From Generator to Socket

The voltage goes up and then comes back down, and every transformation costs money. That round trip is the thing the rest of this lesson has to justify.

Take 100 MW down a line with 5 Ω of resistance. Line loss is I²R, and I = P/V.

Voltage up 36 times means current down 36 times, and loss down 36² ≈ 1300 times. Transmission at generation voltage is not inefficient; the conductor would vaporise.

Two related facts follow. Loss depends on the current, so it depends on the power factor — reactive current heats the line without delivering anything, which is why power factor correction has an economic value. And loss depends on R, which sets conductor size, which sets tower cost.

• Insulation. Clearances, insulator string length and tower dimensions all grow with voltage, and so does the land the corridor needs.
• Corona. Above a certain surface field the air around the conductor ionises — a real power loss, audible hiss, ozone and radio interference. Bundled conductors exist to reduce the surface gradient.
• Equipment cost. Transformers, circuit breakers and instrument transformers get sharply more expensive with each insulation class.
• Ferranti effect. A long, lightly loaded line has receiving-end voltage *higher* than sending-end, because of line capacitance — a problem that grows with voltage and length.

The standard voltages — 132, 220, 400, 765 kV — are not physical constants. They are where the saving on losses stops being worth the cost of insulating for the next step.

Distribution is the same optimisation with different inputs, and it comes out the other way. Distances are a few kilometres, so I²R is small at modest voltage; the number of connection points is enormous, so each one must be cheap; and the clearances that transmission needs cannot exist along a residential street.

This is worth stating explicitly because it is often taught as though low distribution voltage were a compromise. It is the optimum for its own conditions.

The whole argument above depends on changing voltage cheaply and efficiently. The only device that does so is a transformer, which needs a changing flux — and therefore AC. A transformer is over 99% efficient, has no moving parts, and lasts decades.

There is a second benefit that is easy to overlook: AC current passes through zero a hundred times a second, and that natural zero is what allows a circuit breaker to interrupt a fault current. Breaking a large DC current is far harder, because there is no moment at which the arc wants to extinguish.

HVDC is used where its converter cost is justified: long submarine cables, where AC charging current would consume the whole rating; very long overhead links; and connecting two grids that are not synchronised with each other.

A power system stores essentially no energy. What little it has is the rotational inertia of the machines already spinning, and that buys seconds, not minutes.

1. 1Demand exceeds generation — the extra energy comes out of the spinning machines, and they slow down.
2. 2Every machine on the grid is electrically locked together, so they all slow together and the frequency falls.
3. 3Governors sense the fall and open steam or water valves to admit more power.
4. 4Generation exceeds demand — the machines speed up and the frequency rises, and the process runs in reverse.

So frequency is a continent-wide, real-time measure of supply against demand. It is held within a fraction of a hertz, and a sustained deviation means something serious. This is why load frequency control is a module rather than a footnote.