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Comment by dgacmu | Hacker News Reader

This is not correct. Resistive losses are linear with distance. There are some other issues such as getting out of phase, which can require a transformer (and its associated losses), but there's absolutely nothing exponential.

For the basics:

http://www.learnabout-electronics.org/Resistors/resistors_03...

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Naively that's true, but if you consider a distribution grid with a series of transmission line segments at a given voltage, after each segment the voltage is increased to normalise it to the target transmission voltage. Each stage results in a proportional loss of power transmitted, resulting in an exponential loss as distance increases.

Achieving a linear transmission loss ignores bounds on the source voltage. In this case, you may as well choose a transmission voltage of infinity and say resistive losses are constant because current tends to zero.

No? If I lose a fixed percent at each stage, my losses as a function of distance are slightly sublinear. Ex: 10% per stage, I lose 10% at first loss, then 9%, and so on. Further, if I have intermediate transformers, my current on later segments is lower, which means that my resistive heating is lower, which means my resistance (and therefore loss) is lower.

Consider supplying a fixed amount of power P to a load. If each stage loses 10% of the power transmitted, after one stage you need to supply 1.1P, after the second stage, you must supply that power plus ten percent, and so on, so you need to supply 1.1^N P after N stages.

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