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.
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