DESIGN , MODELLING AND SIMULATION OF TWO-PHASE TWO-STAGE ELECTRONIC SYSTEM WITH ORTHOGONAL OUTPUT FOR SUPPLYING OF TWO-PHASE ASM

This paper deals with the two-stage two-phase electronic systems with orthogonal output voltages and currents DC/AC/AC. Design of two-stage DC/AC/AC high frequency converter with two-phase orthogonal output using single-phase matrix converter is also introduced. Output voltages of them are strongly nonharmonic ones, so they must be pulse-modulated due to requested nearly sinusoidal currents with low total harmonic distortion. Simulation experiment results of matrix converter for both steady and transient states for IM motors are given in the paper, also experimental verification under R-L load, so far. The simulation 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
In the very early days of commercial electric power, some installations used two-phase four-wire systems for motors [1].Two-phase systems have been replaced with three-phase systems.Two-phase supply with 90 degrees between phases can be derived from a three-phase system using a Scott-connected transformer.Two-phase circuits typically use two separate pairs of current-carrying conductors, alternatively three wires may be used, but the common conductor carries the vector sum of the phase currents, which requires a larger conductor.
Nowadays, the low-cost two-phase drives are again developed and produced.They are dedicated for industrial and residential applications when 3-phase system of electrical energy is missing.But they are used 3-phase low cost motors which are supplied asymmetrically into two phases from the voltage converter, Fig. 1, [4].
On the other side, it can be also easily created using power electronic converters e.g. from battery supply, with two-phase transfer of energy for zero distance.DC/2AC, Fig. 2, and DC/HF_AC/2AC, Figs.3a, b and Fig. 4, converter system can generate two-phase orthogonal output with variable voltage and frequency [2], [3].

Two-stage Two-phase systems with HF AC interlink matrix converters (DC/HF_AC/2AC)
This DC/HF_AC/2AC system usually consist of single-phase voltage inverter, AC interlink, HF transformer, 2-phase converter and 2-phase AC motor.Due to AC interlink direct converter (cyclo or matrix converter) is the best choice.System with matrix converter and high frequency AC interlink can generate two-phase orthogonal output with both variable voltage and frequency [4] - [6].Switching frequency of the converter is rather high (~tens of kHz).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.Proposed scheme of two-stage two-phase converter system is shown in Fig. 3a.Basically, it consists of singlephase fast IGBT inverter, and of two single-phase matrix converters, both in full-bridge connection.Since the switches of the inverter operate with hard commutation, switches of matrix converters are partially soft-commutated in the zero-voltage instants of the AC voltage interlink using unipolar PWM.Therefore, the expected efficiency of the system can be higher as usually by using of classical three-phase inverter.Inverter of first stage can be connected as: The advantage is then less number of semiconductor devices of the converters (four instead six).Disadvantage of the half-bridge is, of course, double voltage stress of the semiconductor switching elements.About to 2-phase AC electric motors there are many works, [4], [7] - [9] and others.

PWM modulation Strategies for Half-Bridge Matrix Converter
Theoretical analysis of single-phase matrix converter has been done, e.g.[10], [11].Equivalent circuit diagram of Half-bridge single phase converters two-phase system is depicted in Fig. 6.It is important and clear visible from these figures that during switching at the end of the period of HF AC supply (n.T s ) the switching losses will be zero due to zero value of commutation voltage.Switching frequency can be set from some kHz for high power applications up to several tens of kHz for low power applications.It deals with sinusoidal bipolar pulse-width-modulation contrary to unipolar regular PWM [13].Switching-pulse-width can be determined based on equivalence of average values of reference waveform and resulting average value of positive and negative switching pulses area during switching period, Fig. 9.

Fig. 9. PWM with even multiply of f 1
The switching instant is equal to: ( and the area under sine wave during k-switched interval S Δ (k) is: The total harmonic distortion of the current is given by [10]:

Two-Phase Induction Motor
Permanent progress in the field of power electronic devices has given a rise to two-phase induction machine (TPIM).These machines have two equal stator windings spatially shifted by 90 degrees.Supply is carried out by two phase converter with currents shifted 90 degrees in time.By means of this supply a waveform of flux density rotating in the air gap, similar to that of the three phase machines, is produced and vibrations and unfavourable noise are thus suppressed [14].
Let us consider the equivalent circuit of TPIM.Subscripts D and Q mean phases of TPIM (first and second).Subscripts ns and ps mean negative sequence and positive sequence of rotating fields in TPIM.Parameters R s , X s , R r ´, X r ´ and X m are stator resistance, stator leakage reactance, rotor resistance referred to stator, leakage reactance referred to stator and magnetizing inductance, respectively.K is a ratio of turns of the phase D over the turns of the phase Q.The negative sequence of rotating field in air-gap is suppressed by symmetrical two-phase supply.´. (6) Flux linkages can be written as: ( )  (10) In the case of squirrel-cage rotor the rotor voltages are equal to zero, thus: If r is angular displacement between stator and rotor axes, then is angular speed of the rotor.
An expression for the instantaneous electromagnetic torque can be obtained by applying the principle of virtual displacement.This relation (positive for motor action) is expressed as: where p is a number of pole-pairs.The real TPIM was used with name-plate:

PC simulation
Simulation model for R-L load has been modelled in OrCAD programming environment and simulation model for PMSM motor load has been modelled in MatLab programming environment.
Simulation results of single-phase half-bridge matrix converter with R-L load are shown in Fig. 11 and the output voltages (in different topologies of converter) in detail are depicted in Fig. 12.
Parameters for simulation of R-L load are:  Torque-speed characteristics were investigated by several methods of calculation and modeling [14], [16].The obtained characteristics are shown in the next section (Experimental Verification, Fig. 17) due to comparison possibility with measured values.

Experimental Verification
Experimental verification (measurement) of torquespeed characteristic has been done using two-stage two- phase power electronic converter consists of single-phase full-bridge voltage inverter and two single-phase fullbridge matrix converters (switching frequency f sw = 5kHz) for test rig system.There is shown test rig in Fig. 15.All system is controlled by Freescale DSP 56F8013DEMO.Measured output waveforms of voltage and current of the two-phase power electronic system with TPIM motor are presented in Fig. 16.
The Q winding is supplied by voltage of converter U Q , equal in magnitude to D winding and shifted by 90 electrical degrees of the D winding [15].

Conclusion
The simulated results was compared with real measurement and the results give good coincidence, Fig. 17.The parameters used in simulation model of TPIM have been calculated by several methods and majority once give good real results.It was found out that torque of TPIM is higher by PWM supply by 5 kHz switching frequency than in case of simply rectangular supply (the no-harmonic rectangular voltage supply decreases the TPIM performance, because of high harmonic spectrum).The torque by sinusoidal supply is lower than in case of PWM supply.It is caused by not regular phase shift, due to complicated supply aparature [14].Using chosen halfbridge connection for both inverter and matrix converters with bipolar PWM the number of power switching elements of the two-stage converter can be reduced and smaller then those of classical three-phase voltage inverter.

1 )Fig. 5 .
Fig. 5. Circuit diagram of half-bridge converters system with a) central points of AC source; b) central points of motor loads

Fig. 6 .
Fig. 6. Circuit diagram of half bridge converters system with HF transformer and central points of the source Contrary to bridge-matrix converter the half-bridge connection doesn't provide unipolar PWM control, so the bipolar pulse switching technique should be used.The orthogonal voltages with bipolar PWM control are depicted in Fig 7.

Fig. 7 .Fig. 8 .
Fig. 7. Output orthogonal voltages of the half-bridge matrix converter system with bipolar PWMSwitching strategy of one half-bridge matrix converter, based on 'even' bipolar PWM, can be explained using Figs.8, in greater details.Fourier analysis is useful and needed for determination of total harmonic distortion of the phase current of the matrix converter[10],[12].

Fig. 14
Fig.14 Simulated torque-speed characteristic for two-phase harmonics supply of TPIM (and its approximation)

Fig. 15 .
Fig. 15. Circuit diagram of investigated of two-phase induction machine

Fig. 16 .
Fig. 16.Measured output voltages and currents of the physical model of two-phase power electronic system (f SW = 5 kHz) Experimental measurements of torque-speed characteristics, Fig. 17, have been done at full nominal supply voltage with this type of control: