## 1 Introduction
### Thirty Six-Impulse Rectifiers
Where: U\({}_{\text{a}}\), U\({}_{\text{b}}\) i U\({}_{\text{c}}\)- three-phase voltages occurring in the electrical machine PMSM, U\({}_{\text{a}}\), U\({}_{\text{b}}\): i U\({}_{\text{c}}\)- three-phase voltages in phase a, b and c shifted by angle \(-\frac{2}{3}\pi\), U\({}_{\text{a}}\)-, U\({}_{\text{b}}\)- i U\({}_{\text{c}}\)- three-phase voltages in phase a, b and c shifted by angle \(+\frac{2}{3}\pi\), U\({}_{\text{ab}}\)- three-phase voltage between phase b and c, U\({}_{\text{c}}\)- three-phase voltage between phase c and a, U\({}_{\text{b}}\)- three-phase voltage between phase b and c.  
In accordance with the switching diagram shown in the figure above, it is possible to switch the transformation of three-phase AC voltage and current into DC by means of eight methods. This means that the system uses six switching states along with an additional two calculated from the switching period (T1, T2 and T0). Exemplary Computer Simulations of the Selected AAES Power System Component in the Field of the PES System on the Example of the ATRU Unit in Accordance with the Concept of MEA  
Simulation studies were carried out in the Matlab/Simulink programming environment, on the basis of which a mathematical model of the system was developed, with the following simplifying assumptions:  
- the influence of magnetic hysteresis was omitted,  
- the influence of temperature on the circuit parameters was omitted,  
- ideal valves are adopted,  
- the system is powered from a symmetrical three-phase source without a cable zero,  
- the system is loaded with a current source. The simplifying assumptions made cause minimal noise in the analyzed system of the electrical system of the aircraft, which translates into a better display of results and the appearance of additional higher harmonics in the AC voltage signal at the input of the ATRU unit. In addition, these assumptions translate into a smaller occurrence of eddy currents in the supply system of the ATRU unit, and thus to lower losses during idle operation. The mentioned assumptions also affect the correct cooperation of rectifier circuits with powered devices in the ATRU module, because they require them to generate electricity with certain parameters. The most important parameters are voltage and current. Failure to observe the minimum permissible values of these parameters results in a malfunction or shutdown of the control system, and thus the generation of insufficient voltage and output current on the ATRU unit. Analogously, exceeding the nominal parameters may cause damage to the electronic components in the controllers. During implementation of the ATRU unit control system, an algorithm is used, using the PWM signal. The basic property of such a follow-up control in a closed system is the induction of such a value of the current that is set by the preset signal. The sequence of pulses from the comparator is first synchronized by means of the D-trigger, synchronized by the generator of the synchronization pulse sequence, and then sent to the rectifier system as control pulses [20]. Analyzing the above-mentioned waveforms, one can conclude that the rectified output voltage builds up without over-voltages, and its determined value is established after six periods of the supply voltage. The value of the variable component in the rectified output voltage is determined to be below 3%. The applied control algorithm of the converter actually shapes the sinusoidal current in the reactor circuit. In the figures above (Figures 6 and 7), the current, choke and set signal \(U_{z}\) waveforms are presented in the form of rectified half-wave sine waves, while Figures 8 and 9 show the current and voltage waveforms of the ATRU unit. Moreover, it should be noted that the current of the choke repeats the shape of the set signal, where the instantaneous values of the choke current pulsate around the signal set in the zone as determined by the comparator hysteresis loop. In turn, the current shape approaches the signal given the smaller the value of the hysteresis zone.