# A Reliable Routing Algorithm Based on Path Satisfaction in the Energy Internet
## 3 Network Architecture and System Model
### System Model
#### 3.2.1 Link Model  
A. Link Satisfaction  
The EI communication network topology is modeled as an undirected graph \(G\) (\(V\), \(E\)), and the symbols of \(V\), \(E\) are the set of nodes and communication link set of the networks. Here, the node set not only concludes switching equipment in the IP layer but also transmission devices in the optical layer. Aiming at different services carried in the EI communication network, the latency is the key to measuring the service performance. Also, other indicators, such as the node grade difference [35], link availability, and shared risk link group (SRLG), impact the routing selection process as well. Traditional routing algorithms pay less attention to resource utilization and status in the physical network. The link spectrum connectivity, which indicates the frequency adjacency on a link, is also considered in routing selection. To obtain reliable routing paths for services, we defined the metric of link satisfaction, which is related to the node grade discrepancy, link availability, and link spectrum connectivity. The above factors are analyzed as follows. * Node grade discrepancy. It is well known that the communication devices in the EI are deployed in substations with different voltage scales. Here, nodes denote different substations, given that the routing path with a longer distance has a higher transmission delay. According to the regulations of information exchange and region division in the smart grid [36; 37], the traversed nodes of a routing path located in the different substations should have identical or similar grades, and cross-grade data transmission is not encouraged at all. In practice, to reduce power consumption and save expenditures, the high-voltage or ultra-high-voltage (HV or UHV) transmission power line always adopts the detour path with the aid of multiple nearby low-voltage substations to complete remote power delivery. Consequently, it is possible to switch services to a longer-distance routing path. It is necessary to define the concept of node grade discrepancy to avoid this situation. The node grade discrepancy is a normalized value calculated by the neighboring node voltage scale. Generally, the lower the node discrepancy is, the higher the probability of this link as the next hop. Suppose there are overall \(\mu\) voltage values, and the voltage set is denoted as \(\widetilde{U}=\{\widetilde{v}_{1},\widetilde{v}_{2},\ldots,\widetilde{v}_{\mu}\}\) (unit: kV), e.g., 66 kV, 110 kV, 220 kV, or 500 kV. For node \(i\), the node grade discrepancy is denoted as \(g_{i}\), which ranges from 1 to \(\mu\). Therefore, the node grade discrepancy relevant to the two terminals of the link \(e\), i.e., \(i\) and \(j\), is given as follows:  
\[D_{e}=\frac{\left|g_{i}-g_{j}\right|}{\sum_{x,y\in V,\ l\in E}\left|g_{x}-g_{y }\right|},\forall g_{i},g_{j}\in[1,\mu],\ i,j\in V,e\in E \tag{1}\]  
where \(l\) is the link between any node pair \((x,y)\), and \(D_{e}\) is the normalization of the node discrepancy of link \(e\). * Link Availability. This measures the accuracy of routing computation, and it is related to the link betweenness centrality, link importance, and link reliability. The metric of link betweenness centrality is used to measure the role of a link in the network according to the theory of complex networks. It is the ratio of the number of the shortest paths passing through a link to the number of the shortest paths of any node pairs in the network, as follows: \[\psi_{e}=\sum_{ \begin{subarray}{c}x,y\in V\\ (i,j)\
eq(x,y)\end{subarray} }\frac{\psi_{x,y}(e)}{\psi_{x,y}}\quad e\in E\] (2) where \(\psi_{x,y}(e)\) and \(\psi_{x,y}(e)\) describe the total number of the shortest paths between node \(x\) and \(y\), and the number of shortest paths passing through the link \(e\)\((i,j)\), respectively. The metric of link importance is used to measure the importance of some links in the EI, since links in the EI are the abstraction of the communication fibers, which are laid along the power lines used to connect different voltage substations.