The point is that the grid provides voltage, not power as such. The power is determined by the load. It's like a battery. The battery just sits there with it's power (energy) not going anyway until you add a load. A generator can be running and providing a voltage but if there's no load, there's no power being used or generated.
As the load on the grid increases, then the power stations sense that the generators are being loaded more and crank up the power driving the genrator: more coal to the boiler, reactor power increased, more water through the turbines, etc.