## 4 Simulation and Results Analysis
### Comparison of Online Optimization
In particular, it can be seen from Figure 16b that, after achieving the steady-state, the fluctuation frequency and steady-state error in the curve after optimization were lowered, but the oscillation amplitude increased compared with the curve before optimization. It can be noted from the figure that there were many oscillations and fluctuations, both in the rising process and the steady process of the VSI startup. The oscillations and fluctuations of the curves also helped to verify the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Optimum Value and Controller Parameters** & **Original Value** & **Optimal Value** \\ \hline bestSmellbestIndex1 & 2.42 \(\times\) 10\({}^{-5}\) & 0.00373 \\ bestSmellbestIndex2 & 2.2 \(\times\) 10\({}^{-3}\) & 0.07049 \\ bestSmellbestIndex3 & 4.49 \(\times\) 10\({}^{-4}\) & \(-9.95\times\) 10\({}^{-5}\) \\ bestSmellbestIndex4 & 2.94 \(\times\) 10\({}^{-3}\) & \(-\)0.06804 \\ kp1 & 0.5 & 0.4264 \\ ki1 & 20 & 19.7319 \\ kp2 & 0.5 & 1.1136 \\ ki2 & 20 & 19.7449 \\ kp3 & 0.5 & 0.1799 \\ ki3 & 20 & 10.2169 \\ kp4 & 0.5 & 0.8494 \\ ki4 & 20 & 19.6006 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The initial parameters and online optimal parameters comparison table. Figure 15: Experimental platform. low inertia, high sensitivity, and the oscillation ripple wave with a small signal disturbance of VSIs, as described in [PERSON]'s work [34]. Table 5 reveals that the response speed of the online self-tuned controller was improved with the online parameter self-tuning method, and the rising time during the step-response was longer than that of the initial controller and the offline optimized controller. In terms of steady-state error, the initial controller had steady-state error in the process of reactive power adjustment, while that of the offline controller was relatively smaller. The overshoot of the offline optimized controller was significantly smaller than that of the initial controller and the online self-tuned controller. In the steady-state of the controller after parameter optimization, the fluctuation amplitude was large, but the fluctuation frequency declined. Since the fluctuation amplitude still fell within an acceptable steady-state margin, no further optimization was needed. Therefore, we can introduce smell discrimination criteria (smell) to further improve the problem of fluctuation amplitude during the optimization. The experimental results in Figure 16 are essentially a zero initial-state step-response. All state variables needed to be regulated from the zero initial-state to the target state. Therefore, the difference of the comparison curves was not obvious in Figure 16. In order to comprehensively compare the performance of the original controller, the offline optimized controller, and the online self-tuned controller, the IAEs in the process of the step-response in the zero initial-state were compared horizontally. Figure 17 gives the comparisons of the IAEs of different control loops. It can be seen from the figure that a dramatic drop was witnessed by the IAEs of online optimization in active power adjustment and q component adjustment, along with slight rises in reactive power adjustment and d component adjustment. This was a result of the fact that multiple PI controllers in serial and parallel structures worked together to constitute a complicated closed-loop control network, and any changes of a parameter affected other controller properties. Moreover, there were many zero initial-state variables  
Figure 16: The comparison curves of the system startup process. (**a**) The active power output curves. (**b**) The reactive power output curves.