Approximating the boundary of attraction region is very important to the application of the energy function method. Starting from the mathematical model of power system applied in energy function methods

the stability boundaries of one- machine infinite-bus system and IEEE three-machine nine-bus test system are approximated by applying the semi-tensor based stability boundary approximation algorithm. The critical clearing time is calculated based on the approximated boundary. Compared with the traditional stability boundary in the energy function method

the approximation enhances the accuracy of the direct method on transient stability analysis. The efficiency of the semi-tensor based stability boundary approximation algorithm is shown in the paper. The problems hindering the application of semi-tensor theory on large-scale power system are also pointed out in the paper.