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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. The circulating current loss factor for the cable configuration concerned is to be multiplied by a certain factor f.
Posted 2025-04-09
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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. The IEC 60287-1-1 standard provides a simple method to calculate the influence of unbalance to circulating current.
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:
$$\lambda_{11,cb} = f_{cb} \lambda_{11,sb}$$
$$f_{cb} = \frac{p_{cb}^2 + q_{cb}^2 + 1 - p_{cb} - p_{cb}q_{cb} - q_{cb}}{(p_{cb} + q_{cb} + 1)^2}$$
Where in any major section, the two longer minor sections are p and q times the length of the shortest minor section (i.e. the minor section lengths are a, pa and qa, where the shortest section is a).
$$p_{cb} = a_{S2} / a_{S1}, p_{cb} = a_{S3} / a_{S1}$$This formula deals only with differences in the length of minor sections. Any variations in spacing must also be taken into account.
Where lengths of the minor sections are not known, IEC 60287-1-1 recommends a value of 0.004.
For solid bonded installations, meaning bonded at both ends, the loss factor caused by circulating current losses is calculated as follows. This equation applies for two single-core, three single-core in trefoil, and three-core cables as well as three single-core cables in flat formation transposed.
The calculation of the circulating currents for solid bonded three single-core cables in non-transposed flat formation is more complicated. You find the full formulas in our documentation.
Our calculator is for educational purposes to demonstrate the IEC method calculates f depending on the unbalanced minor sections lengths.
The IEC standard values of p = 1.0 and q = 1.2 for installations where lengths of the minor sections are not known and that this results in a value of $f_{cb}$ = 0.004. Using our calculator one can see that this actually results in a value of 0.00391 to be precise.
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