## 4 Simulation and Results Analysis
### Simulation of the Optimization Process
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Controller Parameters**} & \multirow{2}{*}{**Initial Parameters**} & \multicolumn{2}{c}{**Optimal Parameters**} \\ \cline{3-4}  & & **100-Population** & **200-Population** \\ \hline Kp1 & 0.5 & 0.5112 & 0.5177 \\ Ki1 & 20 & 20.0196 & 20.0368 \\ Kp2 & 0.5 & 0.4978 & 0.5296 \\ Ki2 & 20 & 20.0212 & 20.0249 \\ Kp3 & 0.5 & 0.4894 & 0.4886 \\ Ki3 & 20 & 20.0202 & 20.026  
The improved dynamic performance of the controller after parameter optimization has been proven by Figure 10, shown above. Figure 11 shows the poles and zeros analysis results of the initial and optimal control loop. The initial control loop had three domain poles to influence the control performance (Figure 11a). The zeros were concentrated near the origin point. The three domain poles influenced each other. Figure 11b shows the new poles and zeros results after parameter optimization. There was only one domain pole on the negative real-axis. The other domain poles, which were close to the zero points, cannot be regarded as effective domain poles. The system changed to become more controllable and more stable. The inverter output current and output power simulation comparison curves are shown in Figures 12 and 13, and the parameters of the simulation circuit element are given in Table 1 in Appendix A. The detailed indicators comparing the results of dynamic performances have been listed in Table 3. The active power target was 12 kW, and the reactive power target was 3 kVar. The curves showed the VSI start operation process with grid support. The sampling time was 5 \(\times\) 10\({}^{-5}\) s, and the control time of the controller was 2 \(\times\) 10\({}^{-4}\) s in the simulation process. In Figure 12a, the results showed that the overshoot reduced from 32.3% to 9.1%, and the settling time shortened from 1.151 s to 0.38 s. These dynamic characteristic indicators in Figure 12b also reduced from 12.73% to 4.46% and shortened from 0.4 s to 0.375 s. With the improvement of the control performance of the \(d\)-axis and \(q\)-axis, the peak amplitude of current output exceeding the set value reduced from 28.79% to 7.58%, and the settling time shortened from 0.805 s to 0.3 s (as Figure 12c shows). Figure 11: Poles and zeros comparison results. (**a**) The poles and zeros of the initial control parameters. (**b**) The poles and zeros after control parameter optimization. The curves of Figure 13 show active and reactive power output comparison results. According to Figure 13a and Table 3, the overshoot of the active power reduced from 31.6% to 8.3%, the settling time shortened from 1.146 s to 0.353 s, and the average steady-state error reduced from 5.83% to 0.96%. These characteristic indicators of the comparison results in Figure 13b also have been reduced and shortened (as Table 3 shows). With the improvement of settling time, overshoot time, and rise  
Figure 12: The current output curves. (**a**) The \(d\)-axis current comparison curves. (**b**) The \(q\)-axis current comparison curves. (**c**) The AC current output comparison curves of Phase A.