Reducing the computational burden of transient stability assessment (TSA) by filtering out most risk-free faults effectively and rapidly without any false-filtering will be significant especially for on-line and uncertainty TSA. This paper presents such a rapid and robust case screening algorithm based on Extended Equal Area Criterion (EEAC). The time-varying degree of an equivalent image system can be reflected by comparing the analysis results of Static EEAC (SEEAC), which neglects all time-varying factors, and that of Dynamic EEAC (DEEAC), which partially considers the time-varying factors. The stable faults can be hierarchically screened out with 3 rules. Different sequences for performing the 3 rules can only affect the computational efficiency, but not the robustness of this algorithm. Excellent performance of this framework is verified by 28 sets of data from 7 actual Chinese provincial power systems with various operating conditions: all the actual unstable contingencies are captured and the screening rate of actual stable cases is above 86%. The average computational time is 86%–96% reduced comparing to TSA with the full IEEAC method.