## 4 Simulation and Results Analysis
### Comparison of Online Optimization
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dynamic Performance Indicators** & **Initial** & **Offline** & **Online** \\ \hline Rise time (P, s) & 0.0200 & 0.0184 & 0.0140 \\ Average steady-state error (P, \%) & 1.3\% & 1.28\% & 1.22\% \\ Overshot (P, \%) & 18.4\% & 16.5\% & 17.8\% \\ Rise time (Q, s) & 0.0230 & 0.0220 & 0.012  
that needed to be regulated in the zero initial step-response, and the step-response characteristics of each part were different for the zero initial-state. Under the comprehensive limitations of the reasons mentioned above and the various interferences (e.g., noise interference, communication delay, and response delay of the system components), the performance contrast shown in Figure 17 is not obvious. As mentioned above, the result of IAE was affected by the parameter-coupling relationship of the PI controller in the parameter tuning process. The results of IAEs were affected by the parameter-coupling relationship of the PI controllers. A comparison result of the IAE values needed to be considered rather than one of the IAE values. The IAE indicator value was not fixed because of the influence of factors such as integration time, sampling time, control time, operating conditions, step amplitude, equipment parameters, environmental noise interference, and population size of the optimization algorithm. Therefore, the optimization tuning result was not judged according to the comparison value of the IAEs of a certain working condition or that of a certain control ring, but was based on the comprehensive comparison of the IAE values of all the control rings under different operating conditions. In order to further verify the improvement of VSI output performance by optimizing parameters, an experimental comparison of variable load output during normal operation of the system was conducted (as Figure 18 shows). Due to the change in load demand, the target-setting values of the VSI output changed from 10 kW and 3 kVar to 10 kW and 3 kVar when the operation time was 35.5 s. The detailed indicator comparison results of the step-response process are listed in Table 6. Compared with the initial parameter results, the overshoot of response curves with online optimization and offline optimization (in Figure 18a) reduced from 38.5% to 28% and 26%, respectively. The settling time shortened from the 0.157 s to 0.092 s and 0.087 s, respectively. The indicators of \(d\)-axis in Figure 18b also have been improved. According to Figure 18 and Table 6, the response speed of the controller with optimization parameters improved, and the overshoot, oscillation, and average steady-state errors were reduced. The IAE comparison results of the variable load process are shown in Figure 19. It can be seen that the IAE value of the controller with optimized parameters was greatly reduced in each control loop. Compared with the startup phase in Figure 17, the performance improvement was more obvious during normal operation because of the reduction of the zero initial-state variables of the device. Figure 17: Comparison startup process integral absolute errors (IAEs) of the original controller, online optimization controller, and offline optimization controller. The IAE1-P represents active power, the IAE2-Q represents reactive power, the IAE3-d axis represents the \(d\)-axis component, and the IAE4-q axis represents the \(q\)-axis component under the IAE index.