How Is Electricity Actually Made?

Spinning a magnet, and everything else is detail

Junior level — plain language, no maths

Almost every kilowatt-hour you have ever used was made the same way: by spinning a magnet inside a coil of wire. That is it. A magnet moving past a wire pushes the electrons in that wire along, and if the magnet keeps turning, the electrons keep being pushed - first one way, then the other, fifty times a second. That back-and-forth is the alternating current in your walls.

Everything people argue about - coal, gas, nuclear, hydro, wind - is only a different way of turning the same shaft. Water falling through a dam pushes a wheel. Wind pushes blades. And coal, gas and nuclear all do something oddly old-fashioned: they boil water. The steam rushes through a turbine, the turbine turns the magnet, and the magnet does the actual electricity-making. About four fifths of the world's electricity comes from spinning something, and the odd one out is the solar panel, which has no moving parts at all.

Now the uncomfortable part. When you burn fuel to make steam, you cannot turn all that heat into motion. Nature charges a fee, and the size of the fee depends on how hot your steam is compared with the cold end where the steam is condensed back to water. A good modern plant converts about 40% of the fuel into electricity; a combined-cycle gas plant, which is really two engines stacked on top of each other, reaches about 60%. The rest leaves as warm water and as the white plume above a cooling tower - which is not smoke, just steam.

One more thing worth knowing. The speed of the spin sets the frequency of the electricity: 3000 turns per minute gives exactly the 50 hertz Europe runs on. Every big generator on the grid turns in lockstep at that speed, all day, every day - which is why slowing them down even slightly is such a serious event.

Faraday's law, synchronous speed and the Carnot tax

Student level — the core equations

The whole business rests on one equation. Faraday's law of induction says the voltage induced in a coil is \(\mathcal{E} = -N\,d\Phi/dt\): not the magnetic field, but its rate of change. Spin a magnet at angular frequency \(\omega\) inside a coil and the flux varies as \(\Phi = \Phi_0\cos\omega t\), so the induced EMF is \(\mathcal{E} = N\Phi_0\omega\sin\omega t\) - a sine wave whose amplitude grows with speed and whose frequency is the speed. Alternating current is not a design choice; it is what a rotating machine naturally produces.

That ties rotation to grid frequency exactly. For a machine with \(p\) poles, \(f = pn/120\) with \(n\) in rpm, so a two-pole turbogenerator must turn at 3000 rpm for 50 Hz and 3600 for 60 Hz. Hydro machines, which turn slowly, simply use many poles instead. Once synchronised, a generator cannot drift: extra torque on the shaft does not speed it up, it advances the rotor's angle against the grid and pushes out more power.

The other half of the story is thermodynamic. A thermal plant is a heat engine, so the second law caps it at \(\eta_{\text{Carnot}} = 1 - T_c/T_h\) in kelvin. Steam at 600 °C rejecting to a river at 30 °C gives a ceiling of about 65%; real Rankine plants achieve roughly two thirds of that, so 40-45%. The cold end matters as much as the hot end, which is why a plant's efficiency drops in a heatwave, and why every serious plant sits next to a river, the sea, or a cooling tower.

The way past the ceiling is to raise \(T_h\), and gas turbines do it spectacularly: combustion at 1400-1600 °C, far beyond what steam tubing can survive. So a combined-cycle plant runs a gas turbine first and then uses its 600 °C exhaust to raise steam for a second, conventional cycle underneath - two engines in series, reaching close to 60%. That single arrangement is the most efficient heat engine ever put into commercial service.

The synchronous machine, the Rankine cycle, and what disappears when the spinning stops

Scholar level — full mathematical depth

01The synchronous machine as a coupled oscillator

A synchronous generator does not push power onto the grid by spinning faster - it cannot, because the grid holds its speed. What changes is the torque angle \(\delta\) between the rotor's field and the stator's rotating field, and the electrical power transferred follows \(P = \frac{EV}{X_s}\sin\delta\). Apply more mechanical torque and \(\delta\) advances until the electrical power matches; the machine is a spring, not a throttle. The same expression sets the stability limit at \(\delta = 90^\circ\), beyond which more torque produces less power and the machine slips poles. Reactive power is controlled independently through the rotor excitation, which is why the same machine can support grid voltage while delivering a fixed real power.

02The Rankine cycle, and why every refinement exists

Steam plants use Rankine rather than Carnot because condensing to liquid before pumping costs almost nothing, whereas compressing a vapour costs a great deal. Every subsequent refinement is an attack on the same ratio: superheating raises the mean temperature of heat addition and keeps the turbine exhaust dry; reheat sends steam back to the boiler mid-expansion for the same reason; regenerative feedwater heating bleeds steam to preheat the water, raising the average temperature at which heat enters. Supercritical and ultra-supercritical plants push above the critical point at 374 °C and 221 bar, where there is no phase boundary at all, reaching 600-620 °C and about 45% efficiency - limited now by metallurgy rather than by thermodynamics.

03Why the cold end is not a detail

\(\eta_{\text{Carnot}} = 1 - T_c/T_h\) is symmetric in a way that intuition is not: lowering the condenser temperature by 10 K helps about as much as raising the boiler by 30 K, because \(T_c\) sits in the numerator of the fraction being subtracted. This is why condenser vacuum is obsessive maintenance work, why once-through cooling on a cold sea is worth a couple of efficiency points over a cooling tower, and why output falls in summer just as demand for air conditioning peaks - a coincidence with real consequences for the network.

04Stacking cycles

The combined cycle exists because no single working fluid spans 1500 °C to 30 °C well. A gas turbine handles the top, expanding combustion products from around 1500 °C - possible only with single-crystal blades, internal air cooling and thermal barrier coatings - and rejects at roughly 600 °C, which is a superb heat source for a steam cycle underneath. The composite efficiency \(\eta = \eta_{gt} + \eta_{st}(1-\eta_{gt})\) reaches 62-64% in the best machines. The same logic drives cogeneration in the other direction: if you want the rejected heat for buildings or industry, total fuel utilisation can exceed 85%, at the price of a slightly lower electrical yield.

05What the spinning mass was also providing

A rotating generator delivers several services simultaneously, and only one of them appears on the invoice. It supplies energy; it supplies inertia, since its kinetic energy resists frequency change; it supplies short-circuit current, which is what protection relays need in order to detect and clear faults; and it supplies a voltage waveform that other equipment can synchronise to. Replace it with an inverter and you keep the first, must synthesise the second, lose most of the third, and have to decide deliberately whether the inverter follows the grid's waveform or forms one. Grid-forming control is the answer, and its deployment is the quiet technical story of this decade.

06What actually changed

For a century, generating electricity meant a heat engine, and the interesting engineering was thermodynamics. Wind and solar broke that: one is a direct mechanical extraction with no thermal cycle at all, the other converts photons to carriers with no cycle, no working fluid and no Carnot ceiling - which is why a 22% solar panel is not embarrassed by a 60% gas turbine, since the two numbers divide by entirely different denominators, one free and one bought. What remains true is the system arithmetic: the electricity has to be made at the instant it is used, at a fixed frequency, and the machine that does it has to be able to hold that frequency. The turbine's replacement has to do the same job, whether or not anything is spinning.