Critical splitting time for power grids under multi-frequency oscillation

For a system that may have multi-frequency oscillations, this paper divided its dynamics into the dynamics between clusters and the dynamics within clusters. And this deviation method can be used for the subsystems with poor coherence. Based on EEAC and transient energy methods, this paper found that under multi-frequency oscillations circumstances, generally, there will be a critical splitting time for its critical instability mode. When the moment of implementation of splitting is greater than the critical splitting time, the sub-systems after splitting are likely to occur successively instability. However, if the splitting control can be taken before the critical splitting time, the subsystems will have a large chance to be stable.