## Framework of ECPSs
### Model of ECPSs  
Owing to the wide application of sensors, routers, controllers, and actuators in ECPSs, power grids and communication networks deeply interact with each other. According to [PERSON]'s study [39], the topology of a power grid can be abstract as a graph \(G(V,E)\), where \(V\) and \(E\) represent power buses and branches, respectively. Similarly, the topology of a communication network can be abstract as \(G_{c}(V_{c},E_{c})\), where \(V_{c}\) and \(E_{c}\) represent communication nodes and lines, respectively.  
In our framework, each bus or branch in a power grid is equipped with a controller and a sensor. That is to say, we consider a highly intelligent smart grid. Figure 2 shows the framework of  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Item** & **System Scale 1** & \begin{tabular}{c} **Algorithm** \\ **Complexity 2** \\ \end{tabular} & **Control Parameter** & \begin{tabular}{c} **Platform** \\ **Type** \\ \end{tabular} & \
\begin{tabular}{c} **Considering** \\ **Cyber Attack** \\ \end{tabular} &
\begin{tabular}{c} **Failure** \\ **Propagation** \\ \end{tabular} \\ \hline Our & Large & Low & Bus/Branch/Power & Simulator & Yes/Multiple & Yes \\ \hline [15] & Large & Medium & Control Command & Simulator & Yes/Single & No \\ \hline [16; 17] & Small & High & Angle/Frequency & Simulator & Yes/Single & No \\ \hline [20; 21; 22; 23] & Small & High & Control Command & Simulator & Yes/Single & No \\ \hline [24] & Medium & Medium & Control Command & Simulator & Yes/Single & No \\ \hline [26; 27] & Large & Low & Node/Line & Simulator & Yes/- & Yes \\ \hline [29] & Large & Low & Power & Simulator & Yes/Single & No \\ \hline [30] & Small & High & Angle/Frequency & Simulator & No & No \\ \hline [31] & Large & Low & Node & Simulator & Yes/Single & Yes \\ \hline [32; 33] & Small & - & - & Hardware & No & No \\ \hline [34] & Medium & - & Angle/Frequency & OPNET & No & No \\ \hline [35] & Medium & - & Pack loss/Delay & NS-2 & Yes & No \\ \hline [36; 37] & Medium & - & Angle/Frequency & HIL & No & No \\ \hline \hline \end{tabular}  
* System Scale (Small: nodes \(<\) 10; Medium: 10 \(<\) nodes \(<\) 40; Large: nodes \(>\) 40). 2 Algorithm Complexity (Low: DC power flow; Medium: Linear state equation; High: AC power flow/ Nonlinear state equation).  
\end{table}
Table 1: The comparisons with existing solution approaches of vulnerability analyses with electrical cyber-physical systems (ECPSs).  
a regional ECPS. In this two-layer model, the upper layer with nodes numbered 1 to 10 represent a communication network, and \(C_{k}\) is the control center, while the lower layer with power nodes labeled A to E and breakers on branches labeled \(b-1\) to \(b-5\) represent a power grid. The dashed lines with double-sided arrows are information channels between the power grids and communication networks. In the real word, ECPSs in a large area can be divided into several regional ECPSs by physical distances or locations. In this paper, we consider each regional ECPS a local control center \(C_{k}\) with centralized control structures, while in large-scale areas, several regional ECPSs are controlled by a distributed control structures.