## 5 Simulation
From Figure 16, it can be seen that, when there is no harmonic voltage in the power grid, both \(u_{\text{s}}\) and \(i_{\text{s}}\) are sine waves. THD(\(u_{\text{s}}\)) = 0%, THD(\(i_{\text{s}}\)) = 1.25% and PF = 1. The FFT of Figure 16 is presented in Figure 17.  
In Figure 17, FFT of \(u_{\text{s}}\) is free of harmonic components. \(i_{\text{s}}\) contains only a small amount of 2 nd, 3 rd, and 5 th harmonics. The conclusion that can be drawn is that, when the power grid voltage is a standard sine wave, the AC-side current is harmonics-free. At the same time, the simulation results in Figures 16 and 17 serve as a control experiment. When the integer multiple harmonics are injected, the simulation results of \(u_{\text{s}}\) and \(i_{\text{s}}\) are displayed in the time period of 0.3-0.4 s in Figure 18a. Under the influence of the 3 rd harmonic voltage, the current exhibits significant distortion, with THD(\(u_{\text{s}}\)) = 2.43%, and THD(\(i_{\text{s}}\)) = 32.74%. FFT(\(u_{\text{s}}\)) is demonstrated in Figure 18b. FFT(\(i_{\text{s}}\)) before 0.4 s is depicted in Figure 18c. At \(t=0.4\), the HSCM is applied. In Figure 18a, during the time period of 0.4-0.5 s, the current waveform is significantly improved, with the THD(\(i_{\text{s}}\)) = 1.35%, and the value of PF has changed from 0.963 to 0.998. FFT(\(i_{\text{s}}\)) after 0.4 s is shown in Figure 18d. From this, it can be seen that the harmonic content is significantly reduced. Figure 17: FFT of \(u_{\text{s}}\) and \(i_{\text{s}}\) in Figure 16.  
Figure 18: The simulation results of injecting the integer multiple harmonics. From Figures 19a and 16, it can be seen that, when the interharmonics are present, the sinusoidal quality of \(i_{\text{s}}\) is very low. Figures 17 and 19c illustrate that the harmonic content of \(i_{\text{s}}\) is relatively high with \(\text{THD}(i_{\text{s}})=35.03\%\). After the action of HSCM, the current waveform becomes a sine wave, with \(\text{THD}(i_{\text{s}})=1.43\%\). PF has improved from 0.947 to 0.998. The harmonic components in Figure 19d are minimal. From Figures 16 and 20a, it can be seen that, when supraharmonics are added to \(u_{\text{s}}\), they do not cause distortion in \(i_{\text{s}}\). Regardless of whether HSCM is in action or not, \(i_{\text{s}}\) always presents as a sine wave. In Figure 20b, \(u_{\text{s}}\) contains only high-frequency harmonics. Comparing Figure 17 with Figure 20c,d, it is evident that before the action of HSCM, \(\text{THD}(i_{\text{s}})=1.53\%\), and after the action of HSCM, \(\text{THD}(i_{\text{s}})=0.24\%\). Therefore, supraharmonics exert a minor influence on \(i_{\text{s}}\), and HSCM has improved the situation of low-frequency harmonics in \(i_{\text{s}}\). When the circuit is in a steady state, a voltage disturbance of \(u_{\text{s1}}=502\text{cos}(100\pi\text{t})\) is introduced at \(t=0.3\) s, followed by another voltage disturbance of \(u_{\text{s2}}=-1002\text{cos}(100\pi\text{t})\) at \(t=0.5\) s. The simulated waveform is shown in Figure 21.  
In Figure 21, the intervals are set as follows. Interval I: from \(t=0.1\) s to \(t=0.3\) s, Interval II: from \(t=0.3\) s to \(t=0.5\) s, Interval III: from \(t=0.5\) s to \(t=0.7\) s. In Figure 21a, before the effect of HSCM, when \(u_{\text{s1}}\) is superimposed on \(u_{\text{s}}\), \(i_{\text{s}}\) drops and distortion occurs. The addition of \(u_{\text{s2}}\) causes \(i_{\text{s}}\) to overshoot. Figure 21b shows the waveform of \(u_{\text{s}}\) and \(i_{\text{s}}\) after the disturbance is added with HSCM in effect. Whether influenced by \(u_{\text{s1}}\) or \(u_{\text{s2}}\), the transition of \(i_{\text{s}}\) is smoother compared to that in Figure 21a, without overshoot or distortion. Not only that, but the PF and Total THD in Figure 21b are both better than those in Figure 21a. FFT(\(i_{\text{s}}\)) with \(u_{\text{s1}}\) and \(u_{\text{s2}}\) are shown in Figure 22.  
Figure 19: The simulation results of injecting the interharmonics. Figure 21: The simulation results after the introduction of voltage disturbances.