
Nope, just takes a bit of energy to operate turbines
although you can lose efficiency.
I believe nuke plants can run at various power levels with roughly the same efficiency. Of course, my nuclear power experience was in submarines; we did a lot of load cycling (changing power levels all the time) and didn't worry too much about efficiency, other than the fact that we wanted the core to last the life of the sub.
Again, steam-based power (e.g. fuel oil or coal) can run pretty well at lower power levels -- again I do have some naval experience with fuel oil systems (1200 psi superheated steam frigate) and IIRC efficiency at different powers isn't a big concern.
However, while gas turbines can run at low power levels, they aren't very efficient. Gas turbines have incredible power to weight ratios, are moderate polluters, and are reasonably efficient when at high power. Many of the new power plants, including in California, are natural gas-powered turbines. These plants would be more binary -- you'd probably want to run each turbine at pretty much capacity or not at all. And, of course, it was natural gas pricing that went soaring, thus directly affecting the price of natural gas produced electricity.
Tony