## 3 Results
### Validation of DNSGA-II-A (Random Solution Injection Strategy)  
The scenario is configured as a 10 kV distribution network integrated with a wind farm subjected to abrupt wind power surges, with initial parameters set as shown in Table 2: a sudden wind speed increase causes wind power output \(P_{\rm wind}\) to rise from 1 MW to 3 MW within 5 s, with a fluctuation rate \(\sigma_{\rm wind}=0.4\) (standard deviation). An individual in the initial population is configured with \(I_{\rm set1}=1.0\) kA, \(\cdot I_{\rm set2}=0.8\) kA, adjustment coefficient k = 0.5, and a replacement ratio of 50%. (Here, Protection 1 refers to the protection device 202 in Figure 2, and Protection 2 refers to the protection device 302 in Figure 2). According to the DNSGA-II-A (random solution injection strategy) algorithm process, generate random solutions by calculating the perturbation range \(\alpha=k\cdot\sigma_{\rm wind}=0.5\times 0.4=0.2\), defined as \(U(1-0.2,1+0.2)=U(0.8,1.2)\). Generate new settings \(I_{\rm set}^{\rm new}\) assuming a uniformly distributed random number \(U(0.8,1.2)=1.1\), then \(I_{\rm set1}^{\rm new}=1.0\) kA \(\times 1.1=1.1\) kA, \(I_{\rm set2}^{\rm new}=0.8\) kA \(\times 1.1=0.88\) kA. Replace the worst individual (with the largest F value) in the current population with the new solution. The final optimized parameters are: \(I_{\rm set1}=1.1\) kA, \(I_{\rm set2}=0.88\) kA, \(t_{\rm delay}=0.2\) s, \(\Delta t=0.25\) s. The comparison of parameters before and after optimization is shown in Table 3.  
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. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Value** \\ \hline Voltage level (kV) & 10 \\ Wind Power Change Rate (MW/s) & 0.4 \\ Volatility (standard deviation) & 0.4 \\ Initial protection setpoint 1 (kA) & 1.0 \\ Initial protection setpoint 2 (kA) & 0.8 \\ Adjustment coefficient & 0.5 \\ replacement ratio & 50\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Initial parameter setting in a sudden wind surge scenario. Figure 3: Simulation diagram of a 10 kV typical distribution network with wind farm integration in RSCAD. 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 4 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 4 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. The waveform data diagram of the fault current obtained through simulation is shown in Figure 4. The diagram respectively illustrates 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 fixed values before and after adjustment. From the simulation waveform diagram, it can be obtained that due to the integration of photovoltaic power sources, the fault current flowing through Protection 1 rises above the original protection setting value. At this time, if the fault current value exceeds the protection setting value, Protection 1 will malfunction. In contrast to the original protection setting value, the optimized setting value is increased by 10%, which effectively avoids the malfunction caused by the sudden increase in wind power output leading to the short-circuit current exceeding the original setting value.