Electrodynamic forces from short-circuit current on busbars and cables (IEC 60865-1) — why support spacing matters as much as cross-section

The guide on busbar trunking systems (IEC 61439-6) lists short-circuit withstand as one of the properties a busbar system must be verified against. This article covers the underlying physics and calculation method behind that short-circuit withstand: the electrodynamic force that two parallel, current-carrying conductors exert on each other during a short circuit, as calculated per IEC 60865-1.

The principle: two parallel current-carrying conductors attract or repel each other

Two parallel conductors carrying current in the same direction attract each other through their magnetic fields; carrying current in opposite directions (as with a phase-to-phase short circuit, where the fault current flows "out" through one conductor and "back" through the other) produces a repulsive force. Under normal operation this force is negligibly small, but during a short circuit — with a current many times the rated operating current — the force can become large enough to deform busbars, break support insulators or force cable bundles apart.

The calculation method: peak force proportional to the square of the peak current

IEC 60865-1 expresses the peak electrodynamic force between two parallel conductors as proportional to:

F ∝ ip² × (L / d)

ip is the peak value of the short-circuit current (not the RMS value) — the brief, highest instantaneous value occurring in the first cycle after the short circuit starts, which is considerably higher than the RMS short-circuit current (see the guide on prospective short-circuit current for the relationship between the RMS and peak values via the κ factor).
L is the span — the distance between two consecutive fixing or support points of the conductor.
d is the spacing between the parallel conductors (for example the phase spacing of a busbar system).

Because the force increases quadratically with the peak current, and linearly with the ratio between span and phase spacing, a relatively modest reduction in phase spacing — or a relatively modest increase in support span — can significantly raise the mechanical load on the structure and its fixings.

Note: this article covers the calculation principle from IEC 60865-1 based on independently verified sources. The exact proportionality constant, the required deflection and stress check of the conductor itself, and the mechanical strength calculation of the support structure are given in the full standard text — consult it for any concrete design.

A separate assessment alongside thermal short-circuit sizing

The k²S² calculation (adiabatic short-circuit formula, see the guide on short-circuit protection §434) determines whether a conductor can thermally withstand a short circuit without its insulation overheating. The electrodynamic force calculation per IEC 60865-1 is a separate, mechanical assessment: even a conductor that is thermally well within its rating can mechanically fail (deflection, broken support insulators, loosened fixings) at too large a support span or too small a phase spacing, before the thermal limit is even reached.

Practical relevance

When designing a busbar system or a cable bundle with a high prospective short-circuit current, the mechanical support structure must be checked against the electrodynamic peak force in addition to the thermal short-circuit sizing: a busbar system manufacturer typically states a maximum support spacing that already accounts for this calculation for that specific system's short-circuit withstand class; for a custom-assembled busbar joint or cable bundle this must be checked explicitly.

Common mistakes

Checking only the thermal (k²S²) short-circuit sizing and skipping the mechanical electrodynamic force calculation — a conductor can pass thermally and still fail mechanically during a short circuit.
Using the RMS short-circuit current instead of the peak value ip in the force calculation — the peak value, which is considerably higher, governs the mechanical peak force.
Increasing the support spacing of a busbar or cable bundle (for example to save material) without recalculating the resulting increase in electrodynamic force on the remaining support points.
Assuming a larger phase spacing is always disadvantageous — for the electrodynamic force the opposite holds: a larger spacing between the conductors reduces the force at equal peak current and span.