Skin effect and proximity effect at large cable cross-sections — why AC resistance exceeds DC resistance

The guide on cable resistance and reactance in voltage-drop calculations covers the resistive and inductive terms R and X in the voltage-drop formula. This article goes deeper into a detail that only becomes relevant at larger cable cross-sections: why the actual AC resistance of a conductor exceeds its DC resistance, and why that difference grows with cross-section.

Skin effect: current crowding toward the outside

Under DC, current distributes evenly across the entire cross-section of a conductor. Under AC, however, the conductor's own time-varying magnetic field induces eddy currents that oppose current density at the centre and reinforce it near the outer edge — the skin effect. The result is that current concentrates in a thinner layer near the surface, so the effective cross-section through which current flows is smaller than the geometric cross-section, and the AC resistance ends up higher than the DC resistance. This effect grows stronger as the conductor diameter increases and as frequency rises.

Proximity effect: extra crowding from neighbouring conductors

When multiple current-carrying conductors lie close together — such as the three phases of a three-phase cable, or several cables side by side in a cable tray — the magnetic field of each conductor also affects the current distribution in the neighbouring conductors. This proximity effect shifts the current density within each conductor further toward the side facing away from the neighbouring conductor (or, depending on current direction, toward the side facing it), which further raises the effective AC resistance on top of the skin effect alone.

How IEC 60287-1-1 accounts for this

IEC 60287-1-1 (the standard for calculating cable current-carrying capacity) expresses the AC resistance of a conductor as the DC resistance increased by a skin-effect factor ys and a proximity-effect factor yp:

R(AC) = R(DC) × (1 + ys + yp)

Both factors are functions of the conductor cross-section, the conductor construction (solid versus stranded/compacted), and the frequency, and are calculated in the standard via derived parameters (xs, xp).

Why this becomes noticeable mainly at large cross-sections

At small cable cross-sections (on the order of a few tens of mm²), the conductor diameter is small relative to the so-called skin depth at 50 Hz, so the skin and proximity effects remain negligible and the AC resistance barely differs from the DC resistance. As the cross-section grows — particularly from roughly a few hundred mm² upward — the diameter becomes large enough relative to the skin depth that the effects become noticeable: the AC resistance can then come out several percent to a few tens of percent higher than the DC resistance of that same conductor.

Note: the exact threshold above which the skin and proximity effects become significant depends on conductor material, construction, and frequency; for an accurate calculation at a specific cable cross-section, the formulas and parameters in IEC 60287-1-1 or the cable manufacturer's data apply.

Why large power feeds often run over several parallel conductors

Because skin and proximity effects increase with conductor diameter, one very large conductor per phase for a large power feed is not necessarily the most efficient solution: the AC resistance of that single large conductor is proportionally higher than when the same total cross-sectional area is split over several thinner conductors in parallel per phase. As long as the conditions for equal current sharing between the parallel conductors are met (see the guide on parallel cables — equal length, equal cross-section, equal route), the combined AC resistance of several smaller, parallel-connected conductors generally remains lower than that of a single large conductor with the same total cross-section.

Practical relevance

When sizing a supply cable for a large power feed — for example a main cable to a large-consumer connection or a charging plaza — from cross-sections of a few hundred mm² upward it is no longer sufficient to calculate with the DC resistance alone: both the current-carrying capacity (via the increased AC resistance, which leads to extra heat generation) and the voltage drop can come out differently than a DC-based calculation suggests. Splitting such a supply over several parallel, smaller conductors per phase is then often the more practical choice, both from a resistance standpoint and from handling and bending-radius considerations.

Common mistakes

Using the DC resistance of a large conductor for an AC calculation without applying the skin- and proximity-effect correction — this underestimates both the resistance and the resulting heat generation and voltage drop.
Assuming the skin effect is negligible for every cable cross-section, because this is indeed the case for small, commonly used installation cross-sections — at large cross-sections that assumption no longer holds.
Choosing one very large conductor for a large power feed without considering the option of several parallel, smaller conductors per phase, while the latter option often gives a lower effective AC resistance due to the skin and proximity effects.
Forgetting the proximity effect in a calculation that only accounts for the skin effect of a conductor in isolation, while multiple conductors lie close together in the same cable tray or joint.