# What's the current best you can expect shipping power long distances?

I see Hawaii is putting all sorts of plants out to capture volcanic geothermal, tropical wind, and equatorial solar energy. Yet they worry about the dropoff from have to transmit the power to the population centers. That doesn’t seem like a long distance problem, compared with headline proposals to send power to Europe from Sahara solar and wind plants.

Just how good are the long lines these days? How far does the power cord stretch?

I’ve love to see numbers, so I’ll offer what I can as a sort of bump.

Energy transmission loss is partly related to voltage. Transmitting low voltage causes very large drops in energy even over short distances. (Back before AC, it was thought you’d need a power station every mile to efficiently deliver power to homes). That’s why long-distance transmission lines use very high voltages.

In Hawaii’s case, it’s possible that they’re willing to take higher energy losses because it’s cheaper to deal with lower voltage transmission lines. After all, they’re not transporting it across country.

As inverters become more and more efficient, you will see high voltage DC lines becoming more and more common.

So far as I know, the two biggest sources of energy loss are resistive losses and radiative losses. Resistive losses can be decreased by going to very high voltage and low current. It’s a lot easier to step the voltage up and current down using AC than it is with DC, which is why our power grid is currently set up as AC.

On the other hand, though, you also get radiative losses: Basically, the entire electrical grid acts as an antenna, and beams energy out into space. The efficiency of this process depends on the length of the wire and the frequency: At the frequencies we use, a grid the size of the whole country would have catastrophic losses, so they break it up into three (mostly) separate grids.

But DC doesn’t have any radiative losses, and it’s now possible to step up DC to high voltages. So you can get the best of both worlds, that way.

Wiki has an unusually good article on High Voltage DC Transmission systems.

In addition to what was already mentioned, there are other issues with DC transmission as well. AC has to be designed to handle the peak voltage, but you only effectively get about 70 percent of that out of it. DC always runs at peak, so for the same amount of power, you can use smaller wires, smaller insulators, etc. for DC, which is a big cost savings. On the other hand, DC requires more expensive “transformers” and switch gear, especially since DC will naturally draw a very impressive arc at high voltages (which is not a good thing when you are trying to open up a switch), where AC by comparison will naturally tend to extinguish the arc since it crosses zero twice per cycle. At some point, the cost of the equipment outweighs the savings you get from the wire, so you’ll never see DC used below a certain distance. The cost of inverters, rectifiers, etc, keeps coming down, which means that you can expect to see DC used on shorter and shorter distances in the future.

There are trade-offs for AC as well. Higher voltages are more efficient, but require greater insulation, bigger towers, etc. so you end up with the same sort of thing. You have to balance your efficiency savings against equipment costs, which is the issue that Hawaii is running into.

Hawaii’s big island is 93 miles across (if google isn’t lying to me). To put that in perspective, the longest power line currently in use is the Inga-Shaba high voltage DC transmission line, which is roughly 1200 miles long. We can make the power cord stretch pretty far these days if we have to.

Is that right? I would have thought that, at least for wire size, the RMS voltage would be what mattered, which for sinusoidal AC is the 70 percent of peak that you mentioned.

A voltage signal has a peak voltage and an RMS voltage. When specifying the minimum “voltage withstand” parameters of the insulators, you must (obviously) use the voltage signal’s peak voltage value.

In a DC system, the peak voltage is equal to the RMS voltage. In an AC system that uses a sine wave, the peak voltage is sqrt(2) times higher than the RMS voltage. If, for example, you have an AC system that runs at 50,000 V RMS, the insulators must be able to withstand at least 70,711 V. To ensure reliability, the engineers would likely specify a minimum “voltage withstand” value of 100,000 V, just to be safe.

I don’t think it’s quite as simple as just looking at peak voltage. One of the causes of power outages is power lines sagging as they get too hot in hot weather when carrying large currents. Won’t the amount of sag for a line carrying DC, versus the same line carrying AC, to be the same when they have the same power transmission, not peak voltage?

I said that RMS is what’s important “at least for wire size”.

How much power do these generate? I doubt they are geared up for powering anything other than Hawaii. I dont see how a strategically placed nuclear power station wouldnt be the most acceptable solution.

Oh, distance from Hawaii to LA: 2,500 miles. Over water. I dont see how could be economically feasible. Heck, we can barely run fiber optic that long without a cut in the lines every couple of years. You dont want to cut a high-voltage power line at sea.

It’s useful for killing Jaws, though.

The amount by which the wire heats up will depend on the RMS values, but the energy that goes into heat is precisely the energy that’s being lost via resistance, which is what we’re mitigating by using high voltages in the first place. If your wires are heating up appreciably from the current running through them, you’re doing it wrong. They might still sag from hot weather, but that has nothing to do with what kind of current is running through them.

You’re not getting to 100°C just from the temperature of the air.

Except for Hawaii, and Nevada, everybody else would vote for placing a bunch of nuclear reactors in central Nevada, if the power would drop too much in transit. And if the central Nevadans complain, we could just buy them both off with a million dollars each.