A coherence identifying method based on the linearized model for power systems at the non-equilibrium point is proposed， which can take into account the impact of faults. The theoretical derivation of the linearization at the non-equilibrium point is presented and the general laws of the dynamic characteristics of power systems at the non-equilibrium point are obtained. Two novel coherence identifying algorithms for power systems are designed and tested on the 4-generator 11-bus system and the IEEE 39-bus system， respectively. Through a comparison with the time domain transient simulation results， the efficiency of the algorithms is proved. Finally， the merits of this method as well as its possible applications in future are pointed out.