Underground cables with multiple conductors

 As the capacity required from an underground cable increases, you can only go so far in meeting that by putting in bigger conductors.  After a certain point, you have to install a whole extra set of conductors instead.  How does this affect the magnetic field?  On this page we build up the field from successively more sets of conductors.

This is the geometry of conductors we will use to illustrate the principles.  In practice, where space permits, each group of three conductors would probably be spaced more widely apart, and we give examples of this at the end of the page.

diagram showing dimensions of cables with muliple groups

Consider first of all a single current of 500 A in one group of conductors only (the first group of three on the left-hand side).  This will be our reference case that we compare all the subsequent calculations to.

graph of field from single current 

Now suppose we add a second circuit, also carrying 500 A, this time in the last group of conductors on the right-hand side.  The field depends on whether the phasing is transposed (T) or untransposed (U) (the concept of phasing applies just as much to underground cables as to overhead lines):

 graph showing field from two currents

There is a peak of field over each separate group of conductors.  To the sides, the field is either larger or smaller than the single current depending on the phasing (untransposed - fields reinforce - resultant field is larger; transposed - fields partially cancel - resultant field is smaller.  But note that the phasing that cancels to the sides actually reinforces over the cables themselves and vice versa).

Now suppose we have 500 A in each of the four conductor groups (two groups per circuit).  We'll assume the two groups in each circuit are transposed with respect to each other.  The two circuits could then also be transposed with respect to each other as well.  But with four groups - four phasing orders - to play with, it turns out you can get an even lower resultant field by an alternative phasing, and we show both.

graph showing field from four currents

The two groups in each circuit are close enough together that they produce a single peak in field, but the field dips between the two circuits.

A note on currents

Because we've been adding groups of conductors each with 500 A in them, we now have a total of 2000 A compared to the 500 A we considered in the single group of conductors.  Although the only reason for using two groups per circuit would be to get increased capacity, for comparison purposes, we can look at the fields when we keep the total current the same, 500 A, in each case.

 graph showing field from four currents 500 A

Alternatively, we could look at the maximum possible field.  A typical rating for one of these cables might be 2000 A, and the field with 2000 A in each of the two groups of conductors in each of the two circuits looks like this:

 graph showing field from four currents

Cables with wider spacings

If space permits, underground cables might often be laid out with each conductor group more widely spaced from the next, and space for a haul road down the middle, like this:

diagram of cable dimensions wider spacing 

The magnetic field follows the same principles as before, but with a distinct peak from each group of conductors and dips between them:

 graph of field from four separated currents

And three groups of conductors per circuit?

If the required rating is high enough, it may be necessary to go to three groups of conductors per circuit, and here is an example of one possible such arrangement and the field it produces:

 diagram of cable with six groups

 graph showing field from six currents

Note that the phasing gets even more complicated with a total of six conductor groups.  This graph is for an arrangement that produces a high degree of cancellation to the sides, but not necessarily the optimum.

Notes

All calculations are for 1 m above ground level.

National Grid cables are often rated at 1600 A or 2000 A.  We chose 500 A for these comparisons because this is a typical load for National Grid circuits (and is what we use for many of our graphs for overhead lines as well).  The results can be scaled to any chosen current.

These calculations ignore zero-sequence currents, and assume the currents in each circuit are identical, which results in greater reduction in the field from transposed phasing than would usually be found in practice (this is discussed in detail for overhead lines)..

See also: