# IpDFT-Tuned Estimation Algorithms for PMUs: Overview and Performance Comparison
## 3 Estimation Results and Performance Analysis
### Results in Transient Conditions  
To compare the behavior of the three considered IpDFT-tuned estimation algorithms in transient conditions, both the response times associated with synchrophasor, frequency and ROCOF estimation, and the measurement delay times are computed in the worst-case conditions specified in the Standard [10]. In this case, the testing conditions are: either amplitude step changes equal to \(\pm\)10% of the nominal amplitude or phase step changes of \(\pm\)10\({}^{\circ}\). It is worth recalling that the response times are defined as the temporal intervals between the instants at which, as a result of a step input change, the measured values of synchrophasor, frequency or ROCOF exceed a specified TVE, \(|\)FE\(|\) or \(|\)RFE\(|\) threshold (i.e., 1%, 5 mHz or 0.4 Hz/s, respectively, in the case of _P Class_ PMUs, or 1%, 5 mHz or 0.1 Hz/s in the case of _M Class_ PMUs) and the times after which the measured values steadily remain under such thresholds. During the transients, the maximum over- or undershoots affecting amplitude or phase estimates (depending on the type of applied input step) are also of interest, as they are required to be smaller than 5% or 10% of the input step size for _P Class_ and _M Class_ PMUs, respectively. The measurement delay time is defined as \"the time interval between the instant that a step change is applied to the input of a PMU and the measurement time when the stepped parameter achieves a value that is half-way between the initial and final steady-state values\" [10]. In the present study, the _P Class_ and _M Class_ maximum response times and the maximum measurement delay times (obtained by shifting sample-by-sample the instants at which the steps occur) are shown in Table 6a,b over 2-cycle and 4-cycle observation intervals and in Table 7a,b over 6-cycle and 8-cycle observation intervals, respectively. \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}{**Synchronybox Resp. Time**} & \multicolumn{4}{c}{**Frequency Resp. Time (cycles)**} & \multicolumn{4}{c}{**ROCOF Resp. Time (cycles)**} \\ \cline{3-14}
**Test Type** & \multicolumn{2}{c}{ \begin{tabular}{c} **Obs.** \\ **Inter.** \\ **Length** \\ **Lycles** \\ \end{tabular}  } & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**DCF**} & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**DCF**} & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**DCF**} & \multicolumn{2}{c}{**Time**} & \multicolumn{2}{c}{**DCF**} \\ \cline{3-14}  & \multicolumn{2}{c}{**DCF**} & \multicolumn{2}{c}{**Tuned**} & \multicolumn{2}{c}{**TUNLS**} & \multicolumn{2}{c}{**TSD**} & \multicolumn{2}{c}{**TUNLS**} & \multicolumn{2}{c}{**TSD**} & \multicolumn{2}{c}{**TUNLS**} & \multicolumn{2}{c}{**TSD**} \\ \cline{3-14}  & & & & & & & & & & & & & & & & & \\ \hline \(\pm 10\%\) & 2 & 2 & 1.05 & 0.56 & 1.23 & 1.18 & 4.5 & 1.84 & 1.88 & 9.15 & 2.76 & 6 & 2.89 & 1.80 & **9.32** & 2.96 \\ amp. step & 4 & 2 & 1.99 & 0.94 & 1.04 & **2.29** & 4.5 & 3.56 & 3.66 & 2.73 & 4.45 & 6 & 4.68 & 3.43 & **7.97** & 4.91 \\ \hline \(\pm 10^{7}\) phase & 2 & 2 & 1.25 & 1.00 & 1.35 & 1.43 & 4.5 & 1.85 & 1.88 & **9.25** & 2.88 & 6 & 2.88 & **1.84** & **9.35** & 2.99 \\ step & 4 & 2 & **2.35** & 1.10 & 1.20 & **2.68** & 4.5 & 3.42 & 3.61 & 4.33 & **4.74** & 6 & 4.64 & 3.58 & **8.18** & 4.98 \\ \hline \multicolumn{14}{c}{(b)} \\ \cline{3-14}  & \multicolumn{2}{c}{**Test Type**} & \multicolumn{2}{c}{**Obs. Inter. **} & \multicolumn{4}{c}{**Dely Time(ms)**} & \multicolumn{4}{c}{**DCF**} \\ \cline{3-14}  & \multicolumn{2}{c}{**T**} & \multicolumn{2}{c}{**(cycles]**} & \multicolumn{2}{c}{**Lim. **} & \multicolumn{2}{c}{**1 pDFTc**} & \multicolumn{2}{c}{**Tuned TUNLS**} & \multicolumn{2}{c}{**TSD**} \\ \cline{3-14}  & & & & & & & & & & & & & & \\ \hline \(\pm 10\%\) amp. step & 2 & 5 & 1.50 & 1.67 & 3.00 & 1.80 & & & & & & \\ \hline \(\pm 10\%\) amp.