# Analysis of Controllability in Cyber-Physical Power Systems under a Novel Load-Capacity Model
###### Abstract  
In cyber-physical power systems (CPPSs), system collapse can occur as a result of a failure in a particular component. In this paper, an approach is presented to build the load-capacity model of CPPSs using the concept of electrical betweenness and information entropy, which takes into account real-time node loads and the allocation of power and information flows within CPPSs. By introducing an innovative load redistribution strategy and comparing it with conventional load distribution strategies, the superior effectiveness of the proposed strategy in minimizing system failures and averting system collapses has been demonstrated. The controllability of the system after cascading failures under different coupling strategies and capacity parameters is investigated through the analysis of different information network topologies and network parameters. It was observed that CPPSs constructed using small-world networks, which couple high-degree nodes from the information network to high-betweenness nodes from the power grid, exhibit improved resilience. Furthermore, increasing the capacity parameter of the power network yields more favorable results compared to increasing the capacity parameter of the information network. In addition, our research results are validated using the IEEE 39-node system and the Chinese 132-node system. cyber-physical power system; network controllability; cascading failure; load redistribution; coupling topology 20231130461110304611103046111030461103046110304611030461103046110304611030461103046110304611030461103046110304611030461103046110304611030461030461103046103046  
power systems. In addition, disruptions and anomalous conditions within the power system can also have a detrimental impact on the information systems [8]. Unlike other intricate networks, the cyber-physical power system embodies a higher degree of intricacy, which reduces its resilience in the face of abrupt power fluctuations or on-site failures, further accentuating the vulnerabilities within the network. The failure of a specific component within the CPPS can lead to cascading failures and, in severe cases, to the total collapse of the system. In 2010, [PERSON] [9] introduced the concept of interdependent networks in power systems, emphasizing that a failure in one network can cause failures in nodes of other networks that depend on it, which is referred to as cascading failures. Subsequently, many researchers built on this concept and used complex network theory to study the mechanisms of cascading failures in various systems. They proposed cascading failure models such as load capacity models [10; 11], epidemic models [12], OPA failure models (ORNL-PSERC-Alaska, OPA), sandpile models [13], and power flow models [14] to explain the causes behind cascading failure phenomena. Regarding the common load capacity models, various researchers have proposed different load redistribution strategies. [PERSON] [10], based on the betweenness centrality of each node, defined initial load and overload functions for each node and then proposed an evaluation method for the importance of network nodes based on these measures. [PERSON] [15] proposed the strategy of redistributing the load among the nearest neighbors. As shown in the approach, the load of each failed node is distributed to its neighbors. On the other hand, [PERSON] [16] ranked the importance of nodes and lines based on the DC power flow in the power system to reduce the damage caused by cascading failure attacks. [PERSON] [17] proposed a dependency network model between the power grid and the scheduling data network based on dynamic flow. In recent years, numerous scholars and researchers have extended the concept of cascading failure in single-layer networks to the realms of dual-layer and even multi-layer networks. [PERSON] [18] and [PERSON] [19], respectively, delve into the impact of non-local cascading failures and network inter-similarity on the robustness of multi-layered multiplex networks.