CHOOSING MODULATION STRATEGIES FOR 2-STAGE COMBINE LLC- AND DIRECT CONVERTER–MODELLING, SIMULATION, APPLICATION CHOOSING MODULATION STRATEGIES FOR 2-STAGE COMBINE LLC- AND DIRECT CONVERTER–MODELLING, SIMULATION, APPLICATION

design of and control strategy of 2-stage combine LLC- and matrix converter, supplied from DC voltage source. It deals with comparison of the four different switching control modes: phase-mode control, sinusoidal PWM mode control, pulse-depletion


Introduction
It's known that direct converters can be operated from AC network (or generator) by voltage with relative low frequency of 50-, 60-, 100-, 400 Hz using triac-(or thyristor) switches with phasecontrol. On the other side, matrix converters with fast IGBT and MOSFET switching devices can operate with relatively high frequencies of tens-up hundreds kHz. The AC voltage source can be effectively created by LLC type resonant converter.

Overal connection of converter system
The block scheme of converter system is presented in Fig. 1, [1], [3].
Converter system consisting of two branches operates with two phase output voltage shifted by 90 degrees created by matrix converters MXC1 and MXC2. High frequency transformers provide galvanic insulation and increase battery voltage to the rate value for the motor. LLC resonant converters work at switching frequency of 10-up hundreds kHz and must be synchronized each to other.

Operation of One Single Branch
Power circuitry scheme of converters The main power schemes are depicted in Fig. 2.
Operation of 1-stage LLC converter is illustrates in work [2]. Important is that converter operates at zero-voltage-switching (ZVS) mode with consequently minimal switching losses.
Design of LLC resonant converter is described in detail in [2] - [4]. Regarding to its simulated output quantities it is shown in Figs  Output voltage is slightly decreasing during each half-period, and at higher switching frequencies it can be more trapezoidal and distorted one according to fixed dead-time of the converter switches (see experimental section).
The second stage matrix converter can be in half-or full bridge connection. It also operates at ZVS mode. Its output voltage can be controlled by different control modes with different achieved quality.

Modelling and Simulation of Half-Bridge Matrix Converter with RL Load at Different switching Strategies
Simulated time waveforms of the output voltage and current are shown in the next Figs. 5 -8 using different switching modes. This type of control mode uses also unequal sample-and switching frequency. So, during sample interval the packet of pulses of input voltage is generated. Its average value could follow average value of reference voltage.

Numerical analysis and THD calculation of output voltages
The numerical Fourier analysis was used for content of harmonics of investigated voltage waveforms (detailed in appendix). G Low frequency triac switches converter -phase control mode Calculated value of THD referred to fundamental harmonic component: Calculated value of THD referred to total rms value of voltage waveform:

Numerical analysis and THD calculation of output currents
The numerical Fourier analysis was also used for content of harmonics of investigated current waveforms (detailed in appendix).

Experimentation with 2-Stage Converter System Under R-L Load
Experimental verification was done using a single-phase LLC inverter and single-phase bridge matrix converter for test rig system, Fig. 14 and 15, respectively.
Output voltage and current of first-stage LLC converter are depicted in Fig. 16a.
Output voltage and current of matrix converter stage are depicted in Fig. 16b.
The second stage was assembled with classical IGBT devices type of IRG4PH40KD, Fig. 14. It is also possible to use bidirectional types.

Conclusions
The LLC-connection and the half-bridge connection of matrix converters with bipolar PWM modulation were chosen for the next applications. Using of those the number of power switching elements of the two-stage converter can be reduced and smaller then those of classical three-phase voltage inverter.
Comparison of different switching mode showed that since the sinusoidal PWM mode is the best from point of view of total harmonic distortion of the output quantities, the pulse depletion mode is the most suitable from the point of view of switching losses of the converter in bridge connection. So, the trade-off between both strategies should be taken into account. Let's notice that LLC operates with soft commutation and switching-off process of matrix converters is provided by AC interlink. So, the switching-off losses of the converters are minimized, and the efficiency higher than classical connection.
Experimental verification shows very good agreement between experimental-and theoretical analysis results, so far for R-L load. Based on this it is possible to provide the design and power dimensioning of the converters.

APPENDIX -Voltage-and Current Analysis of AC/AC Half -Bridge Matrix Converter System
Equivalent circuit diagram of half-bridge single phase converter (one of two-phase orthogonal systems) is depicted in Fig. 21a, and bipolar pulse-width modulation in Fig. 21b.
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 during switching period (Fig. 14b). There are defined both amplitude-and frequency modulation ratios m a and m f as where U 1m is reference amplitude of fundamental harmonic, U is magnitude of supply voltage, f s is switching frequency, f 1 is fundamental frequency.
So, the peak amplitude of the fundamental harmonic component (equal to reference voltage) is m a times U, and varies linearly with m a (provided m a Յ 1).
Then total voltage time waveform will be [8]: where switching instant is equal to: