# A Setting Optimization Ensemble for a Distributed Power Grid Protective Relay
## 5 Case Study: Simulation Results and Comparative Analysis  
In this paper, we utilized a typical power protection system with a simple network topology, whose relevant data were provided by the existing project of National Key Laboratory of Disaster Prevention and Reduction of Power network distribution network model test site in Changsha University of Science and Technology, as an illustrative example. Our focus was on optimizing the value of the phase-to-phase distance protection segment, a protective mechanism commonly employed in pairs of transmission lines to determine the distance between the fault point and the protection point by measuring the phase difference of fault current and voltage, thereby safeguarding the power system, specifically protection 1-18, to assess the effectiveness of the proposed method. To evaluate the operational timeliness of the method in a distributed environment, we conducted simulations using ten computing terminals. The structural depiction of the system in the case study is presented in Figure 4.  
Figure 4: Structure of the system in the case study. Figure 3: Overall algorithm flow chart. The initial values before the optimization of the above system usually include line impedance and relay impedance setting values, which are given in Tables 3 and 4, respectively. On one hand, the effectiveness of the proposed method was validated through testing. Fixed-value optimization was conducted for devices No. 1-18 in the example network depicted in the above figure. The optimal setting results for each protection in the system by IFE-QGO are presented in the following table (Table 5):  
The operation time of each relay protection device and the overall system operation time after IFE-QGO optimization can be obtained by analyzing the table provided. The \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Detection Number** & **Impedance Setting/\(\Omega\)** & **Protection Number** & **Impedance Setting/\(\Omega\)** \\ \hline
1 & 24.09 & 10 & 11.69 \\
2 & 13.17 & 11 & 27.75 \\
3 & 24.44 & 12 & 19.18 \\
4 & 18.58 & 13 & 10.01 \\
5 & 8.31 & 14 & 15.72 \\
6 & 15.70 & 15 & 8.49 \\
7 & 10.11 & 16 & 27.23 \\
8 & 17.43 & 17 & 12.35 \\
9 & 9.89 & 18 & 14.81 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The initial relay impedance setting values before optimization. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Line Starting Point** & **Line Ending Point** & **Line Impedance/\(\Omega\)** \\ \hline
1 & 3 & 14.48 \\
2 & 4 & 5.22 \\
5 & 6 & 5.76 \\
7 & 8 & 4.82 \\
9 & 10 & 5.11 \\
11 & 12 & 17.97 \\
13 & 14 & 7.23 \\
15 & 16 & 9.65 \\
17 & 18 & 12.  
results of IFE-QGO processing were compared with the existing project parameters, as illustrated in Table 6.  
As can be seen from the above table, the overall operation time of the system after IFE-QGO is 9.005 s, which is 21.696% shorter than the existing situation. Implementing the stepwise coordination method for the same case, the results are presented in the following table for comparison. The Table 7 reveals that the overall operation time of 20.6 s.  
Compared with the results of Tables 4 and 5, the overall operational time of the IFE-QGO-optimized system amounts to only 43.71% of that required by the stepwise coordination method. It can be seen that the tuning optimization method based on IFE-QGO can enhance the tuning energy and reduce the total action time. Meanwhile, a comparison is made between the optimization method based on IFE-QGO and the GA and PSO algorithms mentioned in the citation, which are extensively employed in diverse engineering problems, alongside IFE-QGO's distinctive and unique optimization method of QGO. The iterative evolution curve and global convergence running time are shown in Figure 5 and Table 8. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Protection Number** & \multicolumn{2}{c}{**Action Time/s**} \\ \cline{2-3}  & **Before Optimization** & **After Optimization** \\ \hline  
\hline Total Action time/s & 11.5000 & 9.0050 \\ \hline \hline \end{tabular}
\end{table}