The Electricity supply organisations, can decide to turn various things (loads), in your own homes, off, e.g. at peak times. With the householders, being unable (legally), to do anything about it.
smart meters already give them this capability
Well no, that gives them control over the entire installation. Which they won't exercise because they would be liable for any injury which could occur as the result of loss of power.
Hopefully you're right, but that's interesting, as that would mean they would be liable in case of any power loss due to the grid, which does happen occasionally. Are they? Or are they not in this case, just because they can prove it's for instance due to an external factor that's beyond their control? And is it always the case?
That aside, even if they can't do this, that still gives them the opportunity to have a power consumption profile for each installation, and decide to, for instance, change the price, not just depending on fixed hours for everyone, but personalized depending on your own profile entirely - you could for instance be paying a lot more all the time, because your power consumption profile is considered not "green" enough.
But that's just the tip of the iceberg. It may just be a matter of a decade until power grids become "smart" enough that every appliance connected to them can be uniquely identified, and then they could definitely decide to deny access to power to some appliance depending on its power rating, hour of day, etc. Fun days ahead. =)