## 3 Novel Framework for Advanced Synchrophasor Analysis in Modern Control Centres
### Disturbance Classification  
From machine learning perspective, the PMU based identification and localization of grid disturbances can be solved with a time-series classification (TSC) system. A general classification system comprises of the following sub-modules:  
* _preprocessing_: normalize the input data into a suitable data range,
* _feature extraction_: extract relevant features to distinguish between the given classes,
* _classification_: compute affiliation values (e.g., probabilities) for each class using the features and
* _decision-making_: final class assignment of the current observation based on the maximum affiliation value. In particular, the feature extraction from multidimensional sequential data is a challenging task that takes into account the spatiotemporal relationships within the input data. Current TSC approaches include sequence-based, similarity-based (e.g., dynamic time warping), feature-based (e.g., symbolic piecewise aggregation) and model-based techniques (e.g., hidden Markov models, neural networks)-see [53; 54]. Especially recurrent neural networks like long short-term memories (LSTM) or gated recurrent units (GRU) provide state-of-the-art results when dealing with high-dimensional sequential inputs like speech, text or video data-see [55; 56; 57]. Compared to existing approaches, see Section 2.3, the _disturbance classification module_ uses a single prediction model to simultaneously identify and locate grid disturbances from phasor measurements. Dynamic simulations are used to create the training data for a predefined set of contingencies. The input matrix for the classification algorithm comprises of \(K\) normalized measurements from multiple PMU sensors of the grid (no full observability required) over a fixed time span \(T\)-see (7). The target values of the classifier are the disturbance location \(y_{\text{Loc}}\) and the disturbance type \(y_{\text{Type}}\), which are summarized within the class label \(y\)-see (8). \[\mathbf{X}_{\text{N}}= \begin{bmatrix}x_{k}\end{bmatrix} _{k=1}^{k=K}\text{ with }\underline{x}_{k}= \begin{bmatrix}x_{k}^{\prime}\end{bmatrix} _{l=0}^{t=T} \text{ and }\mathbf{X}_{\text{N}}\in\mathbb{R}^{T\times K} \tag{7}\]  
\[y= \begin{bmatrix}y_{\text{Loc}},y_{\text{Type}}\end{bmatrix}  \tag{8}\] \begin{table}
\begin{tabular}{c c} \hline \hline
**Z-Score** & **Anomaly Level** \\ \hline
0–1 & Normal \\
1–2 & Low \\
2–3 & Medium \\
3–4 & High \\ >4 & Extreme \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Overview z-scores and corresponding anomaly levels. \begin{table}
\begin{tabular}{c c} \hline \hline
**Feature** & **Description** \\ \hline \multicolumn{3}{c}{_Basis: time-domain values_} \\ F1 & absolute slope \\ F2 & Variance \\ \multicolumn{3}{c}{_Basis: Stockwell transform coefficients_} \\ F3 & energy variance along time axis \\ F4 & energy variance along frequency axis \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Features for z-score based disturbance detection. First investigations of a simultaneous disturbance identification and localization were performed in [58] by comparing five different classification approaches. From these results and additional research [59], recurrent neural networks were rated as very suitable for the online classification of grid disturbances regarding the classification accuracy and prediction time. Recurrent neural networks like LSTMs or GRUs can capture autoregressive, non-linear dependencies and time-varying patterns in high-dimensional sequential data by utilizing flexible gating mechanisms within the LSTM or GRU cells. Within this study, GRUs were preferred over LSTMs to increase the robustness and to minimize overfitting problems. The principle workflow of the GRU-based disturbance classification approach is shown in Figure 6.  
In the feature extraction step, a hidden state matrix \(\mathbf{H}\) is computed by a single GRU layer with \(Q\) dimensions given the normalized measurement matrix \(\mathbf{X}_{\text{N}}\) and the learned parameters \(\underline{\theta}_{\text{F}}\).