# Research on Power Cyber-Physical Cross-Domain Attack Paths Based on Graph Knowledge
## 3 Method for Constructing Attack Graph of Electric Power Cyber-Physical Fusion System
### Cascading Fault Vulnerability Assessment Indicators  
When the transient stable nodes are disturbed, some physical space nodes will fail. Therefore, after topological analysis of the physical space power grid and AC power flow analysis and calculation, it is necessary to detect the edge capacity of the physical space power grid. During this period, overloaded edges will cause protection actions and be removed. At the same time, if the power flow convergence fails, it means that the generators in the physical space power grid working subset node network cannot meet the initial load demand, and load shedding optimization operations need to be performed. The objective function and constraint conditions of the load shedding optimization operation are shown in Formulas (8) and (9). \[\min\sum_{i}C_{i} \tag{8}\] \begin{table}
\begin{tabular}{c c c} \hline
**Levels** & **Vertices** & **Vertex Objects** \\ \hline \multirow{8}{*}{L2} & v3 & Measuring instrument measurement deviation \\ \cline{2-3}  & v4 & Control system error action \\ \cline{2-3}  & v5 & Control and signaling devices issue incorrect instructions \\ \cline{2-3}  & v6 & Control and signaling devices refuse to execute instructions \\ \cline{2-3}  & v7 & Control and signaling equipment out of service \\ \cline{2-3}  & v8 & Protection equipment setting value modification—malfunction \\ \cline{2-3}  & v9 & Protection equipment setting value modification-refuse to move \\ \cline{2-3}  & v10 & Protection equipment stops operating \\ \hline \multirow{8}{*}{L3} & v11 & Generator connected to the grid or off-grid \\ \cline{2-3}  & v12 & Adjust power operating parameters \\ \cline{2-3}  & v13 & Close/open power transmission and transformation equipment \\ \cline{2-3}  & v14 & Adjust operating parameters of power transmission equipment \\ \cline{2-3}  & v15 & Load switching \\ \cline{2-3}  & v16 & Load regulation operating parameters \\ \hline L4 & v17 & Physical space system cascading failures \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 4: Layered attack diagram of power cyber-physical fusion system. \[\left\{ \begin{array}{l}P_{i}(V,\delta)-P_{Di}+C_{i}=0\\ Q_{i}(V,\delta)-Q_{Di}=0\\ P_{\text{Gin}}^{\text{min}}\leq P_{i}(V,\delta)\leq P_{\text{Gin}}^{\text{max}} \\ Q_{\text{Gin}}^{\text{min}}\leq Q_{i}(V,\delta)\leq Q_{\text{Gin}}^{\text{max}} \\ 0\leq C_{i}\leq P_{Di}\\ T_{k}(V,\delta)\leq T_{k}^{\text{max}}\\ V_{i}^{\text{min}}\leq V_{i}\leq V_{i}^{\text{max}}\end{array} \right. \tag{9}\]  
Therefore, the vulnerability assessment index of power physical space cascading faults in this paper is composed of two factors: topological integrity and information physical layer operating characteristics. The power network topology integrity coefficient is the proportion of physical layer cascading failure nodes to the total nodes after being attacked by cyber-physical cross-domain attacks; the power grid physical layer operating characteristic coefficient is expressed by the load shedding ratio, which reflects the degree to which the power grid meets the needs of power users. Therefore, the cascading fault vulnerability assessment coefficient of the power cyber-physical fusion system in this paper is shown in Formula (10). \[\left\{ \begin{array}{l}\text{R}_{physical}=\dfrac{N_{physical}-ord(P_{i})}{N _{physical}}\\ R_{loaded}=\dfrac{\sum\limits_{n_{physical}}{\sum\limits_{i}{L_{load}}}}\\ \end{array} \right. \tag{10}\]  
In the formula, N\({}_{physical}\) is the total number of physical layer nodes, i is the iteration number of cascading failures, ord\((P_{2i})\) is the betweenness of the physical layer connected network. T is the total load shedding amount after the cascading fault ends, j is the complete set of physical layer power grid nodes, and \(\sum\text{L}_{\text{load}}\) is the total system load before the power grid failure.