# BPDM-GCN: Backup Path Design Method Based on Graph Convolutional Neural Network
## 4 Backup Path Design Method Based on BPDM-GCN
### Backup Path Implementation Method Based on Incremental Shortest Path Tree  
Because of variations in the physical distances between nodes within the communication network topology of the wide-area measurement system, selecting a longer link as the backup path can lead to increased recovery delays when transmitting phasor data from a faulty link along this backup route. In order to reduce the phasor data transmission delay in the backup path, this paper considers link load balancing and the shortest path in depth and designs a backup path implementation method based on the incremental shortest path tree according to the link weights output by the improved DDPG algorithm based on GCN in Section 3.1. This paper employs the incremental shortest path tree algorithm to compute the shortest backup path from origin node \(s\) to destination node \(d\) within the communication network of the wide-area measurement system. This algorithm dynamically adjusts to real-time changes in network topology, efficiently updating the shortest path between nodes as required. In the context of a WAMS communication network, the transmission characteristics of phasor data dictate that all switches connected to the PMU transmit phasor data to the switch that is linked to the PDC. This paper utilizes the Dijkstra algorithm to establish the shortest path tree \(T\), with the switch connected to the PDC designated as destination node \(d\), based on the link weights detailed in Section 3.1. This tree serves as the primary route for transmitting phasor data within the communication network of the wide-area measurement system. The source node \(s\) transmits phasor data to the root node \(d\) following the path delineated in the shortest path tree. In order to ensure the reliability of phasor data transmission in the shortest path tree \(T\) in the communication network of the wide-area measurement system, the backup path \(backup\_path_{s,d}\) is calculated for the shortest path tree \(T\) from the source node \(s\) to the root node \(d\) based on the incremental shortest path tree algorithm. During the backup path calculation process, the incremental shortest path tree algorithm efficiently updates shortest path information through incremental updates, thereby minimizing computational resources and time required. The algorithmic steps for computing the backup path using the incremental shortest path tree are as follows: (1) Initialize the link weights in tree \(T\) to infinity and establish the link relationships between nodes in the communication network topology of the wide-area measurement system. (2) Using node \(s\) as the root node in the network topology, employ the Dijkstra algorithm to construct the shortest path tree \(T_{1}\). (3) Disconnect the links between node \(s\) and its neighboring nodes in the shortest path tree \(T_{1}\) sequentially. Based on the priority principle of the incremental shortest path tree, generate an incremental shortest path tree \(T_{2}\) with node \(s\) as the root node. The shortest path from source node \(s\) to destination node \(d\) is selected from the incremental shortest path tree \(T_{2}\) as the backup path. In the event of a malfunction in the network topology, the switch promptly transitions to the designated backup path, ensuring the uninterrupted transmission of phasor data. The particular methodology is illustrated in Algorithm 2. As illustrated in Figure 3, the communication network topology of the wide-area measurement system comprises three distinct nodes: the red node 8, which is a switch node connected to the PDC; the green node, which represents a switch node connected to the PDC; and the node without color marking, which is a regular switch node. According to the link weights obtained in Section 3.1, the shortest path tree is constructed with node 1 as the root node. The main path for transmitting phasor data from node 1 to destination node 8 is \(p_{1,8}=e_{1,7}:e_{7,8}\).