## 4 Transmission Line Fault Detection  
The developed technique is implemented to detect all fault types incident on the power transmission line (PTL). A threshold value of \(5\times 10^{9}\) is utilized to differentiate the fault and healthy phases. The L-G fault is realized at the center of the PTL. The signals of the current measured at the sending end of the PTL, the W-index, the \(S\)-index, and the proposed FI are illustrated in Figure 2(a)-d, respectively. It is clear from Figure 2(b) that the magnitude of the W-index for all phases is near zero prior to the incidence of the fault event. The magnitude of this index for Fault Phase A increases just after the fault occurrence, whereas for the healthy phases, the magnitude of the W-index continues to remain near zero even after the incidence of the fault. As observed from Figure 2(c), the S-index increases after the fault event for Fault Phase-A and continues to be near zero for the healthy phases. Further, from Figure 2(d), it is clear that the FI is zero in the pre-fault condition, increases immediately following the fault incident for Fault Phase A, and remains zero for the healthy phases. The FI associated with Phase A is above the pre-set threshold just after the occurrence of the fault of an LG nature, whereas this FI continues to be zero for healthy Phases B and C. Hence, the algorithm introduced in this manuscript can be effectively implemented for the identification of L-G faults. Figure 2: The proposed technique’s flowchart. By short circuiting Phases A and B, the LL fault is created at middle of the transmission link. Figure 4a-d illustrates the current signal captured at the sending terminal of the transmission link, the W-index, the \(S\)-index, and the F-index, respectively, at the time of the LL fault. From Figure 4b, it is clearly established that the magnitude of the W-index falls to nearly zero prior to the fault incidence, corresponding to all phases. However, just after the fault event, this index corresponding to Fault Phases A and B is increased, whereas for the healthy Phase C, the magnitude of the W-index continues to remain near zero even after the incidence of the fault. As can be inferred from Figure 4c, the S-index related to Phases A and B rises immediately following the fault event  
Figure 4: Identification of the fault with an LL nature: (**a**) signals of the current (**b**) W-index (**c**) S-index, and (**d**) FI. Figure 3: Identification of the fault with the L-G nature: (**a**) signals of the current (**b**) W-index (**c**) S-index and (**d**) FI. and continues to be near zero for the healthy Phase C. Figure 4d shows that the F-index is zero in the pre-fault condition, but increases just after the fault event for Fault Phases A and B. Further, it remains zero for healthy phase C. The FI related to Phases A and B is above the pre-set threshold just after the occurrence of the fault with an LL nature, whereas this F continues to be zero for healthy Phase C. Therefore, to detect the fault with an LL nature, the proposed algorithm is effectively utilized. By grounding Phases A and B, at the same time, the LL-G fault appears in middle of the PTL. The current signal recorded at the sending terminal of the transmission link, the W-index, the S-index, and FI at the time of the LL-G fault are illustrated in Figure 5a-d, respectively. From Figure 5b, it is clearly established that the magnitude of the W-index falls nearly to zero prior to the fault incidence related to all phases. This index related to Fault Phases A and B rises immediately following the fault event, whereas for the healthy Phase C, the magnitude of the W-index continues to remain near zero even after the incidence of the fault.