The total number of N-2 faulty element combinations is huge in large scale power system. Transient angle stability analysis for all N-2 contingencies cannot be finished in given time required by online assessment. The index for contingency severity ranking is proposed to filter out slight cases. The index is calculated based on the stability margins and dynamic modes of the N-1 contingency and sensitivity analysis of another faulty element to generators in the critical cluster. Contingencies with larger index are selected for detailed transient angle stability assessment in order. If the transient angle stability margins of multiple sequential contingencies are greater than 0, subsequent contingencies can be judged stable. Real engineering applications in actual power grid have fully confirmed the validity and practicability of this method.