One particularly interesting tidbit I learned in one of my engineering classes: hydro dams are like giant capacitors. If you can't "push" more energy into the power grid, then you also can't push more water through the turbines; it gets harder to turn the turbines due to electromagnetism.In dynamo-generated power it's harder to turn the tubines when the electricity is "used," that is, when there is current flowing. The more current that is flowing the harder they are to turn.
Turning the wires of the coil in the magnetic field sets up an emf. If you allow that emf to drive a current, you now have current-carrying wires moving through a magnetic field feeling a force opposite their motion. This is felt as resistance by whatever is driving the turbine. So, when you "use" the electricity the turbines are harder to turn, not easier.
This also makes sense in terms of conservation of energy. You are taking the energy out of the water and using it to power the users connected to the electric grid. The more power you want to supply, the more you must take out of the water (or steam, if you are using steam to drive the turbines).
So the inability to push more water through the turbine is due to the turbine delivering max current (that is, it is at full load). Any less load means less current and less resistance.
In fact I understand (not an expert on their construction) that it is a problem when the load reduces at some types of plants because you are still driving the turbines with the same fuel but their resistance drops. You have to adjust the fuel to the turbines to keep everything balanced.
With Nukes this may be a slow processess, so that is perhaps why you hear of plants "dumping" energy-- using it in some (wasted) way just to keep the current in the coils high enough to provide resistance to whatever is driving the turbines.
I've heard of places that pump water into elevated storage so as to use it again when demand suddenly picks up- kind of a capacitor effect- but I don't know anything about it first-hand.