How do we know how much electricity needs to be produced and how much is used?

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Also, how large can the error be between these two?

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We don’t need to know the exact values which is nice

If you have a diesel engine or similar putting mechanical energy into a spinning generator and then you increase the electrical draw on that generator, it’ll slow down. You can either accept the slower generator which changes the frequency or increase the power being supplied to the generator by the diesel engine. If you reduce the electrical load then there’s less push back and the generator will speed up.

Thanks to this you don’t actually need to know how much mechanical energy is being put into the generator or how much electrical energy is being drawn from it. You only need to make sure its spinning at 3600 rpm (60 Hz for North America, its 3k rpm for Europe and 50 Hz systems). If it spins too fast then put less fuel into the systems that are powering the generator. If it spins to slow then increase the mechanical energy you’re supplying.

The generators can only tolerate a fairly small change in frequency (<0.5 Hz) so overall production and overall demand needs to be pretty similar, but you can figure out how much was consumed later as long as you add fuel now to manage the slowdown of the generator.

Electricity is really convenient. Devices draw as much as they need, and as long as we keep the generators turning at the same speed (and have enough of them) we will not overproduce or underproduce.

The difficult part is keeping them turning at the same speed. As we use more electricity, there is more force pushing against the wheels to slow them down. The engine needs to push harder to keep the speed the same. By adjusting the fuel and air flow to the engines, or water flow to turbines, we can make sure that it keeps spinning at roughly the same speed.

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The electric grid needs to run at certain voltage ( 110v /230v at the home ) and a certain ac frequency (50hz eu or 60hz us).

When a (steam) generator runs it produces a certain voltage at a certain frequency depending on the load and rpm.

More load than output and the voltage and frequency(generator goes slower) drop, more output than load voltage and frequency go up.

Electric grid operators turn on/off generators or demand more/less load depending on voltage and frequency the generator are putting out.

Allowed voltage range is +-6% (+10%-6% in eu) they try to keep the Frequency in a +-0.2% ish range.