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Losses in power lines

Current in a line gives heat loss in the resistance. The loss grows with the square of the current. With high voltage less current is needed for the same power, which is why power is transmitted over long distances at very high voltage.

P_{loss} = R\,I^2

power loss in the line

I = \frac{P}{U}

current for a given power

Symbols

$P_{loss}$	loss	W
$R$	line resistance	Ω
$I$	current	A
$U$	voltage	V

Example

1 MW over a line with $R = 2$ Ω:

at 22 kV $I \approx 45$ A and the loss is about 4.1 kW, at 11 kV the loss is four times as large.

Double the voltage gives half the current and only a quarter of the loss.

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Part of Electric Power and Machines: The power system and energy.