why 3 phase electricity instead of 4 or 5, etc?

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why 3 phase electricity instead of 4 or 5, etc?

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It’s 3 phase because they made it that way originally. There’s 3 sets of windings in generators that produce AC and they are timed (phased) 120 degrees apart. They could have built 5 phase but didn’t.

its the minimum you need for what it can do and extra phases dont net you anything but extra cabling effort

Efficiency vs Cost

Single phase power takes 2 wires and has 70.7% efficiency. The voltage is low in parts of the cycle.

Three phase power takes 3 wires and is 93% efficient. That’s a big improvement for 50% more wires

Four phase might be 99% efficient, for four wires. That’s not much improvement for 33% more wires.

You can make a 3 phase system using only 3 wires. If you want a 4 phase system you need at least 4 wires, similarly 5 phases also need 4 wires. But you want the least amount of wires and then 3 phase is best, or in some application a single phase 2 wire system is used. The problem with a single phase system is that you can not start an electric motor using a simple single phase. With a single phase you can generate a magnetic field going up and down but you need it to also go side to side to get the motor to spin, so you need more phases. And that means you need more wires.

A large part of the rationale for multi-phase systems is that they deliver constant power. With 3 sine waves offset by 120 degrees, this can be accomplished.

With two-phase, four-phase, five-phase, etc., you can’t do this except in a trivial sense (a four-phase system that was a three-phase system with a line delivering no power would meet our criteria in a trivial fashion).

You could do it with a 6-, 9-, etc. phase system, but why bother? You’re not getting anything your 3-phase system doesn’t provide and you’re using extra hardware you don’t need.