencePSpice is used for the investigation of the matrix converter. The voltages on the bidirectional switches are shown in Fig. 2. The singlephase output voltage v out (t) is presented in Fig..

4 248 M. Antchev and G. Kunov: Fig. 2. The voltages on the bidirectional switches. Fig.. The singlephase output voltage v out (t). PSPICE Simulation of the Electrical Circuit of the ThreePhase to SinglePhase Matrix Converter. Basic electrical circuit The electrical circuit of the matrix converter is shown in Fig. 4. The principle of operation is illustrated using equivalent circuits, corresponding to the respective intervals, in which the bidirectional switches act.

5 Investigation of ThreePhase to SinglePhase Matrix Converter 249 G Egn E Rgn 5 QN Egn E Eg5n E QN G G5 Rgn 5 Rg5n 5 Q5N FREQ = 5Hz AMPL = OFF = PHASE = FREQ = 5Hz AMPL = OFF = PHASE = 2 FREQ = 5Hz AMPL = OFF = PHASE = 2 A B C G4 Eg4n E Rg4n 5 QP Q4N G6 Eg6n E Rg6n 5 QP Q6N G2 Eg2n E Rg2n 5 Q5P Q2N Rout 2 Q4P Q6P Q2P Fig. 4. Electrical circuit of the matrix converter. In the interval, in which the most positive is the phase A, the switches SW and SW4 (SW 4 = SW) are active. The duration of this interval corresponds to 2. From to 6 the switches SW6 and SW (SW = SW 6), connected to the most negative phase B, are active. The switches SW5 and SW2 are nonactive. This allows to simplify the electrical circuit as shown in Fig. 5. G Egn E Rgn 5 QN G Egn E Rgn 5 QN G Egn E Rgn 5 QN G5 Eg5n E Rg5n 5 Q5N A QP QP A QP Q5P [](A)max [](A)max B (B)max[] Rout C (C)max[] Rout G4 Eg4n E Rg4n 5 Q4N G6 Eg6n E Rg6n 5 Q6N G4 Eg4n E Rg4n 5 Q4N G2 Eg2n E Rg2n 5 Q2N Q4P Q6P Q4P Q2P (6)grad Fig. 5. Equivalent cicuit from to 6. (62)grad Fig. 6. Equivalent cicuit from 6 to 2. The matrix converter is reduced to a singlephase full bridge inverter. The positive halfwave of the voltage on the load resistor R out is obtained when SW

6 25 M. Antchev and G. Kunov: and SW6 are switched on, and the negative halfwave when SW 4 and SW are switched on. From 6 to 2 the most negative is phase C. In this subinterval the active switches are SW, SW4, SW 5 and SW 2 (SW 5 = SW2). The switches SW and SW6 are nonactive. The equivalent circuit is shown in Fig. 6. The positive halfwave of the voltage on the load resistor R out is obtained when SW and SW2 are switched on, and the negative halfwave when SW 4 and SW5 are switched on. Similar considerations are valid for the next intervals when the most positive are phase B or phase C. The basic waveforms, illustrating the principle of operation of the matrix converters are shown in Fig. 7. They are obtained using the CadencePSpice simulator. The sequence of intervals can be seen, in which two couples of switches act simultaneously (connected to the most positive and to the most negative phase for each interval). Fig. 7. The basic waveforms, illustrating the principe of operation of the matrix converter. The obtained rectangular alternating voltage on the load resistor R out can be used for example to supply a resonant converter for induction heating [5, 6].

7 Investigation of ThreePhase to SinglePhase Matrix Converter 25.2 Basic control circuit An example circuit of the system producing the basic control signal for the bidirectional switches, is shown in Fig. 8. The full bridge diode rectifier DD6 together with the optocoupler OCOC6, produce logical impulses QQ6. They define the intervals, in which the phases A,B and C are the most positive or the most negative. The commutation impulses for the couples of switches SW SW4, SW SW6 and SW5 SW 2, are produced by three equal logical circuits. The logical circuit for the switches SW SW 4 is presented in Fig. 8. Q= and Q4= when the phase A is the most positive. In this case (SW 4 = SW ), i.e. G advances in phase G4. The logical values Q= and Q4= when the phase A is the most negative. In this case (SW = SW 4), i.e. G4 advances in phase G. It can be seen from the waveforms presented in Fig.7. OC Rb Q R OC Rb Q R OC5 Rb5 Q5 R5 p = 2 = 5 TD = TR =.us TF =.us PW = us PER = 8.us Qp n = 2 = 5 TD = us TR =.us TF =.us PW = us PER = 8.us Qn FREQ = 5Hz AMPL = OFF = PHASE = FREQ = 5Hz AMPL = OFF = PHASE = 2 FREQ = 5Hz AMPL = OFF = PHASE = 2 a_s b_s c_s D D4 D D6 D5 D2 Rdc 2k Q U7A 2 74ACT8 U8A 2 74ACT8 2 U9A 74ACT2 G OC4 Rb4 Q4 R4 OC6 Rb6 Q6 R6 OC2 Rb2 Q2 R2 Q4 U9A 2 74ACT8 UA 2 74ACT8 2 U2A 74ACT2 G4 Qp Qn Fig. 8. Basic control circuit. 4 Conclusions A threephase to singlephase matrix converter has been investigated. Based on the state matrix vector, a mathematical analysis of the converter is performed giving the relation between the sinusoidal line voltage (current) and the output voltage (current). Based on corresponding equivalent circuits, the principle of operation is considered and the control circuit is constructed. The matrix converter is simulated using the Cadence PSpice and the waveforms illustrating the principle of operation, are obtained.

8 252 M. Antchev and G. Kunov: Acknowledgement The study carried out in this work made is in a connection with Contract UTN 6/25, between the TUSofia and the Ministry of Education and Science of Bulgaria. References [] S. Ratanapanachote, H. J. Cha, and P. N. Enjieti, A digitally controlled switch mode power supply based on matrix converter, IEEE Transaction on Power Electronics, vol. 2, no., pp. 24, 26. [2] T. Scvarenina, The Power Electronics Handbook. CRC Press, 22. [] S. Ikuya, I. Junichi, H. Ohguchi, and A. Odaka, An improvement method of matrix converter drives under input voltage diturbances, IEEE Transaction on Power Electronics, vol. 22, no., pp. 2 8, 27. [4] J. Matti and H.Tuusa, Comparison of simple control strategies of spacevector modulated indirect matrix converter under distorted supply voltage, IEEE Transaction on Power Electronics, vol. 22, no., pp. 9 48, 27. [5] M. H. Antchev and G. Kunov, Study of single phase matrix converter for induction heating application, in Proc. of 4th International Symposium on Power Electronics Ee 27, Novi Sad, Serbia, Nov. 7 9, 27. [6] G. Kunov, E. Gadjeva, and K. Ivanova, Mathematical analysis and investigation using MATLAB of seriesparallel transistor inverter for induction heating application, in Proc. of 4th International Symposium on Power Electronics Ee 27, Novi Sad, Serbia, Nov. 7 9, 27.

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