# Safety Issues Referred to Induced Sheath Voltages in High-Voltage Power Cables--Case Study
## 3 Results of the Induced Voltages Computer Simulations
### Induced Voltages for Both-Ends Bonding or Cross Bonding  
Since single-point bonding in the analyzed cable line is not acceptable, both-ends bonding is considered as an alternative solution. For the both-ends bonding, the induced sheath voltages in the normal operating conditions (10 MW) are close to 0 V. Therefore, they are not presented in the form of the chart in this paper. However, the induced voltages distributions are very interesting in case of the line-to-earth fault. The cable line comprises straight-joints approx. every 1 km. After discussion with the industrial partner involved in the cable line project, it was decided to analyze the induced voltages distribution in case of the earth fault in the selected joints. The line-to-earth fault was consecutively assumed in the following points (Figure 9):  
* p.3: a quarter of the line length;
* p.6: half of the line length;
* p.9: three-quarters of the line length;
* p.12: the consumer substation.  
The distributions of the induced voltages for the aforementioned points of the fault are presented in Figure 10. For the both-ends bonding (Figure 10a) the line-to-earth-fault at point p.12 gives induced voltage practically equal to 0 V. It is obvious because this point is located at the consumer substation,  
Figure 8: Arrangement of the earth continuity conductor (ECC): (a) a distance to the cable line; (b) its transposition.  
Figure 9: Simplified diagram of the cable system presenting points of the assumed consecutive line-to-earth faults.  
which contains an earthing system. An earth fault in points p.3, p.6 or p.9 gives the induced voltages higher than the assumed permissible limit 5 kV (at the point of the fault). The highest value of the voltage is in p.6 (over 7 kV) mainly because it is located at the farthest distance from the earthed points (p.0 and p.12). In the case of the cross bonding (transpositions of the cable sheaths are performed in p.4 and p.8; see Figure 10b), the induced voltages in the characteristic points are only slightly lower compared to the both-ends bonding. Unfortunately, the voltages still exceed the assumed permissible level of 5 kV.  
To decrease the induced voltages below the permissible 5 kV, an additional earthing in point p.6 has been proposed. The earthing is relatively easy to perform in this place--the cables' metallic sheaths are accessible. With this additional earthing, the power cable system is composed of three earthing points (p.0, p.6 and p.12) and the induced voltages distributions are as in Figure 11. As it was expected, in the case of the line-to earth fault in p.6, for the both-ends bonding (Figure 11a), the induced voltage in this point is reduced practically to 0 V. However, one can see that for the arrangement with the cross bonding (Figure 11b), in the case of the line-to earth fault in p.6, the induced voltage between p.0 and p.6 reaches approx. 250 V. Similar voltage distribution is observed between p.6 and p.12, in the case of the line-to earth in p.12. For both arrangements (both-ends bonding and cross bonding), the highest value of the voltage is around 4 kV (line-to-earth in p.3), what is clearly below the permissible value (5 kV).  
Figure 11: Induced sheath voltages as a function of the cable line length, in case of the line-to-earth fault in characteristic points (p.3, p.6, p.9 or p.12); additional earthing in p.6: (**a**) both-ends bonding; (**b**) cross bonding (c-b) in p.2, p.4 as well as in p.8, p.10.  
Figure 10: Induced sheath voltages as a function of the cable line length, in case of the line-to-earth fault in the characteristic points (p.3, p.6, p.9 or p.12): (**a**) both-ends bonding; (**b**) cross bonding (c-b) in p.4 and p.8.  
Thus, the additional earthing in p.6 eliminates in a simple way the problem of too high induced sheath voltages in case of the short-circuit conditions. The both-ends bonding, as well as the cross bonding, can be employed (with additional earthing in p.6) but the latter is a more complicated solution.