# Analysis of Controllability in Cyber-Physical Power Systems under a Novel Load-Capacity Model
## 4 Case Study and Discussion
### The Controllability of CPPS in Different Network Types
#### 4.2.2 Case B: Chinese 132-Node System  
Similarly, the Chinese 132-node system is taken as an example, and the BA network and WS network of the same size are coupled with the Chinese 132-node system to form a CPPS. The controllability of the network with different coupling strategies under three different attack strategies is shown in Figures 9 and 10, respectively.  
Figure 9 shows the controllability changes of a CPPS constructed with a BA network as its information network topology under different attack strategies. (a), (b), and (c) represent the controllability variation curves of the system under random, degree, and betweenness attack strategies, respectively. When the system is subjected to random attacks, the density of driver nodes gradually increases, while the controllability of the system decreases. The system is already in a state of collapse when the number of attacks reaches about 20. Meanwhile, under degree attacks, the controllability of the CPPS constructed with **DDM** and **DBM** strategies differs significantly from that of the CPPS constructed with **BBM** and **BDM** strategies when the number of attacks reaches 4. In comparison, the changes in the controllability of the CPPS under **BBM** and **BDM** strategies are relatively small when faced with multiple-node attacks, allowing for greater opportunities for system adaptation.  
Figure 8: **(a–c)** The \(n_{d}\) variation curves of the CPPS under four different coupling strategies after random attack, degree attack, and betweenness attack, respectively. The CPPS is formed by coupling the IEEE 39-node system and the WS network.  
Finally, under betweenness attacks, the system suddenly collapses when subjected to the fourth attack, and before that, the CPPS under all four coupling strategies was in a partially dysfunctional state.  
Similarly, Figure 10 shows the changes in the controllability of the CPPS using the WS network as the information network when it is subjected to three attack strategies.  
It is noteworthy that in any situation, deliberate attacks on networks do not significantly reduce the controllability of the network compared to random attacks. Deliberate attacks often target \"hub\" nodes that are connected to many other nodes. As a result, when a hub node fails, its neighboring nodes take over the load, preventing any further propagation of failures. In addition, the **BDM** coupling approach better withstands node failures or attacks, as the controllability degradation of the CPPS formed by **BDM** coupling is the slowest compared to the other three methods in all cases.  
After comparing the two methods of constructing information networks, it was found that under the same circumstances, the CPPS composed of a WS network can exhibit stronger controllability when subjected to node attacks or failures. This finding has im  
Figure 9: **(a–c)** The \(n_{d}\) variation curves of the CPPS under four different coupling strategies after random attack, degree attack, and betweenness attack, respectively. The CPPS is formed by coupling the Chinese 132-node system and the BA network.  
portant implications for future designs of information systems and holds certain guiding significance. Small-world networks possess short average paths and high aggregation, which are highly advantageous in a CPPS, as they enable global connectivity and information transfer while maintaining local communication efficiency. Therefore, in the subsequent research, the information network will be constructed as a small-world network of the same size as the power network. Additionally, the power network and the information network will be coupled in a one-to-one manner based on **BDM**, thereby enhancing its adaptability to node attacks or failures.