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Certain edge failures in cyber–physical power systems (CPPSs) can cause cascading failures in the power system. Protecting these critical edges and essential equipment in the supporting communication network can avoid these failures. Here, based on complex network controllability regarding kinetic equations and considering the actual operating conditions of CPPSs, we filter out a class of transmission lines and a class of nodes in the power system communication network of the power system that show a significant impact on network controllability. We further validate the results of the filtering by examining the resulting network robustness. Through simulations, we observe that the power edges and communication nodes screened based on network controllability have the most significant impacts on system controllability. It is therefore crucial to protect these edges and nodes to achieve more stable power grid operation and prevent cascading failures. Finally, we validate our results using a case study on a city in Henan Province, China. Our simulations demonstrate that the addition of a communication system can enhance the controllability of the power system. • Different key components in both power grid and communication network are considered separately. • The impact of different coupling methods on the controllability of the system are evaluated. • The conclusions of this paper are validated in a real power grid. [ABSTRACT FROM AUTHOR]