Sizing the protective conductor — the adiabatic formula versus the simplified table

The PEN conductor break in TN-C-S guide covers what goes wrong when the combined PEN conductor in a TN-C-S installation breaks. This article takes a step back: how is the cross-sectional area of a separate protective conductor (PE) — or of the PEN portion of the combination conductor — actually determined, before any fault occurs?

Two permitted calculation methods

IEC 60364-5-54 §543.1 allows two methods for determining the minimum cross-sectional area of a protective conductor, leaving the choice to the designer/installer:

The adiabatic formula (§543.1.2): S = √(I²t) / k, where I is the rms fault current flowing through the protective conductor for a fault of negligible impedance, t is the disconnection time of the protective device, and k is a material/insulation-dependent constant from tables A.54.2–A.54.6 of the standard. This method calculates the cross-section exactly for the specific installation and protective device, and often yields a smaller, more precisely justified cross-section than the simplified table method.
The simplified table method (§543.1.1, table 54.2): the PE cross-section is derived directly from the phase conductor cross-section S, without having to calculate the actual fault current or disconnection time:
- S ≤ 16 mm² (Cu): PE cross-section = S (equal to the phase conductor).
- 16 mm² < S ≤ 35 mm²: PE cross-section = 16 mm² (fixed).
- S > 35 mm²: PE cross-section = S/2 (half the phase conductor cross-section).

Note: these are two equivalent, but not interchangeable methods — you choose one for a given circuit and calculate entirely according to that method. The simplified table method is faster but often leads to a more generous (larger) PE cross-section than strictly necessary, because it does not account for the actual disconnection time of the specific protective device.

The minimums that always apply

Regardless of which method was used, minimum cross-sections apply that must never be undercut:

A separate PE conductor that is not part of the same cable or enclosure as the phase conductors must be at least 2.5 mm² Cu if mechanically protected, or 4 mm² Cu if not mechanically protected.
An earthing conductor connected to a lightning protection system (see the lightning protection for greenhouses guide for the greenhouse application) must be at least 16 mm² Cu, regardless of the outcome of the adiabatic or table method for the regular installation protection.

Why this is separate from cable current-carrying capacity

The cable cross-section & current-carrying capacity guide determines the cross-section of the phase conductors based on normal operating current, ambient temperature and grouping correction (f2). The protective conductor is not sized the same way: it normally carries no current, and its cross-section is determined solely by its ability to withstand a short-duration fault current until the protective device disconnects, without the conductor itself being damaged (a thermal limit, not a current-carrying limit). A correctly sized phase conductor therefore says nothing about the required PE cross-section — that is a separate calculation.

Practical relevance

When designing a circuit or main feeder, it must be explicitly established which of the two methods is used for the PE cross-section, and that choice must be applied and documented consistently — an installation that uses the table method for one circuit and the adiabatic formula for another without justification is difficult for an inspector to verify for correctness.

Common mistakes

Applying the S/2 rule to every cross-section, even below 35 mm² — the S/2 rule only applies above 35 mm²; between 16–35 mm² the PE cross-section is fixed at 16 mm², and below 16 mm² it equals the phase conductor.
Using the adiabatic formula with the wrong k value — the constant k differs per conductor material (copper/aluminium) and per insulation material and installation method; an incorrect table selection produces an under- or overestimated minimum cross-section.
Forgetting that the 16 mm² minimum for lightning protection earthing is separate from the regular PE calculation — an installation can have a correctly calculated, smaller PE cross-section for normal protection and still require a separate, heavier earthing conductor where a lightning protection system is connected.