# Fault Diagnosis of HV Cable Metal Sheath Grounding System Based on LSTM
## 3 Analytical Calculations of Sheath Currents under Fault Conditions
### Cable Joint Breakdown Fault  
Cable joints are one of the high incidence parts of cable faults, and cable joint breakdown faults may be triggered when the grounding system generates overvoltage or suffers \begin{table}
\begin{tabular}{c c c} \hline \hline
**Fault Type** & **Operation States Type** & **Serial Number** \\ \hline Normal & / & 0 \\  & Sheath loop L1 open circuit & 1 \\ Sheath loop open circuit & Sheath loop L2 open circuit & 2 \\  & Sheath loop L3 open circuit & 3 \\  & Breakdown of joint JA1 & 4 \\  & Breakdown of joint JB1 & 5 \\ Breakdown of cable joint & Breakdown of joint JC1 & 6 \\  & Breakdown of joint JA2 & 7 \\  & Breakdown of joint JB2 & 8 \\  & Breakdown of joint JC2 & 9 \\ Flooding in link box & Flooding in link box J1 & 10 \\  & Flooding in link box J2 & 11 \\  & Joint JA1 sheath grounding & 12 \\  & Joint JB1 sheath grounding & 13 \\ Sheath grounding & Joint JC1 sheath grounding & 14 \\  & Joint JA2 sheath grounding & 15 \\  & Joint JB2 sheath grounding & 16 \\  & Joint JC2 sheath grounding & 17 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: HV cable grounding system sheath fault classification. Figure 5: Equivalent circuit diagram of sheath loop L1 open circuit fault. lightning strikes, or when the production process and construction environment cause burrs or impurities in the insulation part inside the cable joint [16; 17]. The insulation plate of the cable joint is broken through, resulting in shorting of the metal sheath at the left and right ends of the joint, destroying the cross-bonded system, while the sheath current rises rapidly, affecting the safe operation of the whole cable. In the case of a breakdown fault in cable joint JA1, for example, the A1 minor section of sheath loop L1 and the A2 minor section of sheath loop L3 are sent short, and the equivalent circuit diagram is shown in Figure 6 (the sheath induced current in sheath loop L2 is not affected by the breakdown fault in cable joint JA1 and is not drawn in the diagram to simplify the circuit). In Figure 6, \(I_{\text{XL},n}\) and \(I_{\text{XR}n}\) (\(n=1\), \(3\)) are the sheath induced currents on the left and right sides of the nth loop fault point, and \(R_{\text{f}}\) is the fault resistance. According to the mesh current method, the mesh currents \(I_{\text{f1}}\), \(I_{\text{f2}}\), and \(I_{\text{f3}}\) can be calculated from Equation (15). \[\left\{ \begin{array}{l}U_{\text{mA}_{1}}-U_{\text{mC}_{1}}=I_{\text{f1}}(2R _{\text{e}}+Z_{\text{mA}_{1}}+Z_{\text{mC}_{1}})-I_{\text{f2}}R_{\text{f}}-I _{\text{f3}}(R_{\text{e}}+Z_{\text{mC}_{1}})\\ U_{\text{mB}_{2}}+U_{\text{mC}_{3}}-U_{\text{mA}_{2}}-U_{\text{mB}_{3}}=-I_{ \text{f1}}R_{\text{f}}-I_{\text{f3}}(R_{\text{g}}+Z_{\text{mA}_{2}}+Z_{\text{ mB}_{3}})+I_{\text{f2}}(2R_{\text{g}}+Z_{\text{mB}_{2}}+Z_{\text{mC}_{3}}+Z_{ \text{mA}_{2}}+Z_{\text{mB}_{3}})\\ U_{\text{mC}_{1}}+U_{\text{mA}_{2}}+U_{\text{mB}_{3}}=I_{\text{f3}}(R_{\text{e} }+Z_{\text{mC}_{1}}+Z_{\text{mA}_{2}}+Z_{\text{mB}_{3}}+R_{\text{g}})-I_{ \text{f1}}(R_{\text{e}}+Z_{\text{mC}_{1}})-I_{\text{f2}}(R_{\text{g}}+Z_{\text {mA}_{2}}+Z_{\text{mB}_{3}})\end{array} \right. \tag{15}\]  
The sheath induced currents flowing in the sheath loops L1 and L3 are shown in Equation (16). \[\left\{ \begin{array}{l}I_{\text{XL1}}=I_{\text{f1}}\\ I_{\text{XR1}}=I_{\text{f2}}\\ I_{\text{XL3}}=I_{\text{f3}}-I_{\text{f1}}\\ I_{\text{XR3}}=I_{\text{f3}}-I_{\text{f2}}\end{array} \right. \tag{16}\]  
Therefore, when a breakdown fault occurs in cable joint JA1, the sheath current in the grounding box is as shown in Equation (17). \[\left\{