# BPDM-GCN: Backup Path Design Method Based on Graph Convolutional Neural Network
## 5 Experiment and Result Analysis
### Experimental Comparison
#### 5.2.1 Average Fault Link Recovery Delay  
In order to verify the performance of the BPDM-GCN backup path algorithm in the fault link recovery in the communication network topology of the IEEE benchmark power system, the experiment set the link load to 20%, 40%, 60%, and 80% network topology environments in the communication network topology of six IEEE benchmark power systems, and took the fault link recovery delay as the key indicator for experimental comparison. The fault link recovery delay is composed of the delay consumed by the phasor data at the switch and the time consumed by the phasor data from the source node \(s\) to the destination node \(d\) in the backup path. In order to guarantee the veracity of the experimental outcomes, the algorithm randomly generates faulty links in the network topology simulation of six IEEE benchmark test power systems. The BPDM-GCN backup path algorithm is then employed in conjunction with the NRLF_RL, LIR_LFR, and FR_VLAN faulty link recovery methods in multiple experiments, with the objective of statistically analyzing the experimental outcomes in order to guarantee the credibility of the experimental results. The results of the experiments are presented in Figure 4.  
As shown in Figure 4, the fault link recovery delay of the BPDM-GCN backup path algorithm is lower than that of other fault link recovery algorithms as the link load increases. The fault link recovery delays of the NRLF_RL algorithm, the FR_VLAN method, and the LIR_LFR method all increase to varying degrees as the link load increases. The LIR_LFR fault link recovery method designs the backup path with the optimization goal of reducing the number of flow rules and the backup path bandwidth. Due to the special topology of the communication network of the wide-area measurement system, a long backup path is generated, resulting in a large fault recovery delay. The FR_VLAN fault recovery method utilizes VLAN IDs to aggregate data affected by a faulty link and forwards it along the backup path, resulting in reduced transmission delays compared to the LIR_LFR fault recovery method. The NRLF_RL algorithm for large-scale fault network recovery employs reinforcement learning techniques to assess link performance within the network topology and to devise backup paths based on the severity of faulty link impacts, thereby lowering  
\begin{table}
\begin{tabular}{c c c c} \hline
**IEEE Benchmark Power System Name** & **Number of Nodes** & **PDC Location** & **PMU Location** \\ \hline
30-bus & 30 & Bus 17 & 1,2,6,9,10,12,15,19,25,27 \\ \hline
39-bus & 39 & Bus 16 & 2,6,9,10,11,14,17,20,22,23,25,29 \\ \hline
57-bus & 57 & Bus 22 & 1,4,8,10,20,21,24,28,31, 32,36,41,44,46,49,52,55,57 \\ \hline
118-bus & 118 & Bus 69 & 2,5,10,11,12,17,20,23, 25,29,34,37,40,45,49,50, 51,52,59,65,66,71,75,77,80, 85,87,91,94,101,105,110,114,116 \\ \hline \end{tabular}
\end{table}
Table 2: _Cont._congestion likelihood on these alternate routes. Nonetheless, due to insufficient optimization in backup path design, its fault recovery performance requires further enhancement. The BPDM-GCN backup path algorithm is based on GCN enhanced DDPG for iterative training to obtain load-balanced link weights, and then uses the incremental shortest path tree to compute the backup path, so that the faulty link recovery delay is minimized. However, as the link length in the network increases, it leads to a large recovery delay in the IEEE 118 benchmark test power system communication network topology. Compared with the better NRLF_RL fault network recovery algorithm, the BPDM-GCN backup path algorithm reduces the average recovery delay by about 14.29%.