Transmission Losses

Resistance never sleeps: every mile of wire between a power plant and your house bleeds a little power as heat, all day, every day. The grid's only real defense against that bleed is voltage, and higher is better.

Resistive losses in a wire follow P_loss = I2R. For a given power delivery (P = I x V), raising voltage reduces current proportionally. Since losses depend on current squared, doubling voltage cuts losses by 75%. This is why the grid uses 345-765 kV for long-distance transmission, not the 120 V you see at the outlet.

Calculate relative losses. A line carries 500 MW. At 138 kV: I = 3,623 A. At 345 kV: I = 1,449 A. Loss ratio: (1,449/3,623)2 = 0.16. Losses drop to 16% of their original value, an 84% reduction.

Go further. At 765 kV: I = 654 A. Loss ratio vs. 138 kV: (654/3,623)2 = 0.033. Losses fall to 3.3% of the low-voltage case.

If losses keep dropping with higher voltage, what prevents the grid from using 10 million volts?

Diminishing returns and rising costs. Higher voltage requires thicker insulation, taller towers, wider rights-of-way, and protection against corona discharge (air ionization around conductors). Above 765 kV AC, costs rise faster than losses fall.

The I2R loss equation is the single most important reason the modern grid uses transformers and high-voltage transmission.

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