# IpDFT-Tuned Estimation Algorithms for PMUs: Overview and Performance Comparison
## 3 Estimation Results and Performance Analysis
### Results in Transient Conditions
step & 4 & 5 & 1.50 & 1.50 & 1.80 & 1.80 & & & & & & \\ \hline \(\pm 10^{7}\) phase step & 2 & 5 & 1.83 & 2.00 & 4.70 & & & & & & & \\ \hline \(\pm 10^{7}\) phase step & 4 & 5 & 1.83 & 1.83 & & 2.00 & & & & & & \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Obs.**} & \multicolumn{4}{c}{**Synchronized Resp. Time**} & \multicolumn{4}{c}{**Frequency Resp. Time (cycles)**} & \multicolumn{4}{c}{**ROCOF Resp. Time (cycles)**} \\ \cline{3-14}
**Test Type** & \multicolumn{2}{c}{**Longth**} & \multirow{2}{*}{**Lim**} & \multirow{2}{*}{**IoPFTC**} & \multicolumn{2}{c}{**Tuned**} & \multirow{2}{*}{**LII.**} & \multirow{2}{*}{**IoPFTC**} & \multirow{2}{*}{**Tuned**} & \multirow{2}{*}{**Tuned**} & \multirow{2}{*}{**DCF**} & \multirow{2}{*}{**Lim.**} & \multirow{2}{*}{**IoPFTC**} & \multirow{2}{*}{**Tuned**} & \multirow{2}{*}{**LII.**} & \multirow{2}{*}{**IoPFTC**} & \multirow{2}{*}{**Tuned**} & \multirow{2}{*}{**DCF**} \\ \cline{3-14}
**TVDES** & & & & & & & & & & & & & & & & & & & & & & & & \\ \hline \(\pm 10\%\) amp. & 6 & 7 & 2.96 & 1.36 & 1.68 & 1.98 & 14 & 5.17 & 5.37 & 5.78 & 4.14 & 14 & 6.43 & 4.90 & 7.33 & 12.27 \\ \cline{2-14} step & 8 & 7 & 3.93 & 1.78 & 1.81 & 2.60 & 14 & 6.71 & 6.99 & 4.37 & 4.96 & 14 & 8.09 & 6.17 & 8.96 & 8.91 \\ \hline \(\pm 10^{\circ}\) phase & 6 & 7 & 3.49 & 1.56 & 1.94 & 2.32 & 14 & 5.13 & 5.31 & 7.13 & 6.36 & 14 & 6.36 & 5.22 & 7.33 & 12.28 \\ \cline{2-14} step & 8 & 7 & 4.63 & **2.04** & 2.17 & 3.06 & 14 & 6.66 & 6.96 & 7.11 & 7.23 & 14 & 8.05 & 6.78 & 8.98 & 8.91 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Obs. Inter.**} & \multicolumn{4}{c}{**1 Delay Time I (ms)**} \\ \cline{3-14}
**Test Type** & \multicolumn{2}{c}{**Obs. Inter.**} & \multicolumn{4}{c}{**Decf**} \\ \cline{3-14}
**TVDES** & \multicolumn{2}{c}{**LSF**} & \multicolumn{2}{c}{**STD**} \\ \cline{3-14}
**TVDES** & \multicolumn{2}{c}{6} & \multicolumn{2}{c}{5} & \multicolumn{2}{c}{1.50} & \multicolumn{2}{c}{1.50} & \multicolumn{2}{c}{1.50} \\ \cline{3-14}
**TVDES** & \multicolumn{2}{c}{8} & \multicolumn{2}{c}{5} & \multicolumn{2}{c}{1.50} & \multicolumn{2}{c}{1.50} & \multicolumn{2}{c}{2.00} \\ \hline \(\pm 10\%\) amp. step & 6 & 5 & 1.83 & 1.83 & 4.80 & 4.50 \\ \cline{2-14}
**TVDES** & \multicolumn{2}{c}{8} & \multicolumn{2}{c}{5} & \multicolumn{2}{c}{1.83} & \multicolumn{2}{c}{1.83} & \multicolumn{2}{c}{3.00} & \multicolumn{2}{c}{4.70} \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Maximum response times (expressed in nominal power line cycles) associated with synchrophasor, frequency and ROCOF estimation (a) and maximum delay times (b), under the influence of the worst-case amplitude or phase step changes specified in the IEEE/IEC Standard 60255-118-12018 for \(M\) Class PMUs using 6-cycle or 8-cycle observation intervals. The limits specified in the Standard are also shown. The values exceeding the limits are highlighted in bold, whereas the cells containing the best results obtained in each test are shaded. The results in both cases are quite consistent and can be summarized as follows:  
* The limits reported in the Standard are met in almost all cases with a few exceptions. * The maximum synchrophasor and ROCOF response times of the TWLS estimator are always considerably shorter than those of the IpDFTc estimator. However, the IpDFTc frequency estimation response times are generally the shortest ones, except under the effect of amplitude steps when 4-cycle observation intervals are considered. In fact, this is the sole testing condition in which the DCF approach outperforms the other estimators. Furthermore, the over- and undershoots obtained with the IpDFTc estimator are generally smoother than those of the other algorithms. In any case, the over- and undershoots of all considered algorithms are well below the limits reported in the Standard. Therefore, they are not reported for the sake of brevity.