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.
Its the happy medium
Single phase requires two thick conductors to deliver the power. If you do 1000V phase to ground and 100 amps you get 100kW with 2 thick cables
Three phase is three thick ones and one thin neutral (or no neutral if you Delta it). If you stick with 1000V phase to ground and 100 amps per phase you now get 300kW and only 3 thick cables so that’s a 2x improvement in power delivered per wire cost
You could easily do 6 phases but it doesn’t actually help anything.
Once you’re to the point where you have multiple balanced hot phases then each wire is carrying full current and you don’t have any wires wasted on neutral. If you did 6 phases at 1000V phase to ground and 100A each you could deliver 600 kW but it would take 6 wires so its the same power delivered per wire(100kW) as 3 phase.
Big motors and generators are almost always wound as 12 pole. You could increase the number of poles but this mostly increases the speed of the motor and not the efficiency. An industrial sized 3 phase 480V or higher AC motor is already 98% efficient or higher, the big generators used in power stations are 99%. More phases would increase the complexity of the motor but there’s no efficiency left to get.
At one phase, you have the power fluctuating between -1 and 1. At two phase power you have the power fluctuating between 0 and 1. At three phase power you have the power fluctuating between .58 and 1.
It will never be perfect, and each phase you add gets exponentially more expensive to get and install equipment for.
Between .6 and 1 is enough for 99% of things that require electricity.
That said some super sensitive lab equipment will occasionally run on 4 or 5 phase power.
The first motor to be controlled in speed and direction of rotation needed 3 sin waves at 120 degrees offset.
This system allows you to power heavy machinery with minimal control devices, and can turn the machine one way or the other on demand. The basic form is controllable with a single switch fwd-off-backward.
Generation of the phases is as easy as using them. You make an alternator with 3 sets of coils at 120 degrees from one another.
Adding phases does just make it more bulky or complex with no benefits.
Imagine the grid was made around the concept of “a century ago factories” using this 3 phases to move everything, with rudimental controls.
3 phases do not have any particular downside for all the other applications like lighting, or powering devices with their own transformers like PC, radios, printers, and home electronic things like ovens, blenders, toaster. There was never a need to change the system. If you don’t need 3 phases, you just take a single one and use it. For example for houses. Let’s say there’s 300 houses in your area, the company will connect 100 houses to each phase and call it a day. As long as the grid has similar loads on each phase, everything works.
So it works, it’s as simple as you can get it to be in order to cover all possible applications.
Because 3 phase is perfectly suited to making motors spin without additional components. There’s no advantage to be gained by creating any more.
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