## 4 Identification of Fault Type with Accuracy  
The issue of fault type identification for a three-phase transmission line is discussed in this section. In this regard, a 345 kV frequency-dependent transmission line system with the configuration illustrated in Figure 12 was investigated; other related parameters were already presented in Table 1. The corresponding total p.u.l. transmission line impedance and admittance matrices at f = 1 kHz are as follows:  
\[\mathbf{Z^{\prime}}=\left[ \begin{array}{ccc}0.96+13.1i&0.86+4.5i&0.86+3.6i\\ 0.86+4.5i&0.96+13.16i&0.86+4.5i\\ 0.86+3.6i&0.86+4.5i&0.96+13.16i\end{array} \right]\Omega/\mathrm{km} \tag{19}\]  
\[\mathbf{Y^{\prime}}=\left[ \begin{array}{ccc}5.5\mathrm{e}^{-5}+43i&4.9\mathrm{ e}^{-5}-7.6i&4.7\mathrm{e}^{-5}-3.6i\\ 3.8\mathrm{e}^{-5}-7.6i&4.3\mathrm{e}^{-5}+44i&3.8\mathrm{e}^{-5}-7.6i\\ 4.7\mathrm{e}^{-5}-3.6i&4.9\mathrm{e}^{-5}-7.6i&5.5\mathrm{e}^{-5}+43i\end{array}  \right]\mu\mathrm{S/km} \tag{20}\]  
The fault phenomenon was simulated in an EMTP-RV environment, shown in Figure 13, and \(H_{\mathit{fos}}\) was obtained for each phase (explained in Section 2.2), whereas, \(H_{\mathit{fos}}\) were computed at regular spatial steps along the line by solving the multi-conductor transmission line equation using the BLT formulation (also presented in Section 2). For any fault type scenario, three \(H_{\mathit{fes}}\) must be stored in principle. It was observed that, if only the \(H_{\mathit{fes}}\) of a three-phase fault scenario were correlated with \(H_{\mathit{fos}}\), then the accuracy of the method would be affected. For instance, a fault location of 45 km in Phase \"a\" was considered, and the related \(H_{\mathit{fos}}\) were correlated with the \(H_{\mathit{fes}}\) of the three-phase fault scenario, as shown in Figure 14. The \(\mathrm{GFL}(x_{g})\) were inconsistent over all three phases, with values of 43.9 km, 46.9 km, and 47.30 km for Phases a, b, and c, respectively. Despite the fact that the CCv of Phase \"a\" was greater, i.e., 0.8416, identifying the faulty phase, the estimated fault location was inaccurate. A similar pattern was observed in other scenarios, which are presented comprehensively in Table 3. This was because of the  
Figure 12: Cross-section representation of three-phase transmission line. Figure 13: Schematic representation of the system under study, implemented in EMTP–RV. coupling phenomena that exist between the phases. The data in Table 3 are written as (CCV, \(x_{g}\) (km)). In order to address this issue, another so-called pseudo approach is proposed, in which the \(H_{f\!os}\) for all the possible fault types, e.g., Phases a, b, c, ab, bc, ca, and abc, were stored. For the sake of simplicity, only three scenarios are written in Table 3. Whenever the fault event will occur, to identify the fault type, \(H_{f\!os}\) will be correlated with all the storage data one by one. This will be decided based on the CCV and the consistency of the GFL (\(x_{g}\)) in all three phases. For demonstration purposes, the identical fault scenario in Phase \"a\" at 45 km was repeated, but this time, the related \(H_{f\!os}\) were correlated with \(H_{f\!os}\) of the Phase \"a\" fault type. Figure 15 illustrates that the CCvs in all three phases were \"1.00\" and that the GFL (\(x_{g}\)) were equally consistent and accurate, i.e., 45 km. Thus, the storage data of the fault estimation stage, at which the so-called \"symmetry condition\" is satisfied, determine both the fault type and the location. Figure 14: CCvs as a function of the GFL (\(x_{g}\)): a fault is considered in Phase “a” at 45 km and estimated in all three phases, while the correlation of the \(H_{f\!os}\) and \(H_{f\!os}\) of the 3-phase fault type scenario is shown.