## 4 Simulation Result and Discussion
### Analysis of Case Studies
#### 4.3.2 Case II: PMUs Measurement Error Case  
The data obtained using PMUs in the real world may contain noise which is normally assumed to be white and Gaussian in nature and thus may lead to taking incorrect action if not considered [45]. The IEEE standard [46] recommends that the total vector error should be less than 1% for the correct functioning of PMUs. This scenario analyzes the impact of the measurement error from PMUs on the prediction capability of the proposed model. The performance of other deep learning models and machine learning models is also analyzed here in terms of test accuracy, precision, recall, and F1-score subjected to the PMUs measurement error. The random noise following the normal distribution with mean zero and the standard deviation of 1% [47] is added to the original database analyzed under the base case condition. The results illustrated in Table 6 after the addition of noise in both the training and test data sets show that the performance of the proposed model is resilient to the measurement error for both the test systems under study as compared to Table 5. The result shows that the proposed model can classify the STVS state of the power system with the accuracy of 97.93%, and 96.66% for the IEEE 9 Bus test system and New England 39 Bus test system, respectively. It is also found that the performance of all the classifiers decreases with the addition of PMUs noise, with the DT classifier having inferior performance compared to other classifiers in terms of accuracy, precision, recall, and F1-score.  
In a practical power system, the PMUs may encounter more severe noise and may lead to incorrect STVS assessment. However, a similar approach as described in this section  
Figure 12: Confusion matrix of test results for the proposed model on test systems.  
\begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multirow{2}{*}{**Test System**} & \multirow{2}{*}{**Model**} & \multicolumn{6}{c}{**Performance Evaluation**} \\ \cline{3-8}  & & **Accuracy** & **Precision** & **Recall** & **F1-Score** & **Training Time** & **Testing Time** \\ \hline \multirow{4}{*}{IEEE 9 Bus} & Proposed & 98.66\% & 98.74\% & 98.66\% & 98.68\% & 8 min 23 s & 406 ms \\  & TempCNN & 97.87\% & 97.86\% & 97.87\% & 97.85\% & 5 min 59 s & 359 ms \\  & LSTM & 97.86\% & 97.85\% & 97.86\% & 97.81\% & 19 min 59 s & 915 ms \\  & SVM & 92.87\% & 95.95\% & 92.87\% & 93.73\% & 1 min 9 s & 1.2 s \\  & DT & 91.84\% & 95.42\% & 91.84\% & 92.87\% & 56 s & 4.99 ms \\ \hline \multirow{4}{*}{New England 39 Bus} & Proposed & 96.95\% & 97.01\% & 96.95\% & 96.97\% & 24 min 42 s & 658 ms \\  & TempCNN & 96.44\% & 96.55\% & 96.44\% & 96.47\% & 9 min 11 s & 325 ms \\ \cline{1-1}  & LSTM & 96.37\% & 96.60\% & 96.36\% & 96.42\% & 22 min 54 s & 714 ms \\ \cline{1-1}  & SVM & 92.69\% & 96.82\% & 92.69\% & 92.65\% & 3 min 44 s & 1.27 s \\ \cline{1-1}  & DT & 91.36\% & 92.28\% & 91.36\% & 91.48\% & 3 min 3 s & 6 ms \\ \hline \hline \end{tabular}
\end{table}
Table 5: Comparison of performance of proposed model with other deep learning and machine learning models.  
can be implemented to evaluate the performance of these models in case of severe PMUs measurement error.