## 3 Results
### Prediction Results of Four Input Features, Including the Proposed Electromagnetic Power Feature  
As described in Section 3.1, the optimal penalty coefficients and RBF kernel parameters of the SVM classifiers can be acquired through the training samples with features \(\delta\), \(\omega\), \(V\) and \(P_{e}\), respectively. Theses 4 independent SVM classifiers can then be established to estimate the prediction accuracy of different types of input features on the test samples. The results are shown in Table 1.  
Figure 9: Prediction accuracies of the 4-sample series.  
It can be seen in Table 1 that, among the 4 types of input features, the transient stability prediction accuracy of the feature \(P_{e}\) is the highest, reaching 98.77%, followed by the feature \(V\), etc., The features of \(\delta\) and \(\omega\) have relatively lower accuracies because they may not change much within the 0.06 s-period after the fault clears, namely only 6 post-fault sampling points.  
The prediction results of SVM are further compared with Back Propagation Neural Networks (BP-NN) and Random Forest (RF) in Table 2; the BP-NN algorithm is from [39], and RF uses the built-in function of MATLAB. It can be seen in Table 2 that the accuracy of SVM is higher than that of BP-NN and RF. Therefore, the SVM sub-classifiers are mainly used in this study.  
Tables 3 and 4 further give the confusion matrix of the bus voltage amplitude and the electromagnetic power of the generators, which shows the prediction results of the SVM classifier in more detail. In the tables, the recall rates denote the proportions of transiently stable samples and unstable samples that were accurately predicted, separately.  
It can be seen in Tables 3 and 4 that the recall rates of stable samples are relatively high, always above 99%, but the recall rates of the unstable samples are still not high enough. Therefore, the rest of this paper will focus on improving the prediction performance of unstable samples, that is, to improve the conservativeness of the model.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Electrical Quantity** & **Train Samples** & **Test Samples** & **Train Accuracy/\%** & **Test Accuracy/\%** \\ \hline Generator current \(I\) & & & 99.29 & 97.73 \\ Rotor angle \(\delta\) & & & 99.29 & 98.30 \\ Rotor speed \(\omega\) & 2112 & 1056 & 99.15 & 98.20 \\ Bus voltage amplitude \(V\) & & & 99.95 & 98.39 \\ Electromagnetic power \(P_{e}\) & & & 99.62 & 98.77 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Prediction performance of different types of input features.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Optimal Parameters** & **Electrical Quantity** & **Test Accuracy/\%** \\ \hline \multirow{2}{*}{SVM} & 5-fold: C = 2048, g = 0.25 & Bus voltage amplitude \(V\) & 98.39 \\ \cline{2-4}  & 5-fold: C = 512, g = 0.002 & Electromagnetic power \(P_{e}\) & 98.77 \\ \hline \multirow{2}{*}{BP-NN} & The iteration epochs: 100 & Bus voltage amplitude \(V\) & 97.35 \\ \cline{2-4}  & The batch size: 352 & Electromagnetic power \(P_{e}\) & 98.01 \\ \hline \multirow{2}{*}{RF} & 500 trees, 20 random variables & Bus voltage amplitude \(V\) & 97.82 \\ \cline{2-4}  & 500 trees, 10 random variables & Electromagnetic power \(P_{e}\) & 96.97 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Confusion Matrix for classification results of electromagnetic power.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Test Sets Labels**} & \multicolumn{2}{c}{**Predict Results**} & \multirow{2}{*}{**Recall Rate/\%**} \\ \cline{2-3} \cline{5-5}  & **Stable** & **Unstable** & \\ \hline Stable & 945 & 7 & 99.26 \\ Unstable & 10 & 94 & 90.38 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Confusion Matrix for classification results of bus voltage amplitude.