## 4 Results and Discussion
(**a**) Modeling result displayed in 15 s scale; (**b**) the same modeling results displayed in 2 s.  
Figure 6: Comparison of active power outputs of the SI algorithm and simulated power output when H = 5 s and there is 4173 MW loss of generation. (**a**) Modeling result displayed in 15 s scale; (**b**) the same modeling results displayed in 2 s.  
Figure 7: Comparison of active power outputs of SI algorithm and simulated power output when H = 5 s and there is 1263 MW disconnected load. (**a**) Modeling result displayed in 15 s scale; (**b**) the same modeling results displayed in 2 s.  
The errors were evaluated by using the models for the determination of the error estimates for \(\mathrm{R_{yy}}\), RMSE, and \(\mathrm{R^{2}}\), which are given below, and the results are given in Tables 1-3. As we can see from Table 1, in all three compared options at 4173 and 2273 MW power generator disconnection and 1263 MW power load disconnection, the SI algorithm output signal was fully consistent with the comparable generator, which was based on the mathematical model of a real traditional generator, the transfer of power to the power system in the event of a fault. Based on the obtained results, we recommend using the OE model, because its structure is simpler, and more accurate estimates are obtained compared to when other models are used; therefore, the OE mathematical model is more efficient compared to the ARMAX and BJ models. The following figures compare the performance of the developed SI algorithm with the comparable generator (CSI) in the event of a short circuit in the electrical power system. The upper figures (Figures 8 and 9) represent the change in system frequency during a short circuit in an electrical power system, and the lower figures show the active power outputs of the SI algorithm and CSI simulated power output. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Option No.**} & \multicolumn{3}{c}{**OE Vectors of Parameters of**} & \multirow{2}{*}{**RMSE**} & \multirow{2}{*}{**RMSE**} & \multirow{2}{*}{**R\({}^{2}\)**} \\  & & **Corresponding Polynomials** & & & & \\ \cline{2-6}  & **b** & **f** & **k** & & & \\ \hline Option No. 1 & & & & 0.9990 & \(7.0372\times 10^{-8}\) & 0.9980 \\ \hline Option No. 2 & & & 0.9995 & \(7.4343\times 10^{-9}\) & 0.999 \\ \hline Option No. 3 & & & & 0.9982 & \(9.8166\times 10^{-9}\) & 0.9964 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: \(\mathrm{R_{yy}}\), RMSE, and \(\mathrm{R^{2}}\) coefficients of obtained SI algorithm using OE model and comparable generator. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Option No.**} & \multicolumn{3}{c}{**ABMAX Vectors of Parameters of**} & \multirow{2}{*}{**RMSE**} & \multirow{2}{*}{**RMSE**} & \multirow{2}{*}{**R\({}^{2}\)**} \\  & & & **Corresponding Polynomials** & & & & \\ \cline{2-6}  & **a** & **b** & **c** & **K** & & \\ \hline Option No. 1 & & & & 0.9844 & \(1.0938\times 10^{-6}\) & 0.9690 \\ \hline Option No. 2 & 2 & 2 & 0 & 1 & 0.9926 & \(1.0662\times 10^{-7}\) & 0.9853 \\ \hline Option No. 3 & & & & 0.9861 & \(7.1968\times 10^{-8}\) & 0.9724 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(\mathrm{R_{yy}}\), RMSE, and \(\mathrm{R^{2}}\) coefficients of obtained SI algorithm using ARMAX model and comparable generator. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Option No.**} & \multicolumn{3}{c}{**BJ Vectors of Parameters of**} & \multirow{2}{*}{**R\({}_{yy}\)**} & \multirow{2}{*}{**RMSE**} & \multirow{2}{*}{**R\({}^{2}\)**} \\  & & & **Corresponding Polynomials** & & & & \\ \cline{2-6}  & **b** & **c** & **d** & **f** & **k** & \\ \hline Option No. 1 & & & & & 0.9989 & \(7.3495\times 10^{-8}\) & 0.9978 \\ \hline Option No. 2 & 3 & 3 & 0 & 2 & 0 & 0.9995 & \(7.4228\times 10^{-9}\) & 0.999 \\ \hline Option No. 3 & & & & & 0.9981 & \(1.0206\times 10^{-8}\) & 0.9962 \\ \hline \hline \end{tabular}
\end{table}