Transmission Line Loss: Voltage vs. Distance

Transmission Voltage

Line voltage 132 kV

Line length 200 km

Load delivered 300 MW

Conductor resistance 0.15 Ω/km

Live Readouts

Line current

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Voltage drop

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I²R power loss

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Loss vs. delivered

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How it works

Delivering a fixed power P over a real conductor of resistance R always wastes some of it as heat. For a balanced 3-phase line at power factor 0.95:

I = P / (√3 · V · pf)
R_line = r_per_km × distance
P_loss = 3 · I² · R_line
ΔV ≈ √3 · I · R_line

Because loss scales with the square of current but current is inversely proportional to voltage, doubling the transmission voltage cuts I²R loss to a quarter for the same delivered power — the whole reason grids step voltage up for long-haul lines (33 kV local → 765 kV cross-country) and back down near the load. Longer lines and thinner/worse conductors raise R_line linearly, which raises both the loss and the voltage drop the receiving end has to tolerate.

This is the same trade-off behind siting choices in the article: placing a plant far from load centres is only efficient if the link runs at high enough voltage, or the transmission losses eat the saving.

The moving spheres on the line represent current flow (their speed and glow track I); the conductor itself shifts from teal → amber → red as loss climbs from negligible to dangerous.

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