## 3 Impact of Fault Impedance Mismatch  
As mentioned earlier, during a fault event, the fault impedance can take any value, and the accurate guess of fault impedance in the fault estimation stage is a very difficult task. In this section, the impact of the fault impedance mismatch between the fault occurrence and fault estimation stages of the correlation estimator method is presented. It is worth mentioning that the results shown in Figure 5 were obtained assuming \(Z_{f}\) = 10 \(\Omega\) in both stages. In order to observe the impact of fault the impedance mismatch, Figure 1 and Table 1 (with line length = 50 km) are taken as references for the demonstration. The transfer functions for the fault estimation stage were obtained and stored considering \(Z_{f}\) = 10 \(\Omega\), whereas, in the fault occurrence stage, four different values were considered, i.e., \(Z_{f}\) = 0.0 \(\Omega\), 10 \(\Omega\), 300 \  
Figure 9, where the results presented in Figure 8 were obtained considering \(Z_{f}\) = 1000 \(\Omega\) in the fault estimation stage. It can be seen that the fault location was estimated accurately, which was also confirmed by CCv = 1.00. In addition, \(H_{fos}\) due to \(Z_{f}\) = 300 \(\Omega\) was correlated with a low and high fault impedance \(H_{fes}\), and two GFL (\(x_{g}\)) were computed, i.e., 44.84 km and 45.07 km, respectively. The best candidate among these two will be decided based on the corresponding CCv, and in this case, the CCv of 45.07 km was 0.9501, which is higher than 0.8603 (solid grey line).  
A comprehensive analysis of the impact of the fault impedance mismatch along the line length was performed, which is shown in Figures 10 and 11. It can be seen that, in all cases, the impact was almost negligible for fault locations up to 25 km, and the impact is presented in the form of the relative location error, defined as  
\[e[\%]=\frac{\left|x_{f}-x_{g}\right|}{L}\times 100 \tag{18}\]  
Figure 8: CCvs as a function of the GFL (\(x_{g}\)): considering different values of \(Z_{f}\) in the fault occurrence stage, while in the fault estimation stage, \(Z_{f}\) = 10 \(\Omega\); the test fault location is 45 km.  
Figure 9: CCvs as a function of the GFL (\(x_{g}\)): considering different values of \(Z_{f}\) in the fault occurrence stage, while in the fault estimation stage, \(Z_{f}\) = 1000 \(\Omega\); the test fault location is 45 km.  
On the other hand, as the fault location moves away from the observation point, the impact increased for the cases of \(Z_{f}=300\)\(\Omega\) and \(Z_{f}=1000\)\(\Omega\), while, in the fault estimation stage, \(Z_{f}=10\)\(\Omega\), as shown in Figure 10.  
A similar pattern was observed for the cases of \(Z_{f}=0\)\(\Omega\) and \(Z_{f}=10\)\(\Omega\), when \(Z_{f}=1000\)\(\Omega\) was assumed in the fault estimation stage, as shown in Figure 11. Therefore, this analysis shows that both low and high fault impedances should be taken into account during the fault estimation stage to obtain more accurate results. Then, the fault location candidate with the highest CCv should be selected.  
Figure 11: Impact of the fault impedance mismatch along the line length in terms of the relative location error; in the fault occurrence stage, four different values of fault impedance are considered, while in the fault estimation stage, \(Z_{f}=1000\)\(\Omega\).  
Figure 10: Impact of the fault impedance mismatch along the line length in terms of the relative location error; in the fault occurrence stage, four different values of fault impedance are considered, while in the fault estimation stage, \(Z_{f}=10\)\(\Omega\).