## 2 Proposed Algorithm
### Data Acquisition  
A 330 kV, 50 Hz, 500 km transmission line was modelled using MATLAB/SIMULINK, and 11 different types of faults were induced in the model, and the fault current data were collected and recorded, as shown in the table below. A wavelet transform syntax was applied to obtain the maximum coefficient current for phases A,B and C. \([C,1]\) = wavedec(x,n, wname), where wavedec is the function which decomposes the signal. \(X\) is the signalgenerated, \(n\) is the wavelet layer, wname is the name of wavelet type and \(C\) is the output wavelet decomposition vector, while \(l\) is the number of coefficients by layer.  
The voltage and current of the grid experience transients when faults occur. Using a discrete wavelet transform to analyse these transients, the defect can be categorised [13]. The zero sequence and phase transient currents are analysed to determine the fault that occurred. Wavelet transform identifies the phase-related fault by calculating the energy of transients linked to each phase and ground.  
MATLAB/Simulink was used to simulate the model using the RLC load at the receiving end, while the three-phase source block was used at the sending end; 330 kV, 500 km, 50 Hz and a three-phase transmission line were used for the model. The coefficient of each fault type was calculated and compared with the threshold value by checking the maximum and minimum threshold values.  
Table 1 shows the maximum coefficient value of the different fault types. In contrast, Table 2 represents the maximum and minimum threshold values for each current fault phase.  
\begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline
**Fault Types** & **Coeff of \(I_{a}\)** & **Coeff of \(I_{b}\)** & **Coeff of \(I_{c}\)** & **Coeff of \(V_{a}\)** & **Coeff of \(V_{b}\)** & **Coeff of \(V_{c}\)** \\ \hline ABC-G & 533.0974 & 495.1115 & 575.3335 & 0.0000 & 0.0000 & 0.0000 \\ \hline ABC & 395.1943 & 587.4911 & 474.7873 & \(-0.0001\) & 0.0000 & 0.0001 \\ \hline (AB-G) & 338.5069 & 531.6202 & 32.9732 & 0.6655 & \(-1.6882\) & 1.0227 \\ \hline (AC-G) & 306.5768 & 22.3418 & 620.4303 & 1.5501 & \(-0.1691\) & \(-1.3810\) \\ \hline (BC-G) & 26.1066 & 608.8079 & 294.0561 & \(-1.2685\) & 1.6153 & \(-0.3468\) \\ \hline (A-B) & 855.3816 & 385.9281 & 17.8156 & \(-1.2792\) & 1.6102 & \(-0.3311\) \\ \hline (A-C) & 299.0803 & 19.8595 & 574.5684 & \(-1.2897\) & 1.6050 & \(-0.3154\) \\ \hline (B-C) & 15.3783 & 420.5652 & 355.8047 & \(-1.3001\) & 1.5996 & \(-0.2996\) \\ \hline (A-G) & 307.6007 & 39.5083 & 20.8305 & \(-1.3103\) & 1.5941 & \(-0.2838\) \\ \hline (B-G) & 32.6032 & 199.6292 & 28.3545 & \(-1.3205\) & 1.5885 & \(-0.2680\) \\ \hline (C-G) & 15.1679 & 28.6647 & 364.3873 & 0.4383 & \(-1.6423\) & 1.2040 \\ \hline No Fault & 10.6870 & 15.1958 & 23.0105 & 1.4530 & 0.0390 & \(-1.4920\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Faulty current and voltage data in kA and kV.  
\begin{table}
\begin{tabular}{p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt} p{42.7 pt}} \hline \hline
**Fault Types** & **Threshold of \(I_{a}\) (kA)** & **Threshold of \(I_{b}\) (kA)** & **Threshold of \(I_{c}\) (kA)** & **Threshold of Ground Current (kA)** \\ \hline  & **Max** & **Min** & **Max** & **Min** & **Max** & **Min** & \\ \hline ABC-G & & & & & & 18.6876 \\ \hline ABC & & & & & & 56.9488 \\ \hline AB-G & & & & & 531.6202 & 32.9732 & 25.7012 \\ \hline AC-G & & & 620.4303 & 22.3418 & & & 15.5710 \\ \hline BC-G & 608.8079 & 26.1066 & & & & 20.9355 \\ \hline A-B & & & & & 855.3816 & 17.8156 & 28.2445 \\ \hline A-C & & & 574.5684 & 19.8595 & & & 34.5217 \\ \hline B-C & 420.5652 & 15.3783 & & & & 16.8326 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Threshold value of current at different fault locations.