## 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} \hline \hline  & \multicolumn{3}{c}{_Measurement_} & \multicolumn{3}{c}{_True Value_} & \multicolumn{3}{c}{**Substation Level**} & \multirow{2}{*}{**NR**} \\ \cline{2-2} \cline{4-9}
**Current** & & & & \multicolumn{3}{c}{**Current Estimation**} & & \\ \cline{2-9}  & **M (pu)** & \(\angle\)\({}^{\circ}\) & **M (pu)** & \(\angle\)\({}^{\circ}\) & **M (pu)** & \(\angle\)\({}^{\circ}\) & **\(ERF_{\mathcal{L}}\)** & \\ \hline CB a & 0.273 & 76.108 & 0.277 & 75.412 & 0.274 & 76.955 & 1.37 & 0.45 & 11.43 \\ \hline CB b & 0.019 & 87.367 & 0.001 & \(-93.523\) & 0.016 & \(-56.099\) & 1.18 & 4.83 & 20.95 \\ \hline CB c & **0.287** & **74.055** & **0.277** & \(-104.604\) & **0.068** & \(-98.092\) & **0.05** & **27.44** & **32.38** \\ \hline CB d & 0.665 & \(-95.414\) & 0.683 & \(-94.674\) & 0.672 & \(-94.559\) & 1.69 & 6.43 & 2.99 \\ \hline CB e & 0.045 & 83.710 & 0.000 & \(-95.544\) & 0.020 & 55.465 & 2.23 & 1.19 & 4.35 \\ \hline CB f & 0.690 & 85.915 & 0.683 & 85.326 & 0.680 & 86.016 & 2.55 & 0.85 & 1.56 \\ \hline CB g & 0.652 & 89.972 & 0.665 & 90.739 & 0.653 & 89.762 & 1.11 & 0.78 & 0.41 \\ \hline CB h & 0.007 & 96.894 & 0.000 & \(-94.520\) & 0.005 & 85.032 & 1.33 & 1.07 & 0.31 \\ \hline CB i & 0.675 & \(-89.509\) & 0.665 & \(-89.262\) & 0.672 & \(-89.405\) & 1.47 & 1.73 & 0.47 \\ \hline CB j & 0.268 & \(-91.236\) & 0.253 & \(-91.972\) & 0.264 & \(-90.679\) & 1.33 & 0.57 & 0.69 \\ \hline CB k & 0.243 & 88.654 & 0.253 & 88.030 & 0.247 & 88.361 & 1.71 & 1.89 & 0.69 \\ \hline TL127-1 & 0.279 & 77.299 & 0.278 & 75.455 & - & - & - & - & 11.43 \\ \hline TL127-2 & 0.308 & 75.560 & 0.278 & 75.455 & - & - & - & - & 32.38 \\ \hline TL78-1 & 0.682 & \(-92.871\) & 0.682 & \(-94.675\) & - & - & - & - & 2.99 \\ \hline TL78-2 & 0.683 & \(-93.321\) & 0.682 & \(-94.675\) & - & - & - & - & 1.56 \\ \hline TL67-1 & 0.648 & 89.479 & 0.665 & 90.738 & - & - & - & - & 0.41 \\ \hline TL67-2 & 0.662 & 90.639 & 0.665 & 90.738 & - & - & - & - & 0.47 \\ \hline TL77/L & 0.504 & \(-90.705\) & 0.505 & \(-91.971\) & - & - & - & - & 0.69 \\ \hline
**Average** & - & - & - & - & - & - & 1.46 & 4.29 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: D-LSE of the substation-level current estimation results for substation 7 (BHA) with circuit-breaker c (CB c) current bad data. Magnitude (“M”) is shown in pu, and the angle (\(\angle\)) is in degrees (\({}^{\circ}\)). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{_True Value_} & \multicolumn{3}{c}{_Measurement_} & \multicolumn{3}{c}{**Substation Level**} & \multirow{3}{*}{**NR**} \\ \cline{3-3}
**Current** & & & & \multicolumn{3}{c}{**Current Estimation**} & & \\ \cline{3-3}
**M (pu)** & \(\angle\)\({}^{\circ}\) & **M (pu)** & \(\angle\)\({}^{\circ}\) & **M (pu)** & \(\angle\)\({}^{\circ}\) & **\(ERF_{\mathcal{L}}\)** & \\ \hline CB a & 0.277 & 75.412 & 0.264 & 75.867 & 0.208 & 75.505 & 0.19 & 4.88 & 8.30 \\ \hline CB b & 0.001 & \(-93.523\) & 0.014 & \(-95.401\) & 0.138 & 76.403 & 0.10 & 0.01 & 22.65 \\ \hline
**CB c** & **0.277** & \(-104.604\) & **0.274** & **77.099** & **0.067** & \(-45.902\) & **0.01** & **3.10** & **30.95** \\ \hline CB d & 0.683 & \(-94.674\) & 0.688 & \(-95.953\) & 0.685 & \(-94.962\) & 2.94 & 4.43 & 2.19 \\ \hline CB e & 0.000 & \(-95.544\) & 0.015 & 84.897 & 0.013 & \(-5.012\) & 1.15 & 1.99 & 2.93 \\ \hline CB f & 0.683 & 85.326 & 0.675 & 83.953 & 0.687 & 84.050 & 1.82 & 1.08 & 1.69 \\ \hline CB g & 0.665 & 90.739 & 0.666 & 89.695 & 0.845 & 89.758 & 0.01 & 1.06 & 26.70 \\ \hline CB h & 0.000 & \(-94.520\) & 0.022 & 85.946 & 0.348 & 90.385 & 0.06 & 0.98 & 48.71 \\ \hline CB i & 0.665 & \(-89.262\) & 0.684 & \(-90.771\) & 0.179 & \(-94.176\) & 0.04 & 0.31 & 75.41 \\ \hline CB j & 0.253 & \(-91.972\) & 0.261 & \(-90.571\) & 0.251 & \(-91.487\) & 6.14 & 2.89 & 1.62 \\ \hline CB k & 0.253 & 88.030 & 0.269 & 89.445 & 0.259 & 88.558 & 2.47 & 2.68 & 1.62 \\ \hline \hline \end{tabular}
\end{table}