# Safety Issues Referred to Induced Sheath Voltages in High-Voltage Power Cables--Case Study
## 4 Power Losses for the Analyzed Types of Bonding  
During the selection of the type of bonding, which is to be used in a high-voltage cable system, an analysis of the power losses in this system is recommended to be performed. In the total power losses in the cable system, additional losses produced in the cable sheaths should be included. Generally, power losses \(\Delta P_{\rm 3 sh}\) generated in three cables' sheaths and power losses \(\Delta P_{\rm 3c}\) generated in three cables' conductors (cores) can be calculated according to the following expressions:  
\[\Delta P_{\rm 3 sh}=R_{\rm sh}\Big{(}l_{\rm sh-L1}^{2}+l_{\rm sh-L2}^{2}+l_{\rm sh -L3}^{2}\Big{)} \tag{9}\]  
\[\Delta P_{\rm 3c}=R_{\rm c}\Big{(}l_{\rm L1}^{2}+l_{\rm L2}^{2}+l_{\rm L3}^{2} \Big{)} \tag{10}\]  
where: \(\Delta P_{\rm 3 sh}\) represents the power losses in three cables' sheaths; \(\Delta P_{\rm 3c}\) represents the power losses in three cables' conductors (cores); \(I_{\rm sh-L1}\), \(I_{\rm sh-L2}\), \(I_{\rm sh-L3}\) are the currents flowing through the sheath of the cable in phases L1, L2 and L3, respectively; \(I_{\rm L1}\), \(I_{\rm L2}\), \(I_{\rm L3}\) are the currents flowing through the conductor (core) of the cable in phases L1, L2 and L3, respectively; \(R_{\rm sh}\) is the resistance of the cable's sheath; \(R_{\rm c}\) is the resistance of the cable's conductor (core). One of the main problems in the power losses calculation is to evaluate the real current distribution in each cable sheath (currents \(I_{\rm sh-L1}\), \(I_{\rm sh-L2}\), \(I_{\rm sh-L3}\)). It is relatively difficult to calculate analytically, especially when the arrangement of the cable line is varied or the cross bonding is applied. In this investigation, all the parameters have been calculated on the base of the data obtained from the PowerFactory software, taking into account the arrangement of the cables in every of 161 sections of the cable line. Power losses in the cables' sheaths can be very high in the case of both-ends bonding. Relatively high circulating currents may give a significant heat flux generation across the sheath's resistance, which increases the temperature of the cables. However, in the power cable line under consideration, the contracted transferred power is relatively low compared to the transmission capacity of the line, so the selection of the type of the bonding system, from the point of view of the power losses, is not obvious. The power losses have been evaluated with the use of the aforementioned computer model of the cable system. Figure 12a presents power losses in the cable sheaths (all three phases) for the contracted transferred power (10 MW, tg\(\phi\) = 0.4) and the cable system arrangements, which are to be implemented in practice. The both-ends bonding gives, in fact, the highest value of the power losses, but it is only slightly higher than for the single-point bonding. Generally, for these two aforementioned types of bonding, the power losses are on the low and acceptable level. This is not a typical phenomenon. The almost equal power losses for these two arrangements are the effect of the natural capacitive power of the line. Since the consumer load (active power) in the cable line is at the low level, the natural power forces a reactive (capacitive) current circulation in the system, which gives observable losses. When the cross bonding is used, power losses in the copper sheaths are negligible, due to the compensation of the induced voltages in the consecutive minor sections. The comparison of all the analyzed types of losses (in cores, in sheaths, total; for 10 MW, tg\(\phi\) = 0.4) is presented in Figure 12b. The total power losses (in copper sheaths + aluminium cores) are almost the same, both for the single-point bonding and both-ends bonding. They are within the range 15.4-15.8 kW, whereas for the cross bonding they are at the level of 13 kW. Power losses in the cores are the same for every type of bonding.