## 4 Results and Discussion  
For the results obtained, the rectifier input and output parameters are analyzed. The input parameters are thus analyzed considering the values of currents, voltages, fast Fourier transform (fft) results, power factor (pf) and total harmonic distortion (thd). for the output parameters; the values of the currents and voltage are considered too. The available results of the prototype are also presented and studied. From the input currents, the sinusoidal shape and displacement of 120 degrees between the phases is taken to prove the results. With the results, it can be concluded that the currents are being rectified by each module of the rectifier independently, and correspond to the three-phase system, as shown in Figure 11.  
In order to observe the frequencies that make up the waveforms of the three currents obtained, the FFT was applied as shown in Figure 12, where it is seen that the currents are basically composed only by the fundamental frequency of 50 Hz. The resolution of the calculation could not possibly be better, and the shape near to the 50 Hz zone (1 st harmonic) does not have a high precision. Figure 11: Rectifier input currents (full power, Table 1). Figure 10: Instruments used for measurement in phase \(\alpha\): (**a**) current probe used in current measurement; (**b**) voltage transformer for galvanically isolated measurement. The results obtained at a reduced power (roughly 2 kW per phase), from the prototype, confirm the sinusoidal shape of the phase current. The waveform of the current illustrated in Figure 13 corresponds to the current of phase \(a\) and was obtained by means of a current probe on the 10 mV/A scale as shown in Figure 10a; thus, the measurement on the oscilloscope as shown in Figure 13 is 10 A for each division that gives approximately 13 A peak. This peak value also corroborates with the current value of 9.2 A RMS, represented in Figure 8 (G). The waveform in Figure 11 is similar to that of the current in Figure 13, so the simulation predicts the real results well. In this same Figure 13, it also shows an FFT analysis of the current in phase \(a\). This analysis shows the fundamental frequency and some harmonics with a low value that can be also disregarded. As it is seen from Figure 13, the shape of the current was slightly asymmetrical (the voltage source was weaker), but the first harmonic is the main component of the spectrum. This analysis also corroborates with the analysis made in PSIM as shown in Figure 12.  
Figure 12: FFT of input currents. Figure 13: Waveform in phase \(a\) and respective FFT analysis of the prototype. The voltage and current in phase \(a\) for a 29 \(\Omega\) load are shown in Figure 14, as an example for the other phases (phase \(b\), phase _c_). Note that the voltage and current are sinusoidal and are in phase, which resulted in high PF and low THD. In order to evaluate the behavior of PF and THD more rigorously, several simulations were carried out with different levels of load as described in Section 3, which allowed obtaining Figure 15. In Figure 15a, it can be seen that the value of THD is inversely proportional to load variation, that is, as the load value increases, THD decreases, thus obtaining a maximum THD of 4.98% for a load of 289 \(\Omega\) (1%) and a minimum THD of 1.92% in load 29 \(\Omega\) (100%). The analysis of the PF illustrated in Figure 15b had the opposite behavior to THD. In this analysis, it is noted that the value of PF is directly proportional to the variation of the load, that is, as the load increases, the PF increases, thus obtaining a maximum PF of 99.98% for a load of 29 \(\Omega\) (100%) and a minimum PF of 98.13% at a load of 289 \(\Omega\) (1%). This shows that the proposed rectifier can operate at various load levels (below the nominal load) and yet has the capacity to meet the recommendations of international standards, IEEE 519 and IEC61000-3-2/ IEC61000-3-4, with regard to the quality of electricity.