## 4 Results from Case Studies
### Validation of Synchrophasor Applications Using Field Measurements
#### 4.2.2 Results from Synchrophasor Disturbance Extraction  
The evaluation of the _disturbance extraction module_ is based on the _MVField_ dataset including voltage magnitudes and angles as well as frequencies from different PMU sensors at medium-voltage level. The reporting rate is 30 f.p.s. Before preprocessing, high frequency components are eliminated from the raw measurements using a wavelet based denoising. A chosen time section of about 15 min of the raw voltage phasors and frequencies is given in Figure 13. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Channel**} & \multicolumn{2}{c}{**Spatial**} & \multicolumn{2}{c}{**Temporal**} & \multicolumn{2}{c}{**Total**} \\ \cline{2-6}  & \(\mathbf{r_{C}}\) & \(e_{r}\) & \(\mathbf{r_{C}}\) & \(e_{r}\) & \(\mathbf{r_{C}}\) & \(e_{r}\) \\ \hline Voltage (magnitude) & & 0.035 & & 0.008 & & 0.036 \\ Voltage (angle) & & 0.001 & & 0.001 & & 0.001 \\ Current (magnitude) & 1.656 & 0.034 & 3.571 & 0.006 & 5.814 & 0.035 \\ Current (angle) & & 0.001 & & 0.004 & & 0.003 \\ Frequency & & 0.006 & & 0.008 & & 0.010 \\ ROCOF & & 0.058 & & 0.016 & & 0.060 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Compression rates and reconstruction errors for different measurement channels. Figure 12: Original vs. reconstructed voltage magnitudes (**left**) and frequencies (**right**) after the spatiotemporal data compression. From visual inspection, some disturbances can be noticed including voltage oscillations at 2100 s, 2450 s and 2650 s as well as voltage sags at 1650 s, 1800 s and 2340 s. Additionally, the voltage oscillations seem to coincide with frequency drops of about 50 mHz and 70 mHz. It can be expected that these events are captured from the _disturbance extraction module_ automatically. The chosen hyperparameters of the different submodules are listed in Table 8. The influence of changing hyperparameters is investigated in [49]. The _disturbance extraction module_ is applied on a historical record of a single measurement channel. Within this survey, results are shown for the voltage magnitude measurements. The dataset is sampled with a window length of 3000 time steps (100 s) and normalized into the range [0,1]. The definition of the window length is crucial for the _disturbance extraction module_ and should be selected in accordance with the expected disturbance time spans. The outlier detection algorithms compute outlier scores for all samples depending on their deviation from the major signal behavior. Figure 14 shows the distribution of outlier scores (outlier map) for different combinations of outlier detection and dimension reduction techniques using time domain features. The 10 samples with highest outlier scores (top-10 outliers) are additionally highlighted in red. \begin{table}
\begin{tabular}{c c} \hline \hline
**Hyperparameter** & **Value** \\ \hline S transform max. frequency & 1 Hz \\ DWT decomposition level & 12 \\ DWT wavelet function & Db5 \\ Isomap number of nearest neighbors & 50 \\ SiLiOd distance function & Mahalanobis \\ LOF \& COP distance function & Euclidean \\ LOF \& COP number of nearest neighbors & 50 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Hyperparameters used for the _disturbance extraction module_. Figure 13: Voltage magnitudes (**top**), voltage angles (**bottom left**) and frequency (**bottom right**) raw signals from the _MVField_ dataset. The majority of data points are clustered close together and correspond to samples with very similar features and signal behavior. For the LOF and COP, the outlier score decreases for data points with a high distance to the center, while SiLiOd shows opposite behavior due to the different metric calculation (see also Section 3.3). Additionally, PCA and Isomap compute slightly different feature embeddings, which increases the variance of the results of the different base detectors.