## 4 Simulation and Experimental Verification
### Simulation and Verification  
Figure 5 shows the simulation waveform of the switching process of load resistances \(R_{1}\) and \(R_{2}\) from equal to unequal on the DC side of the VIENNA circuit. The switching of the two load resistances from equal to unequal is completed at the moment of 0.20 s. Figure 5a shows the simulation waveform when no NPV control strategy is adopted, while Figure 5b,c show the simulation waveforms using ZSV-J and the proposed NPV control strategy in this paper, respectively. As shown in Figure 5a, when the two load resistances are equal, the values of \(v_{\text{dc1}}\) and \(v_{\text{dc2}}\) are equal, and when the two load resistances are switched to unequal, the NPV is deviated, the \(v_{\text{dc}}\) fluctuation increases, and the harmonic content also increases. By comparing Figure 5b,c, when the loads are suddenly switched to be unequal, the NPV can be balanced again using both methods through the control process, and the proposed strategy has faster response and less NPV fluctuation than that of ZSV-J. Although the ZSV-J can slow down its PI regulator to make the level of NPV fluctuation reach or even less than that of the proposed strategy, it is at the expense of the response speed; similarly, the PI regulator of ZSV-J can be accelerated to make its adjustment speed reach or even exceed that of the proposed strategy, but it is at the expense of the control effect, and the NPV fluctuation will become higher. Thus, compared with ZSV-J, both in terms of the control effect and the adjustment speed, the proposed strategy is better. Figures 6-9 show the Fourier analysis of \(a\)-phase current \(i_{a}\) in the simulation performed under different control strategies, respectively. Figure 6 shows the Fourier analysis of \(i_{a}\) when NPV is balanced; Figure 7 shows the Fourier analysis of \(i_{a}\) when NPV is unbalanced; Figure 8 shows the Fourier analysis of \(i_{a}\) when NPV is controlled by ZSV-J; Figure 9 shows the Fourier analysis of \(i_{a}\) when NPV is controlled by the proposed NPV control strategy. Figure 5: Performance comparison of the methods when the loads jump from equal to unequal. (**a**) No NPV control strategy is adopted; (**b**) ZSV-J; (**c**) the proposed NPV control method. As shown in Figure 6, The NPV is balanced when the two load resistances on the DC side of the VIENNA circuit are equal, and the THD of \(i_{u}\) is about 2.06% and the DC  
Figure 8: Fourier analysis of \(i_{u}\) when ZSV-J is adopted. (**a**) Harmonic analysis; (**b**) low-frequency harmonics analysis. Figure 6: Fourier analysis of \(i_{u}\) when NPV is balanced. (**a**) Harmonic analysis; (**b**) low-frequency harmonics analysis. Figure 7: Fourier analysis of \(i_{u}\) when NPV is unbalanced. (**a**) Harmonic analysis; (**b**) low-frequency harmonics analysis. Figure 9: Fourier analysis of \(i_{u}\) when the proposed NPV control strategy is adopted. (**a**) Harmonic analysis; (**b**) low-frequency harmonics analysis. harmonic content in the current is almost 0. As shown in Figure 7, when the two load resistances on the DC side become unequal and no NPV control strategy is adopted, the THD of \(i_{u}\) can reach 3.36%, and the DC component content in \(i_{u}\) is about 0.4%. As shown in Figure 8, the THD of \(i_{u}\) is about 3.03% after NPV is balanced by ZSV-J, but the DC harmonic content reaches about 0.8%, which is because the principle of ZSV-J to control NPV is to use the output of the PI controller superimposed on the modulating wave of the control system, and such output is the constant flow when the harmonic components are not considered, and will be introduced into the current control loop, resulting in an increase of DC harmonics in the current (also verified in Figure 8). The simulation results in Figure 9 show that when NPV is controlled by the proposed NPV control strategy, the THD of \(i_{u}\) is about 2.43% and the DC harmonic content is about 0.1%, which is lower than the value obtained by ZSV-J.