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I think the question could be constrained as "what frequency uses the minimum amount of copper to remake the electrical distribution network that exists today?"

This would be a pretty good approximation of the ratio of transmission lines to transformers.

You could build the lot with DC and massively reduce transformers, but transformers are probably a lot more reliable than switching converters everywhere. Not sure which would be cheaper tbh.

Sure, the transformers would be smaller, but your transmission lines would be thicc.

Isn’t it the other way around?

>Generally, for long-distance power transmission, DC lines can be thinner than AC lines because of the "skin effect" in AC, which concentrates current flow near the surface of the conductor, making thicker wires less efficient; therefore, for the same power transmission, a DC line can be smaller in diameter than an AC line

The issue is actually that DC voltage conversion is much harder than AC, because AC can use transformers, and DC can’t.

This is especially a problem at high voltages and currents.

Also, DC arcs don’t self extinguish as well as AC arcs do, so DC arcs are a lot more dangerous and destructive.

It’s why HVDC lines are still relatively rare (and capital expensive), and typically used for long haul or under salt water, where the inductive loss from AC would cost more than the higher capital costs required for DC voltage conversion and stability.

Distribution lines are aluminium.

Why isn't silver used though? It's a better conductor isn't it?

Cost and weight. High voltage electrical lines use aluminium because of the weight, they are mostly aerial lines. Silver is too expensive to use for almost anything.

But suppose it was cheap enough, would it be useful?

this gives a wrong assumption that optimal distribution network is _the same_ for different frequencies

or that it, itself, isn't a consequence of its own series of sunken cost fallacies

It doesn't. That's why I said it would be good approximation. It's a classic optimization problem. Two iterations is a lot more informative than one.

Wouldn't it make sense to do both then? Low frequency or even dc long distance transmission that gets converted to standard frequency closer to the user?

There's considerable losses involved when you want to convert between frequencies. DC also has considerable losses over long distance, so there's a lower bound on the frequency before the efficiency starts to go down again.

Right, with modern technology my understanding is HVDC (essentially 0HZ?) is the way to go now (high voltage to minimize resistive loss, DC to minimize skin effect) if we were building a new grid with the same wires, but not economical to retrofit an existing system that is already working, since it is already working

It is not that DC has more losses. it is that transforming DC voltage is non-trivial. With AC you just need a couple of magnetically coupled inductors, no moving parts, easy to build, efficient, reliable. With DC this does not work, you need to convert it to AC first do the transform then convert it back. Nowdays we can achieve pretty good efficiency doing this with modern semiconducting switches. But historically you needed to use something like a motor-generator and the efficiency losses were enough that just transmitting in ac was the clear winner.

The losses over distance thing is the fundamental conflict between desired properties. For transmission you want as high a voltage as possible, but high voltage is both very dangerous and tricky to contain. So for residential use you want a much lower voltage. we picked ~ 200 volts as fit for purpose for this task. but 200 volts has high loses during long distance transmit. So having a way to transform the current into voltage is critical.

Some of our highest voltage most efficient long distance transmission lines are DC, but this is only possible due to modern semiconducting switches.

https://en.wikipedia.org/wiki/High-voltage_direct_current

Power line losses are proportional to I^2R so whether its DC or AC isn't really the concern. V=IR so assuming R is constant, a higher transmission voltage results in exponentially lower power losses. DC is actually whats currently used for long distances to achieve lowest power line losses (HVDC).

The skin effect is an important difference (and advantage in favor of HVDC) so it is in fact a concern of AC vs DC.

Also inductive losses, which are only a thing in AC.

True, skin effect limits the conductor size (~22mm in Al @60Hz) but overhead transmission already uses bundled conductors to address that as well as to improve mechanical strength, cooling, and reactance. The advantage of HVDC is in the lower dielectric and reactive losses while skin effect is minimal.

>exponentially

quadratically

Objective function: Minimize operational cost Decision variable(s): Electrical system frequency Scope: Global electrical grid

2 meaningless statements.

For instance, I would say that the scope of the global electrical grid includes every phone charger. Not just because the last foot devices are techically connected, but because they are the reason the rest even exists in the first place. So nothing that serves either the long haul or the local at the expense of the other can be called "minimal operational cost".

So trains use their own 25hz or even lower because that's good for long haul. But that would mean phone chargers are undesirably large and heavy. Or maybe it would mean that every house has it's own mini power station that converts the 25hz utility to something actually usable locally.

Meanwhile planes use 400hz 200v 3-phase for some mix of reasons I don't know but it will be a balance of factors that really only applies on planes. Things like not only the power to weight but also the fact that there is no such thing as mile long run on a plane, the greater importance to avoid wires getting hot from high current, etc.

Simply saying "the objective function is 'what is best?' and the scope is 'global'" doesn't turn an undefined scope and objective into defined ones.

Not the original commenter, but here is another angle: If the original grid designers had a time machine and spent 2 decades studying electrical engineering in modern times before going back, what frequency would they have chosen?

Does this help you understand the original commenter's question?

In this imaginary world, does every house and business have it's own power station? Are small electronics powered by dc or ac? Do perhaps power strips incorporate something like a power supply that takes the long haul power and proivide something locally more usable, like how many power strips today incorporate usb power supplies? Is it worth making the grid slightly less efficient for houshold/office usage in trade for making it more efficient for EV charging at every parking spot, or is there something totally different like wireless power in the roads all along the roads...

You're asking how high is up.

Any simulation is an "imaginary world". Anyway, you clearly have no answers and add zero value to the conversation with your lame horse laugh fallacy responses. So, please, the next time someone asks a question out of curiosity (as the original commenter did), spare us your condescending and useless, zero value response.

Maximizing what is best (i.e. NPV) is the goal of many uncertainty studies.