The effective resistance of busbars

Busbars composed of flat bars

the busbar construction is generally accomplished by ensembleplusieurs parallel flat bars for each phase. The spacing between the bars is made equal to their thickness for practical reasons, which results in skin and proximity effects.

Referring to the published results, no precise quantitative estimate of these combined effects can be found in busbar. An order of magnitude for the additional loss coefficient K for 2 copper sections: 100 x 5 and 100 x 10 mm.

For each group of 1, 2, 3, or 4 bars, dots corresponding to the published results surround a shaded area in which the probable value of K should be located. In the absence of more precise results, the search for a value of K for a set of bars of any size can be carried out using the curves of and by likening the set to a single bar of the same height but of a width equal to the total width of the assembly. The resistance Rc is equivalent to that of all the bars in parallel.

the coefficient K is found here in excess, but this extrapolation is only valid for the bars which are not separated by more than their thickness.

Indeed, a generous spacing and a judicious positioning of the bars lead to a reduction in the loss coefficient; the K coefficients for the groups of 3, 4.6, and 8 bars of 100 x 6 mm; the closest bars are spaced 6 mm apart, the farthest 60 mm apart. The relative gain on losses is 20% for 3 bars and 40% for 4 bars, depending on whether they are in one or two batches. It is rare that the use of 5 bundled bars is considered due to the high loss coefficient due to improper use of the center bar.

It has also been proposed to place the 4 bars of a phase on the edges of a square, a solution which offers the advantages of a tubular conductor, but the supports and the grips become quite complicated here. All these indications relate to the skin effect acting simultaneously with the proximity effect, in a group of several bars of the same phase; for 3 phases, if the distance between the closest bars of 2 different phases is less than twice the height of these bars, an inverse proximity effect is added to the two previous effects.

To obtain a value for the coefficient K taking into account the corresponding increase in losses, refer to DIN standards no. 43.671 [23] which gives the coefficient K4 for bars 5 or 10 mm thick, or to reference [24] in which the mean geometric distances of the different forms of conductor allow the corresponding calculation to be carried out.


An arrangement which is of particular interest for the case of the three-phase system is the so-called sandwich: entangled or permuted busbar. The bars of each of the phases are not placed in independent groups for each phase, but are instead placed between them.

A busbar having 2 bars per phase (J, R, V) is thus arranged; proximity effects are eliminated, the current density in each bar is almost identical, and the K coefficient is slightly greater than 1.

Two drawbacks limit the general use of this method: certain complications at the connection and seals level and the difficulty in isolating the phases, even at low voltage.

An additional advantage is the reduction in electrodynamic stresses, to which can be added a reduction in inductance per phase by a factor of 10; this last characteristic of sandwich type bars has a favorable effect on the voltage drop induced in normal operation, but leads to an increase in the value of the short-circuit current.

Minimal heating or reduction of additional losses?

So far, the effects mentioned have only been analyzed from the point of view of increasing the effective resistance of the AC, i.e. the additional losses produced by the Joule Effect . For online video training of busbar and Technical courses visit our educational platform Lyskills.

The normal consequence is increased heating of the conductors, but this is sometimes compensated for by adopting an arrangement which promotes radiant or convection cooling. Currently, heating is the only important criterion taken into account for the design of a high current conductor; however, the minimum heating does not always correspond to the lowest loss coefficient; It can be seen in figure 15 that the coefficient K is more or less the same for a bar of 100 x 10 bars or two of 100 x 5 bars, but due to the larger cooling surface in the latter case, it is possible , at equivalent heating, to obtain a current greater than 10%, therefore losses greater than 20%.

Another characteristic example is the conductor tubular, the optimized shape of which guarantees a K coefficient close to 1; However, this tube has the smallest cooling surface (without any forced ventilation inside) that it is far from having the profile that carries the highest current, for a heating and a section identical to other configurations.

It will sometimes be advisable for the designer of a high current conductor to choose a technology not only according to the heating produced, but also according to the total losses.

Resistivity of metal, copper or aluminum?

It has been assumed in the above that the metal used was copper; It should now be noted that the skin and proximity effects become more pronounced as resistance decreases.

A copper conductor will therefore have a higher loss coefficient equal to that of the same aluminum conductor, but the latter requiring a section 1.6 times greater to obtain the same resistance (for a direct current), loses this advantage over the conductor copper because the two conductors have the same coefficient K for the same shape and the same resistance Rc .

In practice, the replacement of copper by aluminum is not done on the basis of resistance or equivalent resistance. voltage drop but rather on that of equivalent heating; this amounts to multiplying the section by 1.4 to 1.5 only, in order to take into account the improvement in the cooling of the larger surface.

In summary, for equal heating, an aluminum conductor has a better loss coefficient than an equivalent copper conductor; it should not be forgotten, however, that this entails greater losses which must be evacuated and also paid for.

The price per kilo and the much lower density of aluminum are the determining factors that have led to the choice of metal as a high intensity conductor.

Influence of frequency

Only the industrial frequency of 50 Hz has been taken into account in the previous calculations; their accuracy, which is only relative, however makes them valid for frequencies up to 60 Hz. An additional loss coefficient for the skin effect in cylindrical conductors (tubes and flat rods) at 50 or 60 Hz can be used for any other frequency with the given corrections.

Of these frequencies, 25 Hz is hardly ever used; as for 16 2/3 Hz, it can be assimilated to direct current. Serious skin effect problems are resolved by the 400 Hz frequency used for special circuits (marine, aviation, etc.) as soon as the current reaches a few hundred amperes: the “skin” of the copper is reduced to 3 mm at this frequency. For physical training of Electrical Engineering and Automation Engineering, Burraq Engineering Solutions is best Technical Training Institute in Lahore for busbar training.

In industrial networks, harmonic currents having frequencies that are multiples of 50 Hz (harmonics 3 and 11 are the most troublesome) can be superimposed on the fundamental frequency. These currents encounter an effectively increased resistance and significant losses and heating occur.

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