# Feasibility Analysis of Online Uncertainty Metrics for PMU-Based State Estimation
## 5 Simulation Results
### Sensitivity Analysis
As a consequence, it is reasonable to say that TVE and nRMSE provide two different perspectives on the measurement results' reliability. The TVE accounts for the actual estimation errors, but cannot be computed online as it requires the knowledge a priori of the reference values and suffers from the aforementioned definitional uncertainty issues. The nRMSE quantifies the energy that has been neglected by the phasor representation: in the static formulation, it resembles the TVE even if the correlation is guaranteed only in stationary conditions, whereas in the dynamic formulation, it assesses the advantage of an expanded signal model, but is scarcely correlated to the accuracy of zero-order parameters. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Test** & **Model** & \multicolumn{2}{c}{**Corr (\%)**} & \multicolumn{2}{c}{\(p\)**-Value (\%)**} & \multicolumn{2}{c}{**Conf (\%)**} \\ \hline VT & & 0.1 & 0.5 & 0.1 & 0.5 & 0.1 & 0.5 \\ \hline \multirow{2}{*}{SS} & stat & 96.32 & 93.20 & 0.01 & 0.01 & 3.89 & 5.43 \\  & dyn & 13.82 & 1.73 & 17.71 & 89.44 & 39.16 & 39.88 \\ \hline \multirow{2}{*}{PM} & stat & 36.23 & 33.79 & 0.03 & 1.28 & 14.84 & 19.83 \\  & dyn & 8.64 & 5.87 & 39.99 & 56.78 & 39.60 & 39.76 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: TVE vs. nRMSE—Correlation Analysis. Figure 5: Phase modulation: comparison of nRMSE as computed on static and dynamic phasor representation (**a**) and corresponding TVE (**b**) as a function of the selected voltage transformer class. In such analysis, it is difficult to discriminate which uncertainty contribution has the largest impact on the final estimation error. In particular, our analysis focuses on the determination of the definitional uncertainty in the presence of dynamic and non-linear effects. As aforementioned, the model employed to reproduce the distortions introduced by the instrument transformers is limited to their systematic contributions under the assumption that other random effects are mostly covered by narrow- and wide-band spectral components. In order to prove the validity of such an assumption, we performed the same SS and PM tests with another model of instrument transformer taken from the recent literature about PMU and IT contributions [36]. In this case, the model allows for reproducing the typical VT response to fast-changing conditions. Therefore, the transformation produces not only a systematic effect but also a comprehensive distortion of the signal input to the PMU. By running the same numerical tests for the two classes of VT, it is possible to compare the distributions of TVE and nRMSE with the two VT models. Despite the full model producing slightly narrower distributions (due to the absence of uniformly distributed systematic error), the correlation analysis is strongly consistent. In the SS case, the static representation is characterized by correlation levels of more than 95%. In the PM case, instead, the same parameter decreases to less than 40%. Once more, the TVE is more affected by the definitional uncertainty rather than by the distortions produced by correlated (IT) or uncorrelated (noise) sources.