# A Hybrid State Estimator Based on SCADA and PMU Measurements for Medium Voltage Distribution System
## 4 Case Studies
### Comparison of State Estimation Results under the Bad Data Condition  
To verify the robustness of the improved IGGIII at the SCADA data acquisition time, the bad data were assumed to appear in the voltage amplitude at bus 6 and the active power of branches 5-6 (measurement error was 75%). Table 3 shows comparisons of various estimation methods under the conditions of different measurement errors. The errors of bad data always exceed 6-7 \(\sigma\) in the actual situation, and all the four estimation methods could all converge even when the error of bad data reaches 95%. Besides, the execution time was less than 0.5 s, which could ensure that the next state estimation will not be affected and guarantee the timeliness of real-time measurements. The improved IGGIII was superior to the other three estimation methods in terms of iteration, and MAE of voltage amplitude. And the execution time of the improved IGGIII was shorter than that of WLS and EXP. That was because the robust thresholds can effectively distinguish the bad data from the normal data and the recalculated weights could reduce the effect of bad data on the estimation results. However, the execution time of the improved IGGIII was longer than that of initial IGGIII. That was because the recalculated weights and robust thresholds in each iteration increased the execution time. Figures 8 and 9 show the comparisons between the two robust estimation methods with a 50% error in voltage amplitude. It can be seen that the voltage amplitude and phasor angle estimated by the EXP deviated from the power flow values in the vicinity of bad data, while the improved IGGIII could make the estimation results closer to the power flow values. Furthermore, it indicates that the normalized residuals and adaptive robust thresholds could eliminate the effect of bad data effectively. Figure 6: State trace at bus 6 of the 33-bus system under the normal condition: (**a**) voltage amplitude curve, and (**b**) voltage angle curve. Figure 7: State trace at bus 30 of the 33-bus system under the normal condition: (**a**) voltage amplitude curve, and (**b**) voltage angle curve. Figure 8: Bus voltage (amplitude and phase angle) profile curves estimated by different methods: (**a**) voltage amplitude curve, and (**b**) voltage angle curve. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Measurement Error of** & **Estimation** & **Convergence** & **Iterations** &
\begin{tabular}{c} **Execution** \\ **Time** \\ \end{tabular} & **MAE** \\ \hline \multirow{3}{*}{Normal condition} & WLS & Yes & 12 & 0.236 & 0.00500 \\  & EXP & Yes & 6 & 0.165 & 0.00004 \\  & IIGGIII & Yes & 9 & 0.174 & 0.00004 \\  & IGGIII & Yes & 13 & 0.165 & 0.00510 \\ \hline \multirow{3}{*}{5\%} & WLS & Yes & 12 & 0.197 & 0.00452 \\  & EXP & Yes & 7 & 0.167 & 0.00008 \\  & IIGGIII & Yes & 8 & 0.162 & 0.00002 \\  & IGGIII & Yes & 13 & 0.175 & 0.00449 \\ \hline \multirow{3}{*}{10\%} & WLS & Yes & 12 & 0.190 & 0.01125 \\  & EXP & Yes & 7 & 0.199 & 0.00062 \\  & IIGGIII & Yes & 8 & 0.193 & 0.00004 \\  & IGGIII & Yes & 13 & 0.173 & 0.01123 \\ \hline \multirow{3}{*}{50\%} & WLS & Yes & 12 & 0.190 & 0.06593 \\  & EXP & Yes & 11 & 0.336 & 0.00300 \\  & IIGGIII & Yes & 8 & 0.174 & 0.00044 \\  & IGGIII & Yes & 12 & 0.172 & 0.06580 \\ \hline \multirow{3}{*}{95\%} & WLS & Yes & 12 & 0.194 & 0.12745 \\  & EXP & Yes & 12 & 0.201 & 0.00353 \\ \cline{1-1}  & IIGGIII & Yes & 8 & 0.189 & 0.00127 \\ \cline{1-1}  & IGGIII & Yes & 11 & 0.163 & 0.12723 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparisons of various estimation methods. Figure 9: Bus voltage (amplitude and phase angle) estimation errors under different methods: (**a**) the estimation error curve of voltage amplitude, and (**b**) the estimation error curve of voltage angle. Figure 9 further illustrates the estimation errors of the two robust methods.