What I do know is that the older reactors weren't really the type that could "spin up" or "spin down". Control rods always existed on nuclear power plants, even the oldest designs.
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In any case: "Connecting" those rods up to a computer so that the reaction can get hotter or run cooler would be the basis for variable power output.
This has been done literally forever. Why do you think nuclear plants run at 100% capacity 24/7?
The primary reason would be economic. Fuel costs IIRC are really low but capital-expenses (especially safety engineering / politics / convincing the people nearby that the plant is safe) is so costly.
When you have cheap-fuel but expensive machines, it makes sense to run closer to 100%. If you have expensive fuel but cheap machines (ex: Gas turbines), it makes sense to run in a "peaker" fashion.
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That being said: I've heard that older nuclear plants are "baseload" designs, in that they _CANNOT_ turn off or feasibly regulate their power output.
I mean, they obviously "can" turn off, they all have control rods for safety. But they're clearly not using them to regulate the power output.
No, you heard wrong. They're often the last or second to last type of plant that's called upon to alter supply to match demand, but they don't run 100% 24/7.