# 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 Single-Point Bonding  
In the first stage of the analysis, the induced sheath voltages in normal operating conditions, in case of the single-point bonding, have been analyzed. The load current flow in the cable cores, as well as the induced voltages, are calculated by the software taking into account the electromagnetic couplings. All charts presenting the induced voltages include the highest rms values among phases L1, L2, L3. The analyses have been conducted for the following variables:  
* the transferred power equal to 1 MW (an example very low power), 10 MW (contracted/declared consumed power), 80 MW (maximal permissible power in terms of the current-carrying capacity of the cables; a theoretical value, used for the comparison purposes);
* the single-point-bonding at the 110 kV supply service substation (p.0 in Figure 2) or at the consumer substation (p.12 in Figure 2);
* the reactive-to-active power ratio: \(\text{tg}\phi=Q/P=0\) or \(\text{tg}\phi=Q/P=0.4\) (contracted). Figure 5 presents the induced sheath voltages for the case with the \(\text{tg}\phi=0\). When the single-point bonding is performed at the 110 kV supply service substation (Figure 5a), the induced voltages are significantly below the assumed limit 80 V indicated in the standard [10], both for the power 1 MW and the contracted power 10 MW. The value 80 V is many times exceeded in the case of the 80 MW (approx. 330 V), but it is presented only for the comparison purposes. When the single-point bonding is performed at the consumer substation (Figure 5b), the induced voltages are generally higher than for the case presented in Figure 5a. For the transferred power 10 MW, it is close to the permissible limit 80 V at the unearthend end of the line (point p.0). The differences in the induced voltages (Figure 5a vs. Figure 5b) are the effect of the natural load of the cable line (capacitive), which forces a capacitive current flow of a changing value along the length of the cable line. It indicates that the location of the point of the earthing (reference point) is important. Note, that for the case presented in Figure 5a, the induced voltages at the unearthend end are  
Figure 5: Induced sheath voltages as a function of the cable line length, for three values of the transferred power (1 MW, 10 MW, 80 MW), \(\text{tg}\phi=0\): (**a**) single-point bonding at point p.0 in Figure 2; (**b**) single-point bonding at point p.12 in Figure 2.  
practically the same for the power 1 MW and 10 MW. In the case of Figure 5b, the respective voltages at the unearthed end differ about two times. Similar general conclusions flow from the analysis of the results presented in Figure 6 (tg\(\phi\) = 0.4). However, the variations of the induced voltages along the length of the cable line are slightly different than for the tg\(\phi\) = 0, especially if one compares Figure 5a vs. Figure 6a for 1 MW and 10 MW. Thus, the reactive-to-active power ratio tg\(\phi\), natural capacitive power of the cables as well as the location of the point of the single-point bonding and earthing should be taken into account in the safety analysis. In the light of the aforementioned investigation, it can be concluded that for the contracted transferred power (10 MW, tg\(\phi\) = 0.4), the single-point bonding is acceptable, whether in p.0 (preferred) or in p.12. The next step of the analysis is to evaluate the induced sheath voltages in case of the line-to-earth fault at the unearthed end. Like in the previous scenarios, the single-point bonding was assumed alternatively at the 110 kV supply service substation (Figure 7a) or at the consumer substation (Figure 7b). In the short-circuit analysis, the induced voltages have been calculated for the cases without an earth continuity conductor (ECC) or with this conductor. The ECC was laid parallel to the cable line at a distance of 20 cm (Figure 8a). An insulated cable with a copper conductor of the cross-sectional area of 120 mm\({}^{2}\) was assumed as the ECC.