TWO-PHASE TWO-STAGE HF MATRIX CONVERTER FOR SUPPLYING TWO-PHASE MOTOR LOAD TWO-PHASE TWO-STAGE HF MATRIX CONVERTER FOR SUPPLYING TWO-PHASE MOTOR LOAD

under R-L load. The results confirm a very good time-waveform of the phase current and the system seems to be suitable for low-cost application in automotive/aerospace industries and application with high frequency voltage sources.


Introduction -Single-phase HF Matrix converter
The matrix converters are among to direct converters -there is a direct conversion of the input voltage to the output voltage with another frequency. The use of high switching frequency reduces the effect of harmonic current back to the power grid. The bidirectional switches are necessary because they allow flow current in both directions. The basic connection of direct converter -matrix converter (3ϫ3) is shown in Fig. 1a. From this scheme is derived the connection of single-phase matrix converter, Fig. 1b, [1] and [2].
The relations between output and input voltages, and between output currents and vo are: and (1,2) where [M(t)] is modulation matrix, is modulation index, t αA is time of switched state, with restrictions:

Two-stage two-phase systems with HF AC interlink and matrix converters (DC/HF_AC/2AC)
Two-stage two-phase systems with HF AC interlink and matrix converters (DC/HF_AC/2AC) usually consist of a single-phase voltage inverter, AC interlink, HF transformer, 2-phase AC/AC converter and 2-phase AC motor. This is the best choice due to an AC interlink direct converter (cyclo or matrix converter). The system with matrix converter and high frequency AC interlink can generate two-phase orthogonal output with both the variable voltage and the frequency [3], [4] and [5]. The proposed scheme of twostage two-phase converter system is shown in Fig. 2. The switching frequency of the converter is rather high (ϳ tens of kHz) and the second stage operates with twice switching frequency. Since the voltages of the matrix converter system should be orthogonal ones, the second phase converter is the same as the first one and its voltage is shifted by 90 degree. The switches of the inverter operate with hard commutation, the switches of matrix converters are partially soft-commutated in the zero-voltage instants of the AC voltage interlink using unipolar PWM [6]. Therefore, the expected efficiency of the system can be higher than usually by using the classical three-phase inverter .

Control of matrix converter with high-frequency input
The theoretical analysis of single-phase matrix converter has been done, e.g. [4] and [6]. The full-bridge converter provides unipolar and bipolar PWM control. Switching-pulse-width can be determined on the basis of the equivalence of average values of reference waveform and the result is the average value of positive or negative switching pulse area during switching period [7].
The switching instant is equal to: (4) and the area under sine wave during k-switched interval S Δ (k) is: The total harmonic distortion of the current is: Fourier analysis is useful and needed for the determination of total harmonic distortion of the phase current of the matrix converter. Unipolar switching strategy of one full-bridge matrix converter can be explained using Fig. 3 in greater details [4] and [8], [9], [10], [11].

Simulation Experiment
The simulation model of a two-stage converter was modeled in OrCAD programming environment, Fig. 4 and the simulation model of motor load was modeled in MatLab programming environment and they together were connected using Matlab SPLS. The simulation results of two-stage single-phase full-bridge matrix converter with R-L load are shown in Fig. 5. Both stages of converter are realized in full-bridge connection -(unipolar or bipolar PWM can be used). To protect the inverters against overvoltage surges in both stages the floating protection is used, which returns stored energy back to the DC-link and, thereby, improves the efficiency of the converter.

Experimental verification
The switching strategy described in previous chapter is used on the two-phase two-stage converter. The first stage was the voltage source inverter (VSI) and the second stage two matrix converters (MxC) were realized in a bridge connection without transformer in HF interlink. In this case the matrix converter works as a cycloconverter. The block scheme and photo of converter are shown in Figs. 7 and 8.   Fig. 11 we can see that the amplitudes of the stator current are not the same because the two-phase induction machine was unsymmetrical. Maximum efficiency of the proposed two-phase two-stage converter is nearly 94% at switching frequency 5kHz (in first-stage) and 10kHz (in second-stage).

Conclusion
The article shows a new concept of an electric drive system for electric vehicle and industrial application. It consists of the two-stage converter created by the single-phase converter and two single-phase matrix converters commutated by HF-AC input voltage, and two-phase induction TPIM or synchronous motors with PM. Simulation and experimental results showed good agreement between simulated and real output time waveforms. If this type of inverter is used to supply two-phase drive, high efficiency and very good mechanical parameters can be achieved (by two-phaseorthogonal supply of two-phase motor -TPIM, drive develops maximum torque).The maximum efficiency of the proposed twophase two-stage converter is nearly 95% at switching frequency 1kHz (in first-stage) and 2kHz (in second-stage).