Difference in wire gauge for three phase and single phase domestic power supplies

Question

I'm trying to understand why the recommended wire gauge for a domestic supply depends on whether you're getting three phase or single phase power. Specifically I'm talking about when the power rating per phase is the same.

For example, if I look up what wire gauge I need for a 100 meter run of 12kVA single phase power, I get heavier gauge wire than for 100 meter run of 36kVA three phase power. In my head, I'd figured 36kVA three phase was almost the same as having 3 supplies of 12kVA single phase, except that the three phases can share the same neutral wire. So I would have expected the required wire gauge to be the same between 12kVA single phase and 36kVA three phase (with all other things being equal, eg same phase-to-neutral voltage etc).

Is there some reason that you get less voltage drop in the three phase scenario? Or is it some more mundane reason, eg that you consider phase-to-phase voltage instead of phase-to-neutral in the 3-phase case so the drop is the same in absolute terms but smaller in percentage terms?

EDIT: For those who are asking about the specific recommendations I'm referring to, it's those in France (though I believe the rules in other European countries are similar). Eg, have look at this page https://schema-electrique.net/tableau-choix-section-cable-alimentation-electrique.html and scroll down to the section marked "Le disjoncteur de branchement est éloigné du tableau électrique" -- which just means you've got a significant cable run between your meter (by the side of the road) and your distribution board (in your house). Here, it shows, eg, that, for 60A single-phase ("monophasé"), to ensure a voltage drop of no more than 2%, you need 35mm2 copper for a run of up to 58 meters and 70mm2 copper cable for a run of up to 117 meters. Scroll down slightly further and it shows that, for 60A 3-phase ("triphasé"), for the same 2% voltage drop, you only need 35mm2 copper cable for a run of up to 116 meters. Essentially, for 3-phase, at the same ampage, the allowed distances for any given gauge wire are double what they would be for single-phase.

Answer 1

Because 3-phase cancels out neutral losses!

If you calculate load single-phase, for instance 12 KVA is simply 240V @ 50A. Very straightforward stuff. You pay for voltage drop going out on the live wire and you pay again for voltage drop on the return neutral wire.

But now let's arrange 3 such loads in a 3-phase "wye" format. 240V phase to neutral and 240*sqrt(3) volts phase-phase. 36 KVA in all, but with common neutral. Still 50 amps on the phase wires. But wait, NOT 50 amps on the neutral. Not 150 amps either. Since they're balanced, they cancel out and neutral current is zero. What's the voltage drop on 0 amps? One guess.

So the single-phase load pays for voltage drop coming and going,

But the 3-phase loads pay only "coming" -- the return is free.

All wire sizes being equal, balanced 3-phase has half the voltage drop of those same loads with independent neutrals.

However, a voltage drop calculator wants to increase the voltage drop to hit a target voltage drop number such as 3%. So it will downsize the wires to increase voltage drop up to target.

Answer 2

If the load is connected between a ground ("neutral") potential then you'd need the same gauge, but connecting the load between phases presents a higher effective voltage ("RMS") and therefore smaller current is needed for the same power. So it depends how you connect the load.