From plant to socket

Power stations are often far from the people who use their electricity. Hydro dams sit in mountains, wind farms in windy places, big plants near water for cooling. Something has to carry the power over tens or hundreds of kilometres, and the wires waste a little of it as heat.

The key formulas. Electrical power is P = V × I, voltage times current. A wire has a small resistance R, and a current I through it wastes power as heat:

P_loss = I² × R

Now the trick. To deliver a fixed power P, you can use a high voltage and a small current, or a low voltage and a large current. Because the loss goes with I squared, small current wins by a lot. Raise the voltage by 10 times and, for the same power, the current falls to one tenth, so the loss falls to one hundredth.

Worked example (assumed line). Send 100 MW along a line with a total resistance of 10 Ω. This is a simplified single-circuit model, a teaching number; real three-phase lines are more complicated.

• At 11 kV: I = 100 MW / 11 kV ≈ 9,091 A. Loss = 9,091² × 10 Ω ≈ 826 MW. That is more than the 100 MW you wanted to send: it cannot work.
• At 110 kV: I ≈ 909 A. Loss ≈ 909² × 10 ≈ 8.3 MW, about 8 percent.
• At 400 kV: I = 250 A. Loss = 250² × 10 = 0.625 MW, about 0.6 percent.

That is why long lines run at hundreds of kilovolts.

How do you change voltage? With a transformer: two coils of wire on a shared iron core. An alternating current in the first coil makes a changing magnetic flux, which induces an EMF in the second coil. The ratio of voltages equals the ratio of turns: V₂ / V₁ = N₂ / N₁. A transformer only works with changing flux, which is why the grid uses alternating current (AC). (For some very long or undersea lines, HVDC with electronic converters is used instead.) Field Lab has a transformer bench if you want to wind your own coils.

The usual ladder (voltages vary by country):

• Generator: around 11 to 25 kV.
• Step up to transmission at about 110 to 400 kV or more.
• Step down to distribution, often 11 to 33 kV.
• Step down again to the socket: 230 V in much of the world, 120 V in North America.

What gets lost? Across the whole path, from power-station fence to your socket, losses are typically about 5 to 10 percent of the electricity in many countries, and higher in some. A great share is lost in the lower-voltage local wires, not in the high-voltage lines.