# Sizing the neutral conductor

## Influence of the type of earthing system

TT and TN-S schemes

• Single-phase circuits or those of c.s.a. ≤ 16 mm2 (copper) 25 mm2 (aluminium): the c.s.a. of the neutral conductor must be equal to that of the phases
• Three-phase circuits of c.s.a. > 16 mm2 copper or 25 mm2 aluminium: the c.s.a. of the neutral may be chosen to be:

-  Equal to that of the phase conductors, or
-  Smaller, on condition that:
-  The current likely to flow through the neutral in normal conditions is less than the permitted value Iz. The influence of triplen(1)
harmonics must be given particular consideration or
-  The neutral conductor is protected against short-circuit, in accordance with the following Sub-clause G-7.2
-  The size of the neutral conductor is at least equal to 16 mm2 in copper or 25 mm2 in aluminium

 (1) Harmonics of order 3 and multiple of 3

TN-C scheme
The same conditions apply in theory as those mentioned above, but in practice, the neutral conductor must not be open-circuited under any circumstances since it constitutes a PE as well as a neutral conductor (see Figure G58 “c.s.a. of PEN conductor” column).
IT scheme
In general, it is not recommended to distribute the neutral conductor, i.e. a 3-phase 3-wire scheme is preferred. When a 3-phase 4-wire installation is necessary, however, the conditions described above for TT and TN-S schemes are applicable.

## Influence of harmonic currents

Effects of triplen harmonics

Harmonics are generated by the non-linear loads of the installation (computers, fluorescent lighting, rectifiers, power electronic choppers) and can produce high currents in the Neutral. In particular triplen harmonics of the three Phases have a tendency to cumulate in the Neutral as:

• Fundamental currents are out-of-phase by 2π/3 so that their sum is zero
• On the other hand, triplen harmonics of the three Phases are always positioned in the same manner with respect to their own fundamental, and are in phase with each other (see Fig. G63a).

Fig. G63a: Triplen harmonics are in phase and cumulate in the Neutral

Figure G63b shows the load factor of the neutral conductor as a function of the percentage of 3rd harmonic.
In practice, this maximum load factor cannot exceed $\sqrt 3$.

Fig. G63b: Load factor of the neutral conductor vs the percentage of 3rd harmonic

Reduction factors for harmonic currents in four-core and five-core cables with four cores carrying current
The basic calculation of a cable concerns only cables with three loaded conductors i.e there is no current in the neutral conductor. Because of the third harmonic current, there is a current in the neutral. As a result, this neutral current creates an hot environment for the 3 phase conductors and for this reason, a reduction factor for phase conductors is necessary (see Fig. G63).
Reduction factors, applied to the current-carrying capacity of a cable with three loaded conductors, give the current-carrying capacity of a cable with four loaded conductors, where the current in the fourth conductor is due to harmonics. The reduction factors also take the heating effect of the harmonic current in the phase conductors into account.

• Where the neutral current is expected to be higher than the phase current, then the cable size should be selected on the basis of the neutral current
• Where the cable size selection is based on a neutral current which is not significantly higher than the phase current, it is necessary to reduce the tabulated current carrying capacity for three loaded conductors
• If the neutral current is more than 135% of the phase current and the cable size is selected on the basis of the neutral current then the three phase conductors will not be fully loaded. The reduction in heat generated by the phase conductors offsets the heat generated by the neutral conductor to the extent that it is not necessary to apply any reduction factor to the current carrying capacity for three loaded conductors.
• In order to protect cables, the fuse or circuit-breaker has to be sized taking into account the greatest of the values of the line currents (phase or neutral). However, there are special devices (for example the Compact NSX circuit breaker equipped with the OSN tripping unit), that allow the use of a c.s.a. of the phase conductors smaller than the c.s.a. of the neutral conductor. A big economic gain can thus be made.

Compact NSX100 circuit breaker

Third harmonic content of phase current (%) Reduction factor
Size selection is based on  phase current Size selection is based on neutral current
0 -15                                                 1.0 -
15 - 33 0.86 -
33 - 45 - 0.86
> 45 -           1.0(1)

(1) If the neutral current is more than 135 % of the phase current and the cable size is selected on the basis of the neutral current then the three phase conductors will not be fully loaded. The reduction in heat generated by the phase conductors offsets the heat generated by the neutral conductor to the extent that it is not necessary to apply any reduction factor to the current carrying capacity for three loaded conductors.

Fig. G63: Reduction factors for harmonic currents in four-core and five-core cables (according to IEC 60364-5-52)

Examples

Consider a three-phase circuit with a design load of 37 A to be installed using four-core PVC insulated cable clipped to a wall, installation method C. From Figure G24, a 6 mm2 cable with copper conductors has a current-carrying capacity of 40 A and hence is suitable if harmonics are not present in the circuit.

• If 20 % third harmonic is present, then a reduction factor of 0,86 is applied and the design load becomes: 37/0.86 = 43 A. For this load a 10 mm2 cable is necessary.  In this case, the use of a special protective device (Compact NSX equipped with the OSN trip unit for instance) would allow the use of  a 6 mm2 cable for the phases and of 10 mm2 for the neutral.
• If 40 % third harmonic is present, the cable size selection is based on the neutral current which is: 37 x 0,4 x 3 = 44,4 A and a reduction factor of 0,86 is applied, leading to a design load of: 44.4/0.86 = 51.6 A.  For this load a 10 mm2 cable is suitable.
• If 50 % third harmonic is present, the cable size is again selected on the basis of the neutral current, which is: 37 x 0,5 x 3 = 55,5 A.In this case the rating factor is 1 and a 16 mm2 cable is required.  In this case, the use of a special protective device (Compact NSX equipped with the OSN trip for instance) would allow the use of a   6 mm2 cable for the phases and of 10mm2 for the neutral.