# Fault Detection and VSC-HVDC Network Dynamics Analysis for the Faults in Its Host AC Networks
## 3 Simulation Model and Results
### Simulation Results  
Different faults such as single line-to-ground (AG), double line-to-ground (ABG), line-to-line (AB), and symmetrical faults (ABC) were simulated using the test system. The faults were created at different locations (F\({}_{1}\), F\({}_{2}\), F\({}_{3}\) and F\({}_{4}\)) in Figure 2. The AG, ABG, AB,  
Figure 2: MMC HVDC network.  
and ABC faults were created at location F\({}_{1}\), with variations in system parameters such as the fault resistance (R\({}_{i}\)), load angle (\(\delta\)), and fault inception instance (t\({}_{i}\)) mentioned in Table 2 to evaluate the performance of the proposed method.  
Various faults were created at location F\({}_{1}\), and the current signals were collected at the PCC end. The phase A currents were chosen for analysis, as shown in Figure 3.  
The signals obtained for the AG, ABG, AB, and ABC faults denoised the signal and decomposed the signal into various modes based on the frequency components present in the signal. The SST was further used to avoid the mode mixing issue of the EMD technique. The obtained modes were further utilized for analysis. The modes obtained for the ABC faults after applying the EMD-SST on the phase A current signal are shown in Figure 4. Similar to the other fault cases, the same decomposition procedure was applied. From the analysis, and by applying kurtosis analysis, it was observed that IMF-1 was more suitable to be applied for fault analysis compared with the other IMFs. The main reason for this is the information that resides in IMF-1 being more useful for fault analysis, as it contained the maximum frequency component. The variations observed in IMF-1 during normal and fault conditions provided a clear discrimination between the pre-fault and post-fault events. Thus, IMF-1 was further considered for fault identification by the proposed method. For the AG, ABG, and AB fault cases, EMD was applied in a similar manner.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Sl. No.** & **Fault Type** & **Location (km)** & **\(\delta\) (deg)** & **R\({}_{f}\) (\(\Omega\))** & **t\({}_{i}\) (s)** \\ \hline \(1\). & AG & & 30 & 100 & 2.25 \\ \hline \(2\). & ABG & & 45 & 50 & 2.5 \\ \hline \(3\). & AB & & 60 & 20 & 2.75 \\ \hline \(4\). & ABC & & 80 & 5 & 3.0 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results for different fault cases for various load angle, fault resistance and inception isnatnce.  
Figure 3: (a) Current signal for AG fault. (b) Current signal for ABG fault. (c) Current signal for AB fault. (d) Current signal for ABC fault.  
The target signals for all fault cases were processed using EMD. Various IMFs were obtained based on the decomposition level. After the decomposition, IMF-1 came out as the most because it holds the useful information related to fault-generated transients. The instantaneous amplitude and instantaneous frequency information of the first IMF was obtained using the SST with the help of Equations (2) and (3). The energy index for each fault case was calculated using the DTE with the help of Equation (12). The DTE for the AG, ABG, AB, and ABC faults are shown in Figure 5a-d, respectively.  
Before the fault inception instant, the DTE index was below the threshold value. However, the DTE index crossed the threshold value after fault initiation. For the AG fault, the index crossed the threshold value after 4.25 ms of the fault's inception. However, for the ABG, AB, and ABC faults, the index took 3.85 ms, 1.65 ms, and 1.3 ms, respectfully. Similar fault studies were carried out at locations F\({}_{2}\), F\({}_{3}\), and F\({}_{4}\). The results obtained for all symmetrical and asymmetrical faults were computed, and they are presented in Table 3.  
Figure 4: Current signal decomposition for ABC faults.