Abstract: Fast splitting control, as an important part of stability control of large power grid, is an effective measure to block the path of cascading failure, limit the scope of disturbance, and reduce the loss caused by faults. In this paper, the response characteristics of generators and branches in the process of rotor angle swing were studied, and the law of power transfer and instability process in multi-branch interconnected system were analyzed. Secondly, the definition of critical and quasi-critical branches cluster and the identification method based on wide area branch response were proposed, and the rotor angle instability criterion based on the response characteristics of critical branches and the out-of-step cut-set searching method based on joint quasi-critical branches were proposed. Finally, the simulation results for the actual HVDC and AC hybrid power system show that the proposed strategy has the advantages of accurate location of out-of-step cut sets and fast active splitting control; it can effectively reduce the risk of new energy low-voltage off-grid and etc.