## 5 Simulation Results and Discussion
### IEEE 39-Bus Case Study  
The next study will involve an evaluation of the IEEE 39-bus system [42]. The schematic diagram of the IEEE 39-bus test system, which includes 10 generators and 45 lines, is presented in Figure 13. Notably, Figure 14 illustrates the placement of a controllable UPFC in the line between bus 10 and 11. Similar to the previous case study, this study will focus on the optimized coordinated controller of UPFC and PSS to achieve an efficient response and establish the optimal and secure operating point of the power system against sudden disturbances, such as those caused by cyber-physical attacks. The simulation will assume a time step of 0.0001 s, and the rotor angle of generator 2 will serve as the reference angle for this analysis. Figures 15 and 16 are dedicated to examining the total speed deviation, total generation cost, and voltage deviation of the IEEE 39 bus test system. This analysis is conducted after optimizing the coefficient factors of the coordinated controller for UPFC and PSSs using Proportional-Integral control (PM) and various advanced research methods that have been previously developed. According to the findings presented in these figures, the power system and its generators are operating optimally and in a stable condition before the fifth second of real-time simulation. However, in the context of this case study, a sudden cyber-physical attack occurs at the hundredth second, resulting in the disconnection of the line between bus 4 and 14. Remarkably, as depicted in Figures 15 and 16, PM exhibits the swiftest response in restoring the power system to a stable condition with the least \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Disturbance** & **Indexes** & **Operating** & **Speed** & **Voltage** & **CPU-Time for** & **Number of** \\  & & **Cost (S)** & **Deviation (pu)** & **Deviation (pu)** & **Optimization** & **Iterations** \\ \hline \multirow{4}{*}{\begin{tabular}{c} Line outage \\ between \\ buses 4 and 5 \\ \end{tabular} } & \multirow{2}{*}{**PM**} & 1107.48 & 0.00017 & 0.1714 & \multirow{2}{*}{122.1} & \multirow{2}{*}{21} \\ \cline{3-3} \cline{5-6}  & & ✓ & ✓ & ✓ & \\ \cline{2-6}  & & 1107.96 & 0.00256 & 0.1942 & \multirow{2}{*}{186.45} & \multirow{2}{*}{32} \\ \cline{3-3} \cline{5-6}  & & ✗ & ✓ & ✗ & \\ \cline{3-3} \cline{5-6}  & & 1107.98 & 0.00186 & 0.2032 & \multirow{2}{*}{49} \\ \cline{3-3} \cline{5-6}  & & ✗ & ✓ & ✗ & \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Line outage \\ between \\ buses 7 and 8 \\ \end{tabular} } & \multirow{2}{*}{**PM**} & 1112.52 & 0.00011 & 0.1218 & \multirow{2}{*}{122.1} & \multirow{2}{*}{21} \\ \cline{3-3} \cline{5-6}  & & ✓ & ✓ & ✓ & \\ \cline{3-3} \cline{5-6}  & & 1113.84 & 0.00341 & 0.1621 & \multirow{2}{*}{186.45} & \multirow{2}{*}{32} \\ \cline{3-3} \cline{5-6}  & & ✗ & ✓ & ✗ & \\ \cline{3-3} \cline{5-6}  & & ✗ & ✓ & ✗ & \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Line outage \\ between \\ buses 6 and 9 \\ \end{tabular} } & \multirow{2}{*}{**PM**} & 1101.41 & 0.00056 & 0.1023 & \multirow{2}{*}{122.1} & \multirow{2}{*}{21} \\ \cline{3-3} \cline{5-6}  & & ✓ & ✓ & ✓ & \\ \cline{3-3} \cline{5-6}  & & 1102.82 & 0.00423 & 0.1851 & \multirow{2}{*}{186.45} & \multirow{2}{*}{32} \\ \cline{3-3} \cline{5-6}  & & ✗ & ✓ & ✗ & \\ \cline{3-3} \cline{5-6}  & & 1103.05 & 0.00384 & 0.3521 & \multirow{2}{*}{49} \\ \cline{3-3} \cline{5-6}  & & ✗ & ✓ & ✗ & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of performance between the PM and previous SOTA methods in different scenarios of cyber-attacks on the IEEE 9\(-\)bus network. In this regard, as illustrated in Figure 17, it becomes evident that the optimal generation points and rotor angles of the generators within the system undergo a change following the mentioned line outage. As a result, PM dynamically establishes a new stable rotor angle point in real-time, distinguishing itself from previous research approaches.