# Wide-Area Protection System for Radial Smart Distribution Networks
## 4 Simulation Study
\begin{table}
\begin{tabular}{c c c} \hline \hline
**No-Fault Disturbance** & **Details** & **Number** \\ \hline Capacitor switching &
\begin{tabular}{c} Switching capacitor on all network buses in both \\ islanded and connected modes of operation \\ Starting an ASM in all of the network buses in \\ both islanded and connected modes of operation \\ Switching all loads of the network on and off in \\ both islanded and connected modes of operation \\ Switching on all three (DG1, BSS, DFIG) DERs in \\ Denks switching & connected mode of operation, and switching off \\ DG1 and DFIG in islanded mode of operation \\ Relays & R12, R21, R23, R32, R34, R43, R45, R54, R56, R65 \\ Total no-fault samples & 530 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Details of generated no-fault samples. The ANN consists of three hidden layers, each containing 64, 32, and 16 neurons, respectively, utilizing the Log-Sigmoid transfer function. Furthermore, the output layer employs the Purlin transfer function, and the real output is calculated rounding the output value. Three following scenarios are performed to train the ANN:  
* Scenario 1: training based on the mean values of the post-disturbance signals (\(V^{po}\), \(I^{po}\), \(\varphi^{po}\))
* Scenario 2: training based on the integral values of the superimposed signals (\(V^{si}\), \(I^{si}\), \(\varphi^{si}\))
* Scenario 3: training based on the mean values of the post-disturbance signals and the integral value of the superimposed signals (\(V^{po}\), \(I^{po}\), \(\varphi^{po}\), \(V^{si}\), \(I^{si}\), \(\varphi^{si}\))  
Figure 4: 2D scatter plot illustrating superimposed values: (**a**) Voltage and Current, (**b**) Voltage and Phase angle, (**c**) Current and Phase angle. Of the data, 80% (1624 samples) is allocated to the training set, while the remaining 20% (406 samples) is designated for the test and validation set. Training is conducted using the Levenberg-Marquardt method, with the number of epochs set to 30 and the minimum batch size set to 64. The accuracy of the trained model is evaluated by comparing the predicted outputs to real outputs using the following formula:  
\[Acc=\frac{\sum_{i=1}^{N_{\text{ts}}}\left|\mathcal{O}_{i}^{pr}-\mathcal{O}_{i }^{real}\right|}{N_{\text{ts}}} \tag{8}\]  
where \(Acc\) represents accuracy, \(\mathcal{O}_{i}^{pr}\) is the predicted output, \(\mathcal{O}_{i}^{real}\) is the real output, and \(N_{\text{ts}}\) is the number of test samples. The output results for the scenarios are illustrated in Table 4. For Scenario 1, the total accuracy is 93.35%; for Scenario 2, it is 97.04%; and for Scenario 3, it is 99.26%. The proposed approach does not miss any faults, achieving a 100% accuracy in fault detection, despite having two malfunctions. Although it is not absolutely perfect, it is significantly better than the other scenarios, demonstrating the effectiveness of the proposed features. The main reason for this performance is that the proposed ANN is designed to differentiate between fault and no-fault conditions. During a fault condition, the current amplitude exhibits a peak value and then stabilizes at a level slightly below this peak. In contrast, during a no-fault condition, the current stabilizes at a value significantly lower than the initial peak after the first peak. By using the mean and superimposed values (Scenario 3), the proposed approach is able to smooth out the peaks and extract features that are specifically sensitive to fault conditions. Once each of the relays detects a fault, it sends the fault flag along with the fault direction to the CPU, and the CPU decides on the fault section based on the received flags \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Scenario**} & **Total Accuracy** & **Number of Class** & **Number of Class** & **Number of** \\  & **(\%)** & **1 Missed Samples** & **2 Missed Samples** & **Maloperations** \\ \hline \(1\) & 93.35 & 14 & 6 & 7 \\ \(2\) & 97.04 & 1 & 3 & 8 \\ \(3\) & 99.26 & 0 & 0 & 2 \\ \hline \hline \end{tabular}
\end{table}