# Loss factor of shield by circulating currents

This is the loss factor caused by circulating current losses.

The circulating current loss is zero for installations where the sheaths are single-point bonded, and for installations where the sheaths are cross-bonded and each major section is divided into three electrically identical minor sections.

Where a cross-bonded installation contains sections whose unbalance is not negligible, a residual voltage is produced which results in a circulating current loss in that section which must be taken into account. For installations where the actual lengths of the minor sections are known, the loss factor $\lambda_{11}$ can be calculated by multiplying the circulating current loss factor for the cable configuration concerned, calculated as if it were bonded and earthed at both ends of each major section without cross-bonding by a factor $f_{cb}$.

For PAC/GIL, $R_e$ in the following equations is replaced with the electrical resistance $R_{encl}$ of the enclosure.

Symbol
$\lambda_{11}$
Formulae
 $\frac{\frac{R_e}{R_c}}{1+\left(\frac{R_e}{X_s}\right)^2}$ two single-core, three single-core in trefoil, and three-core cable $\frac{\frac{R_e}{R_c}}{1+\left(\frac{R_e}{X_s}\right)^2}$ three single-core in flat formation transposed and two-/three-core cable $\frac{R_e}{R_c} \left(\xi_{X,3}+\xi_{X,2}-\xi_{X,1}\right)$ single-core, flat/rectangular formation, not transposed, other outer phase (leading 3/T/W) $\frac{R_e}{R_c} 4\xi_{X,2}$ single-core, flat/rectangular formation, not transposed, middle phase (1/R/U) $\frac{R_e}{R_c} \left(\xi_{X,3}+\xi_{X,2}+\xi_{X,1}\right)$ single-core, flat/rectangular formation, not transposed, outer phase with greater loss (lagging 2/S/V) $\frac{W_{sar}}{2W_c}$ single-core cables with magnetic armour and screen/sheath $\frac{1.5\frac{R_e}{R_c}}{1+\left(\frac{R_e}{X_s}\right)^2}$ multi-core with separate sheaths (SL type) $\frac{1.5\frac{R_e}{R_c}}{1+\left(\frac{R_e}{X_s}\right)^2}$ pipe-type cables $0$ multi-core with common sheath $f_{cb} \lambda_{11}$ cross-bonded system