## 5 Discussion  
In this section, we assess the vulnerability of the ECPSs and provide protection suggestions based on the simulation results provided by the simulation platform developed in this work. In CASE 1, we set the initial power injection as \(\Delta P=\{50,100,150,200,250 MW\}\). The extra injection of the power can successfully be injected into a power bus if \(\Delta P\) is within the capacity limitation. When \(\Delta P>250 MW\), almost half of the loads are beyond the limitation. Table 3 shows 8 situations in which the extra injection will cause an overloading incident. Table 3 also lists the IDs of possible fault power nodes based on Algorithm 1. **Remark 6**: _The upper right mark '\((*)\)'on node ID represents the different power injection. For example, ID = 25\({}^{(3-5)}\) means that the node with ID = 25 will cause a line overload with \(\Delta p_{3}=150\), \(\Delta p_{4}=200\), and \(\Delta p_{5}=250\)._  
Four important conclusions are made based on the simulation results. First, buses 12, 20, 21, 23, 25, 26, 28, and 29 are vulnerable buses against a single power injection, and bus 20 is the most vulnerable bus in the system. Second, the overloaded branches such as \((6,11)\), \((16,19)\), \((21,22)\), and \((23,24)\) are  
Figure 4: The flow chart of the simulation platform. vulnerable to power flow change. The two possible explanations include the initial higher load rate \(Q\) (such as \(Q_{(6,11)}=70.4\%\), \(Q_{(16,19)}=76.7\%\), \(Q_{(21,22)}=67.7\%\), and \(Q_{(23,24)}=59\%\) (\(Q_{average}=35.9\%\))) and the unreasonable partial design of topology (like branches \((2,25)\) and \((28,29)\)). Third, in this system, the branches near the generators have higher capacity limitations with no generator node being vulnerable. This partial design is worth learning. Last, the results in Table 1 also demonstrate the efficiency of Algorithm 1. In seven of eight situations with ten overloaded branches, the accuracy of the proposed algorithm is 90%. In CASE 2, the simulation program begins with a tripped branch. Table 4 presents 20 possible simulation results which will cause cascading failures, with the ID of the initial faulty branch, the number of remaining branches and buses, the economic cost, and running time in the table. Table 3 does not include the situations if cutting off branches will not disturb the original operation. In order to verify the superiority of Algorithm 4, we take the strategy using average adjustments for comparison. Note that 'A' represents the average adjustments and 'W' represents the weighted adjustments. Based on the simulation results, Figure 5 shows the stability of the system. It can be seen that among the 46 branches, if a branch is randomly tripped, the system is still stable with a probability of  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Faulty**} & \multicolumn{4}{c}{**Remaining**} & \multicolumn{4}{c}{**Cost**} & \multirow{2}{*}{**Running Time**} \\ \cline{2-2} \cline{4-7}  & \multicolumn{2}{c}{**Branch**} & & & \multicolumn{2}{c}{**Bus**} & & \multicolumn{2}{c}{**(100 MVA)**} \\ \cline{2-7}  & **A** & **W** & **A** & **W** & **A** & **W** & **A** & **W** \\ \hline
2–30 & 45 & 45 & 38 & 38 & 2.50 & 2.50 & 1 & 1 \\
4–14 & 21 & 21 & 20  
57%. In the other 43.7%, the system will suffer a splitting incident, while the probability of causing serious cascading failures (less than 20 buses remained) is 31%. Figure 6 presents the vulnerability from the aspect of economic costs. Strategies of average and weighted adjustments are shown together (the black line with circle marks represents for costs with weighted adjustments, while green line with star marks represents the costs with average adjustments). The X-axis is the ID of the initial tripped branch. It can be seen from Figure 4 that if branches \((10,11)\), \((10,32)\), \((19,33)\), \((20,34)\), or \((23,36)\) are cut off at the beginning, the government will pay much more for repairing the system after the cascading failures.