*5.4. Efficiency Comparison*

Figure 7 depicts solving time statistics, where the X-axis represents the number of faults in pre-contingency, and the Y-axis is computation time. As shown in Figure 7, the runtime of M1, M2, and M3 are significantly longer than that of M4 under single contingency (i.e., one fault in pre-contingency). And, all algorithms consume more time to compute TTC with more contingencies considered, except for M4. This is because M1, M2, and M3 all need to calculate DAEs associated with TSCs in iterations, and the dimensions of DAEs are higher as more contingencies are considered. However, M4 surrogates the time-consuming part by learning-aided model, and reduces the computation time. The results claim that the proposed method significantly outperforms other comparative methods with respect to efficiency.

**Figure 7.** Efficiency analysis.
