## 3 Results
### Validation of DNSGA-II-B (Mutated Solution Strategy)  
The scenario is configured as a 10 kV distribution network integrated with a wind farm subjected to gradual wind power variations, with initial parameters set as shown in Table 5: wind power rate of change \(\frac{dP_{\rm wind}}{dt}=0.1\) MW/s, fluctuation rate \(\sigma_{\rm wind}=0.1\), iteration count t = 10; an individual in the initial population is configured with \(I_{\rm set1}=1.0\) kA, -\(I_{\rm set2}=0.8\) kA, and scaling factor \(\eta=0.1\). (Here, Protection 1 refers to the protection device 202 in Figure 2, and Protection 2 refers to the protection device 302 in Figure 2). Apply DNSGA-II-B (mutated solution strategy) to perform Gaussian mutation for addressing gradual wind power variations. Calculate the mutation strength \(\sigma_{\rm mut}=\eta\cdot\frac{\sigma_{\rm pv}}{\sqrt{t}}=0.1\times\frac{0.1 }{\sqrt{10}}\approx 0.0032\). Generate new settings \(I_{\rm set}^{\rm new}\); assuming a normally distributed random number \(N(1,0.0032)=1.005\), then \(I_{\rm set1}^{\rm new}=1.0\) kA \(\times 1.005=1.005\) kA, \(I_{\rm set2}^{\rm new}=0.8\) kA \(\times 1.005=0.804\) kA. Replace the individual with the lowest crowding distance (indicating dense neighboring solutions and high redundancy) in the current population with the new solution. After optimization, the output parameters are \(I_{\rm set1}=1.005\) kA, \(I_{\rm set2}=0.804\) kA, \(t_{\rm delay}=0.18\) s, \(\Delta t=0.22\) s. The comparison of parameters before and after optimization is shown in Table 6.  
To ensure the selectivity of the protection devices' operation, it is necessary to verify the protection operation setting values of the optimized protection devices 202 and 302. If the upper and lower level protection devices cannot effectively coordinate with the optimized protection settings, it is also required to perform optimization calculations on the protection devices of the upper and lower level lines. Table 7 presents a comparison of the protection settings of protection devices 101, 202, 201, 302, 301, and 401 before and after this optimization under the scenario of sudden changes in new energy power. It can be concluded from Table 7 that after the optimization calculation of protection devices 202 and 302, the selective coordination relationship between the protection devices of the upper and lower level lines can still be satisfied, and there is no need to further perform optimization calculations on the protection devices of the upper and lower level lines. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Objective** & **Original Value** & **Optimized Values** & **Adjustment Ratio** \\ \hline Protection Setting \(I_{\rm set1}\) & 1.0 & 1.005 & +0.5\% \\ \hline Protection Setting \(I_{\rm set2}\) & 0.8 & 0.804 & +0.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Algorithm optimization results in wind surge scenario. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Voltage level (kV) & 10 \\ Wind Power Change Rate (MW/s) & 0.1 \\ Volatility (standard deviation) & 0.1 \\ Initial protection setpoint 1 (kA) & 1.0 \\ Initial protection setpoint 2 (kA) & 0.8 \\ Scaling factor & 0.1 \\ Iteration count & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Initial parameter settings in a gradual changing wind scenario. The waveform data diagram of the fault current obtained through simulation is shown in Figure 5. The diagram depicts the magnitude of the fault current flowing through Protection 1 before and after the fault, as well as the setting values of Protection 1's threshold before and after optimization and adjustment, respectively. From the simulation waveform diagram, it can be observed that, similar to the abrupt change scenario, the integration of photovoltaic power sources causes the fault current flowing through Protection 1 to rise above the original protection threshold. When the fault current exceeds this threshold, Protection 1 will malfunction.