## 2 Design Proposal of the Three-Phase Modular Rectifier
### Mitigation of Current Interaction  
If a converter with three rectifiers and a boost converter for each rectifier is built, all connected in parallel, as in Figures 3 and 4, the interactions will appear, thus making difficult the possibility of control. For a better understanding, it will be considered an analysis in a determined angular interval of the period from 30\({}^{\circ}\) to 90\({}^{\circ}\). Only the two most positive phases, presented in Figure 5, will be considered. It is considered that the switch of the boost converter will be in the ON or OFF condition of its switching. During the considered interval, the analysis is made by two switching states, ON and OFF. In the ON switching state, it can be noticed that the first interaction takes place, where the interaction current will pass from diode D1 of the first rectifier and diode D7 of the second rectifier, since these diodes are directly polarized and also present a greater potential difference, that is, \(V_{ina}>0\) and \(V_{inb}<0\) as shown in Figure 3[18; 20; 21]. In order to eliminate the ON switching interaction, a change is made in the boost converter, placing one more diode at the output of the negative terminal of each boost converter, polarized inversely to the direction of the interaction current. With this, the ON switching interaction is thus eliminated [18; 20; 21]. When the switching goes to the OFF state, the second interaction appears. In this second interaction, the current coming out of diode D1 will pass through the output capacitor, connecting to diode D7 of the second rectifier, since \(V_{ina}>0\)_and_\(V_{inb}<0\), as shown in Figure 4[18; 20; 21]. In order to eliminate the off switching interaction, this paper proposes the implementation of a differential-mode choke filter (DMCF) between the boost inductor and the switch, as shown in the rectifier proposed in Figure 2.  
The DMCF will cause the same current that travels in the positive direction (in the primary inductor) to return in the negative direction (in the secondary inductor) of the  
Figure 4: Second interaction of current traveled in phase a.  
Figure 5: Interaction analysis interval. Figure 3: First interaction of current traveled in phase a.  
same phase. It is important to note that there will be no saturation in the DMCF inductors, since the core of the DMCF will cancel the magnetizing generated by the positive and negative currents, as they flow in opposite directions to the core. The mitigation of the current interaction can be explained as follows:  
As previously mentioned, and illustrated in Figure 4, the second interaction occurs because the value of the impedance where the interaction current travels (D1 to D7) is practically the same as the impedance for the normal current path (D1 to D4). Therefore, the secret is to make the impedance value for the normal current path (D1 to D4) as low as possible, in relation to the impedance value of the interaction current path (D1 to D7). This is possible when a DMCF is implemented. This change must be made in each of the three boost converters, in a way that the current of the respective boost converter travels freely along its own desired path and the path for the interaction current is made difficult. Considering the analyzed interval of interaction (Figure 5), the circuit shown in Figure 4 can be simplified, but now including the DMCF, for a better understanding of the mitigation of the interaction. This is made in a mathematical analysis of the mitigation of the interaction current. The simplified wiring diagram is illustrated in Figure 6, where two rectifiers with their respective boost converters and the DMCF, with the normal current path (\(I_{o1}\) and \(I_{o2}\)) and the current interaction path (\(I_{i}\)), can be seen. Following this same figure, a mathematical analysis of the mitigation of the current interaction is made.