## 5 Simulation and Analysis
### Case 3  
In practical engineering, the line parameters of the two branches are not exactly the same, so it is necessary to focus on the study of ZSCC when the filter inductance of the AC side is not equal. In this case, \(L_{1}=3\)mH and \(L_{2}=7\)mH. The ZSCC and the harmonics it contains are shown in Figure 11.  
It can be seen from Figure 11a that when the difference of inductance in the line increased, the ZSCC amplitude also increased, and the peak-to-peak value between 0.5 and 0.6 s was 7.6 A.  
Figure 11: Simulation waveforms in parallel system with unequal inductance and without ZSCC suppression strategy: (**a**) ZSCC of system; (**b**) harmonics contained in ZSCC. Figure 11b is the spectrum of the ZSCC from 0.5 to 0.6 s after fast Fourier transform (FFT) with 50 Hz as the fundamental frequency. The following simulation adopted the same harmonic analysis method. According to Figure 11b, there were low harmonic components in the ZSCC without any measures, with the 3 rd, 9 th, and 15 th harmonics the more prominent. Therefore, it is necessary to take measures to reduce the ZSCC amplitude and suppress low-frequency harmonic components. The traditional PI control strategy is a common control method to suppress ZSCC, as noted in Section 1. Therefore, in order to compare the traditional control strategy and the PI control strategy proposed in this paper, the PI control strategy was first applied to control the ZSCC, and the experimental results were analyzed. The proportional coefficient and integral coefficient of the PI controller were set as 0.02 and 10, respectively. The simulation result is presented in Figure 12.  
As shown in Figure 12a, under the same conditions, the traditional PI suppression strategy could reduce the ZSCC to a certain extent, and the peak-to-peak value was 1.32 A. Compared with no control strategy, the ZSCC amplitude was reduced by 82.6%. However, according to Figure 12b, the PI strategy had no suppression effect on the harmonics in the ZSCC, and the amplit  
Figure 12: Simulation waveforms in parallel system with unequal inductance and with traditional proportional–integral (PI) suppression strategy: (**a**) ZSCC of system; (**b**) harmonics contained in ZSCC. harmonics increased. These results show that the traditional PI suppression strategy is insufficient in suppressing ZSCC. Theoretically, the control strategy proposed in this paper can reduce the ZSCC amplitude and also suppress the low-frequency harmonic components. Therefore, in order to verify its effectiveness, the control strategy proposed in this paper was added to the parallel system, and the simulation results of the ZSCC were observed and analyzed. For parameter setting, in order to maintain consistency with the above PI controller, the proportional and integral coefficients of the PIQR controller were the same as those of the PI controller. The other parameters were \(k_{\text{rz3}}=600\), \(k_{\text{rz9}}=400\), \(k_{\text{rz15}}=200\), \(\omega_{\text{c}}=1\) rad/s. The simulation result is shown in Figure 13.  
Figure 13a shows that the control strategy proposed in this paper could greatly reduce the ZSCC, and the peak-to-peak value was 0.63 A. The ZSCC amplitude with the proposed control strategy was 91.7% less than that without any control measures and 52.27% less than that with the traditional PI control strategy. As can be seen from Figure 13b, the proposed strategy could effectively suppress the specified harmonic components, while the influence on other harmonic components was small. Figure 13: Simulation waveforms in parallel system with unequal inductance and with the proposed suppression strategy: (**a**) ZSCC of system; (**b**) harmonics contained in ZSCC. In addition, the total harmonic distortion (THD) analysis of A-phase current on the AC side of Module 1 was carried out. The THD without the control strategy was 9.21%, the THD with the PI control algorithm was 4.40%, and the THD with the control strategy proposed in this paper was 4.23%.