Comment by Animats
This problem is similar to what electric utilities call "load takeup". After a power outage, when power is turned back on, there are many loads that draw more power at startup.
The shortest term effects are power supplies recharging their capacitors and incandescent bulbs warming up. That's over within a second.
Then it's the motors, which have 2x-3x their running load when starting as they bring their rotating mass up to speed. That extra load lasts for tens of seconds.
If power has been off for more than a few minutes, everything in heating and cooling which normally cycles on and off will want to start. That high load lasts for minutes.
Bringing up a power grid is thus done by sections, not all at once.
If you're subject to peak load billing it's also a good idea to bring your loads online in sections, too. My family owns a small grocery store. I was taught the process for "booting-up" the store after a power outage. It basically amounted to a one-by-one startup of the refrigeration compressors, waiting between each for them to come up to operating pressure and stabilize their current demand.