## 3 Novel Framework for Advanced Synchrophasor Analysis in Modern Control Centres
### Disturbance Extraction (Post-Mortem Analysis)  
The _disturbance extraction module_ detects a predefined number of possible grid disturbances by analyzing historical records of a single phasor measurement signal (e.g., frequency). The lack of positive examples (non-outliers) and negative examples (outliers) as well as the high diversity of outlier types makes an exact prediction very difficult. To minimize the variance of the model predictions, different  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Compression Result** & **Parameters** \\ \hline PCA & PCA scores (principle components) & PCA loadings, sample means \\ DWT & approximation and detailed coefficients & low- and high-pass filters, wavelet expansion coefficients \\ \hline \hline \end{tabular}
\end{table}
Table 1: Overview of the data compression techniques and main parameters.  
Figure 3: Basic principle of the spatiotemporal data compression.  
feature extraction, dimension reduction and outlier score estimation techniques are combined within an ensemble-based approach. Each outlier detection algorithm uses different metrics for the outlier scores, which makes a direct comparison difficult. Therefore, a rank transformation aggregates the outlier scores of the base detectors, such that high rank values correspond to low outlier scores and vice versa. In a final clustering stage, only the samples with the lowest total rank values are chosen. The goal of the clustering algorithm is to group similar disturbance patterns into meaningful classes. Therefore, a similarity matrix is computed using time-warp edit distance (TWED) [45]. The resulting dissimilarity matrix is passed to a hierarchical density based clustering algorithm (HDBSCAN) [46] to identify the cluster groups without prior knowledge about the number of cluster groups. For the _disturbance extraction module_, three outlier detection algorithms are used including local outlier factors (LOF) [47], correlation outlier probabilities (COP) [48] and single-linkage based outlier detection (SiLiOd) [49]. These algorithms compute an outlier score to measure the deviation to the normal or majority signal behavior. The main principles of the three algorithms for the outlier scores are given in Table 2.  
As mentioned earlier, the ensemble-based _disturbance extraction module_ uses multiple base detectors to compute outlier scores and extract potential unusual or abnormal records. The base detectors differentiate with respect to the used dimension reduction technique (PCA or Isomap) and the outlier detection method (LOF, COP or SiLiOd). This leads to a total number of six base detectors within the _disturbance extraction module_. Each base detector calculates in total 13 features including statistical and information-based metrics in time-domain as well as energy based features from Stockwell transform coefficients and discrete wavelet transform coefficients. This comprehensive feature representation allows to capture various signal traits in different disturbed situations like abrupt signal changes, oscillations, or other dynamic variations. A short overview of the different base detectors is given in Figure 4. Further literature can be found in [49; 50].  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Main Principle** & **Outlier Score** \\ \hline LOF & Local density of data points and its neighborhoods & Local outlier factor \\ COP & Deviation within local correlation model using robust PCA & Correlation outlier probability \\ SiLiOd & Hierarchical clustering using shortest distances & Path lengths to final cluster \\ \hline \hline \end{tabular}
\end{table}
Table 2: Overview of the outlier detection techniques and outlier score properties.  
Figure 4: Overview of base detectors for the disturbance extraction.