Neutral wire diameter and phase wires diameter (3 phase current)

I have nothing to do with electrical engineering so this may be lame question.

According to Kirchhoff's law sum of currents of L1+L2+L3 should be same as current of neutral wire. What puzzles me is why neutral wire has the same diameter as phase wires in a cable. Can anyone explain or point what may be stupid about this question?

ADDITIONAL INFO L1/L2/L3 do not have to be equal. I know a building with say 3 flats can be connected to "outer world" with 3 phase cable and each phase is connected to different flat. In such scenario phase currents differ but neutral is common. Doesn't neutral wire conduct sum of all 3 phase currents then?

What happens in the case of a symmetric, non-harmonic generating load is that the fundamental currents cancel each other out when added to form the neutral current -- this is a result of the 120 degree offset between the phases. (Think of it as current flowing from hot to another hot and returning that way instead of returning on the neutral.) There are two cases where this does not hold though: asymmetric loading and triplen harmonics.

In the worst possible asymmetric loading case, the circuit's rated ampacity is placed entirely on a single phase. Assuming that the load is non-harmonic-generating, this means that the neutral current equals the load on the circuit, allowing for equal size hot and neutral wires to be used, and the breaker on the hot side to protect the entire circuit's wiring adequately. (Putting the rated ampacity on two phases doesn't change things, either.)

What's worse, though, is when you have harmonic generating loads spread across the phases. While the fundamental and most of the harmonics cancel, odd harmonics that are also multiples of 3 (3, 9, 15, and so on, called "triplen harmonics" in the electrical world) do not cancel out, leading to a situation where the effective neutral current is higher than expected -- it can be even higher than the circuit ampacity as these harmonics are coming from loads on all three phases and returning on the neutral. The resulting high currents can overload the neutral alone, leading to a fire hazard and the need for a doubled or oversized neutral to counter this.

(They can also overheat the common delta-wye type of power distribution transformer, but that's neither here nor there for this problem.)

• Ignoring the triplen harmonics scenario, it's worth noting that even if two phases are on full current with the third phase taking zero amps, the current into the neutral wire is only the same magnitude as a single phase full load current. Jun 12 '16 at 19:18
• +1 @Andyaka What about the case where one of the phases is shorted to ground on a solidly grounded wye system. Would any current flow on the neutral in such case? The current would flow from the shorted phase through soil back to the grounded star point of the transformer, but since the neutral is also there. Would it see any current
– VMMF
May 2 '19 at 17:40

ADDITIONAL INFO L1/L2/L3 do not have to be equal. I know a building with say 3 flats can be connected to "outer world" with 3 phase cable and each phase is connected to different flat. In such scenario phase currents differ but neutral is common. Doesn't neutral wire conduct sum of all 3 phase currents then?

The individual neutral connections to each flat carry the return current back to the building distribution board. If the loads are exactly balanced the neutral currents will be 120° out of phase with each other and will sum to zero. The ammeter shown in Figure 1 will read zero. simulate this circuit – Schematic created using CircuitLab

Figure 1. Alice, Bob and Charlie's flats are fed from different phases from the building incoming three-phase supply.

On the other hand, consider the three flats situation when Alice and Bob are on holiday and Charlie's is the only occupied flat. Normally their loads would balance reasonably well but now Charlie is the only one pulling power from the phase that he's connected to. All his current must return to the transformer via the neutral wire. Therefore:

• The reading on AM1 will be non-zero. It will be the same as the current into his flat from L3.
• Assuming the L3 wiring is rated for maximum capacity, the neutral wire must be the same gauge as the supply phase wire as it will have to carry the same maximum current.

For 3-phase power normally there is NO current on the neutral wire if phase currents are equal. There is only current on neutral if a phase is not the same current as the other 2 phases. I have done several installations of main service panels where 2 neutral wires were run, also known as a 'double-neutral'. This is to account for some imbalance in the loading of the 3 phases.

Since the phase currents are shifted by 120 degrees, it is a little different. If the load is symetric, then zero current will flow i neutral. If only one phase is connected, then the neutral current will be the same as phase current. This is also the max current that will flow in the neutral, so if the neutral has equal cross seqtion as phase it is a proper way.

The currents in the three phases are 120 degrees out-of-phase with each other. If the three currents are equal, the sum flowing in the Neutral wire will be zero due to the phase differences.