*4.1. Simulation*

In order to verify the validity and e ffectiveness of the proposed control strategy, simulations were carried out with the parameters in Table 1 using PSIM software. Figure 9 shows the comparison of three-phase currents, A-phase voltage, DC current, and DC current reference at 6 A. It can be seen that the proposed VSVM control strategy e ffectively reduces the DC current ripple of AC–DC MC compared with C-SVM and C-VSVM strategies in the range of high-modulation operation. Figure 10 presents the zoom-in on DC current and DC output voltage in one switching period of the sector I under di fferent modulation control strategies. The switching period of the largest line-to-line voltage vector was significantly reduced by the proposed VSVM compared with C-SVM. Therefore, the increasing of DC current is reduced before decreasing when zero vector is applied to the converter. Both switching patterns of the VSVM methods e ffectively reduce the DC current ripple. The proposed optimized switching patterns were applied, and the DC current ripple of AC–DC MC was successfully further reduced while accurately tracking its reference, which is in agreemen<sup>t</sup> with the current ripple analysis in Figure 7. The peak-to-peak values of the DC current ripples of the C-SVM, the C-VSVM, and the proposed VSVM operating at a high modulation index are 2.9 A, 2.4 A, and 1.65A, as shown in Figure 10, respectively. As a result, comparing with the C-SVM and the C-VSVM, the proposed VSVM can reduce the DC current ripples by 43.1% and 31.25%, respectively.


**Figure 9.** Three-phase currents, A-phase voltage, DC current, and DC current reference under different modulation strategies for AC–DC matrix converter at high-modulation operation. (**a**) C-SVM; (**b**) C-VSVM; (**c**) Proposed VSVM.

**Figure 10.** The zoom-in of DC current and DC output voltage under different modulation strategies for AC–DC matrix converter at high-modulation operation. (**a**) C-SVM; (**b**) C-VSVM; (**c**) Proposed VSVM.

The total distortion harmonics (THD) of A-phase source current of C-SVM and VSVM methods are shown in Figure 11. The THD value of the proposed VSVM method is slightly higher than that of the C-SVM method because the four vectors are used to synthesize the input current reference vector in the proposed VSVM to decrease the dc current ripples, including three active vectors and one zero vector, compared with two optimal active vectors and one zero vector of the C-SVM. The distance between the reference current vector and one additional stationary vector used for generating a virtual vector in the proposed VSVM is larger than that of the C-SVM. Besides, the symmetrical switching pattern is applied to guarantee low input current distortion in the C-SVM, whereas the proposed VSVM utilizes unsymmetrical switching patterns to further reduce the dc current ripples. Based on the above factors, the THD of three-phase currents of the proposed VSVM becomes slightly higher than that of the conventional methods, at costs of the reduction of the dc current ripples, although the envelope waveforms of the three-phase input currents are still sinusoidal. The simulation waveforms of three-phase source currents, A-phase source voltage, DC current, and DC current reference at 2 A of AC–DC MC under the C-SVM strategy, the C-VSVM strategy, and the proposed VSVM strategy are illustrated in Figure 12. It can be seen that the effectiveness of the proposed VSVM method in the reduction of DC current ripple correctly operates within the whole range of modulation while maintaining the high performance of AC–DC MC compared with the C-SVM and the C-VSVM methods. Without the proposed optimized switching pattern at low-power mode, the C-VSVM slightly reduces ripple compared with the C-SVM. The zoom-in of DC currents, DC output voltages in one switching period under the proposed VSVM and the C-SVM are presented in Figure 13. The optimized switching patterns for zero vector are applied when the converter operates at low modulation range. The switching period of zero vector is rearranged to avoid the continuous decreasing of DC current. Therefore, the DC current ripple is further reduced by the proposed VSVM strategy, which agrees with the theoretical analysis in Figure 8. In addition, the peak-to-peak values of the DC current ripples of the C-SVM, the C-VSVM, and the proposed VSVM at a low modulation index are 3.15 A, 2.88 A, and 2.04 A, respectively. Thus, it can be known that comparing with the C-SVM and the C-VSVM, the reduction of the DC current ripples by the proposed VSVM can be obtained by 35.23% and 29.17%, respectively. The transient state performances of AC–DC MC under the C-SVM, the C-VSVM, and the proposed VSVM methods are illustrated in Figure 14. The proposed method successfully reduces the DC current ripple in both high- and low-power operation compared with the C-SVM and the C-VSVM methods. The simulation results show the e ffectiveness of the proposed method in the reduction of DC current ripple compared with the conventional methods.

**Figure 11.** THD (total distortion harmonics) of A-phase source current under di fferent modulation strategies for AC–DC matrix converter at high-modulation operation. (**a**) C-SVM; (**b**) C-VSVM; (**c**) Proposed VSVM.

**Figure 12.** Three-phase currents, A-phase voltage, DC current, and DC current reference under di fferent modulation strategies for AC–DC matrix converter at low-modulation operation. (**a**) C-SVM; (**b**) C-VSVM; (**c**) Proposed VSVM.

**Figure 13.** The zoom-in of DC current and DC output voltage under different modulation strategies for AC–DC matrix converter at low-modulation operation. (**a**) C-SVM; (**b**) C-VSVM; (**c**) Proposed VSVM.

**Figure 14.** Three-phase currents, A-phase voltage, DC current, and DC current reference under different modulation strategies for AC–DC matrix converter at transient state. (**a**) C-SVM; (**b**) C-VSVM; (**c**) Proposed VSVM.
