# Safety Issues Referred to Induced Sheath Voltages in High-Voltage Power Cables--Case Study  
[PERSON]  
1 Faculty of Electrical and Control Engineering, Gdansk University of Technology, Narutowicza 11/12, PL-80-233 Gdansk, Poland; [EMAIL_ADDRESS]  
2  
[PERSON]  
1 Faculty of Electrical and Control Engineering, Gdansk University of Technology, Narutowicza 11/12, PL-80-233 Gdansk, Poland; [EMAIL_ADDRESS]  
2  
in the standards [2,3] as well as the report [4]. Figure 1 presents the three aforementioned cable bonding arrangements. The simplest cable sheath bonding arrangement is single-point bonding. In such a solution (Figure 1a) the load current in the cable conductor (core) induces a voltage in the sheath, which value is the highest at the unearthed end of the power cable line. The induced sheath voltages for any cables' formation in a single-circuit system can be calculated (in simplified form) as follows [2]:  
\[V_{\text{L1-sh}}=j\omega I_{\text{L1}}2\cdot 10^{-7}\left[-\frac{1}{2}\ln \left(\frac{2D_{\text{L1-L2}}^{2}}{D_{\text{Cu}}\cdot D_{\text{L1-L3}}}\right) +j\frac{\sqrt{3}}{2}\ln\left(\frac{2D_{\text{L1-L3}}}{D_{\text{Cu}}}\right)\right] \tag{1}\]  
\[V_{\text{L2-sh}}=j\omega I_{\text{L2}}2\cdot 10^{-7}\left[\frac{1}{2}\ln\left( \frac{4D_{\text{L1-L2}}\cdot D_{\text{L2-L3}}}{D_{\text{Cu}}^{2}}\right)+j \frac{\sqrt{3}}{2}\ln\left(\frac{D_{\text{L2-L3}}}{D_{\text{L1-L2}}}\right)\right] \tag{2}\]  
\[V_{\text{L3-sh}}=j\omega I_{\text{L3}}2\cdot 10^{-7}\left[-\frac{1}{2}\ln \left(\frac{2D_{\text{L2-L3}}^{2}}{D_{\text{Cu}}\cdot D_{\text{L1-L3}}}\right) -j\frac{\sqrt{3}}{2}\ln\left(\frac{2D_{\text{L1-L3}}}{D_{\text{Cu}}}\right)\right] \tag{3}\]  
where: \(V_{\text{L1-sh}}\), \(V_{\text{L2-sh}}\), \(V_{\text{L3-sh}}\) are the induced sheath voltages (V/m) in phases L1, L2 and L3, respectively; \(I_{\text{L1}}\), \(I_{\text{L2}}\), \(I_{\text{L3}}\), are the load currents in the cable conductor (core) of phases L1, L2 and L3, respectively; \(D_{\text{cu}}\) is the geometric mean sheath diameter; \(D_{\text{L1-L2}}\) is the axial spacing of phases L1 and L2; \(D_{\text{L2-L3}}\) is the axial spacing of phases L2 and L3; \(D_{\text{L1-L3}}\) is the axial spacing of phases L1 and L3. For more accurate calculation of the voltages, especially taking into account the electromagnetic couplings, computer-based tools should be employed. The computer-aided modelling of the induced sheath voltages with the use of the PSCAD/EMTDC software is presented in [5], whereas [6] presented the calculation by the Pearson Correlation. Multiple-circuit systems require the application of advanced computer-based tools to calculate these voltages, as presented by the authors in [7] or other researchers in [8,9]. To avoid electric shock, the induced voltage-to-earth at the unearthed end should not exceed permissible values determined by the standard [10]. For a long-time of touch voltage duration,  
Figure 1: High-voltage power cables arrangements: (**a**) single-point bonding; (**b**) both-ends bonding; (**c**) cross bonding. the permissible value is equal to 80 V. When the load current is relatively low or a cable line is not long, values of the induced voltages are usually below the permissible limit. A more serious problem occurs in the case of a line-to-earth fault at the unearthed end. If the value of the short-circuit current is high, this current produces a high-value induced voltage, which may damage the cables' non-metallic polyethylene (PE) outer sheath. It is assumed in the engineering practice that during the short-circuit conditions the induced voltage should not exceed 5 kV. To limit values of the induced voltage, an earth continuity conductor (ECC) is buried in the ground, parallel to the cables, what was widely studied in [11]. The extensive analysis conducted in [12] shows that in special cases the ECC may reduce the induced voltages by even over 60% compared to a system without the ECC. Despite this, the induced voltages may still exceed the acceptable level.