## 3 Results and Discussion
### Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**System**} & \multirow{2}{*}{**Level**} & \multicolumn{2}{c}{**Matrix Forming (\(\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{  }}}}}}}}}}}}\)}\)**} & **LSE Matrix Solving (\(\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ }}}}}}}}}}}}}}\)}\)**} & **LSE Time (\(\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{\mathbf{ \mathbf{ }}}}}}}}}}}}}}}\)**} & **P Percentage from PMU Data Rate (\%)** \\ \hline \multirow{5}{*}{Substation} & SBA & 0.3536 \(\pm\) 0.0362 & 0.9834 \(\pm\) 0.0216 & 1.3370 \(\pm\) 0.0537 & 0.004 \\ \cline{2-5}  & RBA & 0.2342 \(\pm\) 0.0401 & 0.7336 \(\pm\) 0.0273 & 0.9678 \(\pm\) 0.0539 & 0.003 \\ \cline{2-5}  & DBSBA & 0.6780 \(\pm\) 0.0415 & 1.3920 \(\pm\) 0.0794 & 2.0700 \(\pm\) 0.0925 & 0.006 \\ \cline{2-5}  & DBDBA & 0.8320 \(\pm\) 0.0769 & 1.9922 \(\pm\) 0.1020 & 2.8242 \(\pm\) 0.1304 & 0.009 \\ \cline{2-5}  & BHA & 1.1480 \(\pm\) 0.0971 & 2.3200 \(\pm\) 0.1097 & 3.4680 \(\pm\) 0.1344 & 0.010 \\ \cline{2-5}  & Area 1 & 3.4281 \(\pm\) 0.4797 & 64.4102 \(\pm\) 2.9906 & 67.8383 \(\pm\) 3.0216 & 0.204 \\ \cline{2-5}  & Area 1–2 & 0.8020 \(\pm\) 0.0170 & 10.4201 \(\pm\) 0.7057 & 11.2221 \(\pm\) 0.8267 & 0.034 \\ \cline{2-5}  & Area 2 & 2.7210 \(\pm\) 0.0378 & 80.6010 \(\pm\) 3.3116 & 83.3220 \(\pm\) 3.5157 & 0.250 \\ \cline{2-5}  & Network & - & 4.9080 \(\pm\) 0.1621 & 136.9012 \(\pm\) 1.5680 & 141.8092 \(\pm\) 1.6198 & 0.425 \\ \hline \multirow{5}{*}{System B} & \multirow{5}{*}{Area} & Area 1 & 22.6467 \(\pm\) 0.4752 & 711.3356 \(\pm\) 18.8965 & 724.2492 \(\pm\) 19.5782 & 2.173 \\ \cline{2-5}  & Area 2 & 16.2833 \(\pm\) 0.4528 & 415.6667 \(\pm\) 13.3265 & 427.9500 \(\pm\) 15.3395 & 1.284 \\ \cline{2-5}  & Area 3 & 0.6417 \(\pm\) 0.0289 & 8.6026 \(\pm\) 0.5887 & 9.2417 \(\pm\) 0.7887 & 0.028 \\ \cline{2-5}  & Area 4 & 0.6213 \(\pm\) 0.0197 & 8.4015 \(\pm\) 0.3489 & 9.0228 \(\pm\) 0.4139 & 0.027 \\ \cline{2-5}  & Area 5 & 0.6669 \(\pm\) 0.0273 & 8.4153 \(\pm\) 0.3287 & 9.0822 \(\pm\) 0.4358 & 0.027 \\ \cline{2-5}  & Network & - & 68.6017 \(\pm\) 0.9396 & 2552.0658 \(\pm\) 41.1131 & 2620.7017 \(\pm\) 45.8850 & 7.863 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Computational time estimated for the substation level, area level, and network level for modified two-area four-machine power system model under steady state. A summarized comparison of the three levels of the D-LSE is presented in Table 8. It can be seen that the substation level's highest computational time was less than that of the area level. Furthermore, the area level's highest computational time was less than the network level's. The robustness considers the ability to accurately estimate under noise (low: \(ERF<2\), medium: \(2<ERF<3\), and high: \(3<ERF\)), which is analyzed using the \(ERF\) in Tables A1 and A2. The resiliency considers estimation algorithm accuracy (low: \(ERF>4\) and medium: \(ERF\leq 4\)) under bad data in measurements, which are analyzed using the \(ERF\) in Sections 3.1.2-3.1.4.