Encountering with the risk of extreme disasters occurring frequently in recent years

cycle structures offer alternative paths for power flow distribution

effectively mitigating the hazard caused by cascading failures. Therefore

based on generalized nodes of the directed weighted power grids

this paper proposes a critical cycle identification method that can resist to high-risk cascading failures

significantly reducing the risk of major blackouts in various N−k scenarios. Firstly

a directed weighted power grid based on the lines' steady state stability margin is defined

demonstrating the structural controllability of the power network. The minimum set of driver nodes of the power system is determined by utilizing the Kuhn-Munkres algorithm

thereby decomposing the power grids into several fully controllable subgraphs. Secondly

the controllable subgraphs are contracted into generalized-nodes to reduce the order of the complex power grid

addressing the challenge of searching for cycle structures in large-scale power grids. Finally

the contribution of cycle structures to the increase in network connectivity is assessed based on the second smallest eigenvector of the Laplacian matrix

and then the critical cycle is identified. Simulation results indicate that even under the high-risk cases of N−k (k≤3) hypothetical scenarios

maintaining the stable operation of the critical cycle could maintain the transient stability of the power system.