You could just keep it spinning nonstop without a load I suppose, but for anything but nuclear it's not gonna be economical.
The thing is, they don't really want to do it if they can save fuel by shutting down.
You'll soon end up with a burning/melted generator.
> "pump some water in a loop"
OK, but you're going to need huge pumps (1000+ MW!). Expensive.
> "or discharge through some resistors"
Again, you'll need extremely large resistors, and a way to dissipate an awful lot of heat. We're talking about a huge amount of energy here!
Could try also melting some salt on the side.