Since the motion of the multi machine system under large disturbance can be divided into relative motion between clusters and relative motion in clusters

the concept of transient energy between clusters and transient energy within clusters can be put forward. The out-of-step time tm can be acquired based on the characteristics of transient energy between clusters of the original system and complementary-cluster energy-barrier criterion. By analyzing the characteristics of the transient energy between clusters of subsystem

the critical clearing time tn can be acquired. The unstable modes can be classified as successive-unstable mode

strict multi-group mode and inexact multi-group mode by comparing the duration of tm

tn and tc(fault clearing time). Besides

splitting strategies are also provided for different instability modes

which have guiding significance for the splitting strategy under multi-frequency oscillation. The correctness of the foregoing analysis has been proved through simulation verification of an actual power grid model.