## 3 Results and Discussion
### Modified Two-Area Four-Machine Power System (System 1)
#### 3.1.1 Steady State with Gaussian White Noise for Topology Change
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{14}{c}{**Topology SIB**} & \multicolumn{14}{c}{**Topology SIC**} \\ \cline{2-14} ID & \multicolumn{2}{c}{_Measurement_} & \multicolumn{2}{c}{_True Value_} & \multicolumn{2}{c}{**Substation Level**} & \multicolumn{2}{c}{**Area Level**} & \multicolumn{2}{c}{**Network Level**} & \multicolumn{2}{c}{_Measurement_} & \multicolumn{2}{c}{_True Value_} & \multicolumn{2}{c}{**Substation Level**} & \multicolumn{2}{c}{**Area Level**} & \multicolumn{2}{c}{**Network Level**} \\ \cline{2-14}  & **M (pu)** & \(\mathcal{L}^{\star}\) & **M (pu)** & \(\mathcal{L}^{\star}\) & **M (pu)** & \(\mathcal{L}^{\star}\) & **M (pu)** & \(\mathcal{L}^{\star}\) & **M (pu)** & \(\mathcal{L}^{\star}\) & **M (pu)** & \(\mathcal{L}^{\star}\) & **M (pu)** & \(\mathcal{L}^{\star}\) & **M (pu)** & \(\mathcal{L}^{\star}\) & **M (pu)** & \(\mathcal{L}^{\star}\) & **M (pu)** \\ \hline
5 & 1.098 & 34.723 & 1.031 & 34.608 & 1.036 & 34.630 & 1.041 & 34.652 & 1.046 & 34.678 & 1.024 & -17.281 & 1.027 & -17.339 & 1.027 & -17.340 & 1.026 & -17.331 & 1.025 & -17.337 \\ \hline St. & 1.013 & 30.536 & 1.205 & 30.044 & 1.013 & 30.516 & 1.020 & 30.504 & 1.019 & 30.505 & 0.973 & -13.888 & 1.022 & -13.244 & 0.973 & -13.188 & 1.002 & -13.203 & 0.991 & -13.199 \\ \hline
6 & 1.072 & 32.286 & 1.029 & 35.107 & 1.072 & 35.226 & 1.047 & 33.155 & 1.056 & 35.182 & 1.051 & -18.360 & 1.024 & -18.283 & 1.051 & -18.360 & 1.066 & -18.317 & 1.038 & -18.327 \\ \hline
6L & 1.043 & 32.244 & 1.026 & 32.361 & 1.043 & 32.234 & 1.029 & 32.312 & 1.030 & 32.289 & 0.997 & -15.488 & 1.021 & -15.506 & 0.997 & -15.488 & 1.011 & -15.599 & 1.007 & -15.496 \\ \hline
12 & 1.063 & 35.144 & 1.034 & 35.161 & 1.063 & 35.144 & 1.046 & 35.154 & 1.049 & 35.152 & 1.059 & -18.658 & 1.027 & -18.614 & 1.099 & -18.658 & 1.041 & -18.630 & 1.047 & -18.637 \\ \hline
7 & 0.999 & 34.771 & 1.033 & 34.784 & 1.023 & 34.769 & 1.020 & 34.760 & 1.041 & 34.746 & 1.001 & -18.313 & 1.026 & -18.240 & 1.022 & -18.249 & 1.017 & -18.270 & 1.011 & -18.288 \\ \hline T. & 1.023 & 33.099 & 1.031 & 33.972 & 1.029 & 33.909 & 1.030 & 33.940 & 1.030 & 33.939 & 0.999 & -17.434 & 1.024 & -17.415 & 0.999 & -17.434 & 1.013 & -17.423 & 1.010 & -17.426 \\ \hline
8 & 1.012 & 31.794 & 1.041 & 31.758 & 1.036 & 31.755 & 1.029 & 13.749 & 1.023 & 31.743 & - & - & - & - & - & - & - & - & - & - & - & - & - & - \\ \hline
13 & 1.002 & 20.907 & 1.032 & 29.241 & 1.002 & 29.097 & 1.020 & 29.188 & 1.017 & 29.157 & 1.051 & 27.920 & 1.033 & 27.845 & 1.051 & 27.920 & 1.040 & 27.875 & 1.043 & 27.883 \\ \hline
9 & 1.006 & 28.913 & 1.032 & 28.870 & 1.006 & 28.931 & 1.020 & 28.892 & 1.015 & 28.901 & 1.058 & 27.931 & 1.031 & 27.971 & 1.053 & 27.931 & 1.040 & 27.442 & 1.044 & 27.424 \\ \hline
9L & 1.067 & 27.753 & 1.208 & 27.758 & 1.057 & 27.753 & 1.044 & 27.739 & 1.049 & 27.765 & 1.022 & 26.337 & 1.029 & 26.399 & 1.022 & 26.350 & 1.025 & 26.334 & 1.025 & 26.342 \\ \hline
10 & 1.064 & 28.704 & 1.028 & 28.785 & 1.064 & 28.704 & 1.044 & 28.754 & 1.048 & 28.735 & 1.034 & 27.769 & 1.028 & 27.658 & 1.034 & 27.796 & 1.002 & 27.698 & 1.031 & 27.726 \\ \hline
10-1L & 1.047 & 25.907 & 1.024 & 26.029 & 1.007 & 25.937 & 1.033 & 25.992 & 1.007 & 25.982 & 1.044 & 24.986 & 1.025 & 24.908 & 1.044 & 24.986 & 1.033 & 24.936 & 1.036 & 24.955 \\ \hline
10-2L & 0.991 & 25.909 & 1.024 & 26.029 & 0.991 & 25.909 & 1.010 & 25.981 & 1.007 & 25.957 & 0.996 & 24.966 & 1.025 & 24.908 & 0.996 & 24.966 & 1.014 & 24.930 & 1.007 & 24.941 \\ \hline
11 & 1.043 & 29.495 & 1.031 & 29.381 & 1.033 & 29.410 & 1.036 & 29.426 & 1.038 & 29.447 & 1.036 & 28.036 & 1.031 & 27.978 & 1.032 & 27.991 & 1.033 & 28.000 & 1.034 & 28.007 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Voltage estimation from the substation level, area level, and network level for modified two-area four-machine power system model under a steady state for Topology SIB (single line outage) and Topology SIC (area separation). Magnitude (“M”) is shown in pu, and the angle (“\(\angle\)) is in degrees (”).