Some designs of nuclear reactors require a lot of time (and energy) to spin up and down, including most early generation, commercial reactors.
Not having power during either the bringup or shutdown steps (which can be measured in days) leads to… very very very bad outcomes.
Reactors can be designed to not need this. A good chunk of passively safe reactors will do this. (Passively safe simply means human monitoring isn’t needed during failure cases, but that happens to correspond well with reactors that can shut down without external inputs).
If a power source is required to shut down, then you have to make damn sure there is one available at all times. Even if during an orderly shutdown you may be able to use the reactors own power, not all shutdowns are orderly, and you really don’t want to be in a position you can’t shut down a malfunctioning reactor because that reactor is the only thing providing power needed to bring the reaction to a stop…
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