I have heard a couple of times that an operating nuclear power plant which was shut down (non-emergency; e.g. for a regular check) needs over 24 hours (up to 72 hours?) to get up running again.
Why does it take that long?
When a reactor is shut down the core produces much less heat, but they do still produce heat through a mechanism known as decay heat. The fact that the core is producing less heat means that the coolant temperature is going to drop, but how far that temperature drops depends on the decay heat generation rate. This in turn is based on operating history, or the power at which the plant was operating before shutdown. This can be large for commercial plants, because they typically operate at or very near capacity and the power companies bring coal or natural gas plants up and down to modulate grid capacity. Decay heat after a day is about half a percent of the power history, which, for a 500 MW plant operating at capacity, means that the decay heat could be 2.5 MW.
So, if there's a brief shutdown, the decay heat generation rate is so high that the primary plant stays hot and thus they can normally start up pretty "quickly". I say "quickly" because, while the primary (radioactive side) of the plant may still be hot, the secondary steam plant will likely have gotten cold. For secondary plant startups, one of the big concerns is moisture formation in the piping. This happens when steam touches the (relatively) cold pipe. Moisture in the steam plant can cause all kinds of terrible things, but primarily the damage comes from water hammer in the piping and moisture impingement of the turbine blades.
For the record: I know this because I was a Navy nuke. In my stint in the Navy, the most terrifying thing I every witnessed on the ship was a steam pipe, maybe 18 inches in diameter, literally jumping 2-3 inches with every water hammer blow, knowing that if the pipe failed that everyone in the engineroom would probably be cooked alive. Keep in mind that, in the video linked above, the steam is likely at or just above atmospheric pressure and very low flow and it still sounds like someone's beating on that radiator with a hammer. That pipe is probably an inch or less in diameter.
The condensate that forms when the steam touches the piping gets "entrained" in the steam flow through the pipe. The steam pushes this plug of water at very high speed, like a hammer (hence "water hammer"), breaking turbine blades and damaging piping and especially piping joints.
There are devices called "moisture traps" or "steam traps" that remove moisture from the system during normal operation, but the volume of condensate formed on cold plant startup is so much that the moisture traps can't keep up. This, combined with the danger presented by water hammer and moisture impingement in the turbine means that steam is admitted to the steam plant very, very, very slowly. The plant operators have to periodically go around to manually-operated steam traps to "blow down" the condensate. (Note: the steam plant in that video is horrendous and I wouldn't work there, but the growling sound it makes when the condensate clears and steam starts to exit is exactly how I remember it sounding)
So to summarize to now: the "quick" (24-hour) startup is typically limited by moisture generation in the secondary steam plant, caused by steam contacting cold pipes.
The primary plant start has the potential to take much, much longer. Most (all?) reactors in the US are pressurized water reactors. This means that, despite being at 2-3 times (or more!) the temperature at which water normally boils, there is enough pressure in the primary plant to keep the water in its liquid form. This is a lot of pressure, and the piping in the primary plant has very thick walls to withstand that pressure.
The thick walls means that there is the potential for the inside of the pipe to be "hot" while the outside of the pipe is "cold". These are relative terms; everything is hot.
Warming up the primary plant is a chicken-and-egg problem. The primary concern here is ensuring that no steam ever forms in the reactor. Steam is actually a pretty good insulator, meaning that, if it ever did form in the reactor, suddenly there would be nothing to cool the fuel, so it would get very very hot very quickly (read: melt).
So, you have to keep the system pressurized high enough that steam doesn't form in the reactor. BUT, if you were to put that much pressure on the piping while it was cold, it would fracture, via a mechanism called, "brittle fracture". This is a sudden and catastrophic failure that can be avoided if the piping is heated to the point that it has some ductility.
So, you need to heat the piping up, but you can't get it so hot that it boils. So you heat it a little, then increase the pressure a little, then heat, pressurize, etc.
Typically there are pauses known as "soaks", which give the metal in the piping time to equalize temperature. This prevents internal stresses from building up because the inside of the pipe is "hot" and the outside is "cold". The soaks normally take a large portion to a majority of the startup time - soaks are generally 12-24 hours.
So, you heat up to a soak point, then typically pressurize to an intermediate pressure, heat to another soak point, then increase pressure to a higher intermediate pressure, then heat and pressurize together. All of this is done to stay under fracture limits known as the "brittle fracture prevention limit", which again, is to ensure that the temperature-pressure the piping is subjected to is such that the pipes don't fall off.
So, once you have warmed up the primary plant, then you can begin to bring the secondary plant online, so it's usually 2 days for the primary and then another day for the secondary - this is the 72 hour startup.
As mentioned, decay heat keeps the primary plant hot for a long time (up to maybe a month), so unless you're in an extended outage you can usually start up pretty "quick", where again "quick" is about 24 hours.
Xenon is a result of the nuclear reaction and a neutron poison. If you don't wait for the xenon to decay, it eats up too many neutrons and you can't go critical. They always say "there are not enough rods to pull." If you have a nice new reactive core, you can get started sooner. If the core is old, you will have to wait a long time before enough xenon (and other poisons) decay.
The plant I used to work at cost about a million dollars a day for an outage. Believe me, if they could start any sooner, they would.
The answer really boils down to two factors: safety and testing. I'm going to give a generic summary of these two things below, but the real answer is quite complicated.
The crux of nuclear plant operation revolves around nuclear safety. I'm not talking about personal safety, which is the purview of the Occupational Safety and Health Administration (OSHA), though that does have some factor. More, this is general safety to the public against a radiologic event. Nuclear plants are designed such that the risk of such an event is minimized as much as possible.
As a plant powers up, it undergoes different Modes. Each Mode has its own set of testing and acceptance criteria that must be met before the plant can be further elevated in Mode. There are a lot of systems, and these things take time. Systems critical to nuclear safety especially have a large amount of scrutiny.
A nuclear plant will only become fully operational once all systems pass their tests and the plant is safe to run.
They are many reasons for the time it takes to startup or return to full power operation in commercial nuclear power plants. In the US there are two main types of plants, Boiling Water Reactors(BWRs) and Pressurized Water Reactors (PWRs). Answers will differ according to the type of reactor and even which version of the type. A common explanation that I did not see mentioned is that all commercial nuclear power plants avoid making >15% thermal power changes in any 4 hour period. This is to protect the integrity of the fuel cladding. I worked in the commercial nuclear power industry for almost 20 years - and have been out of it for over 20 years -so maybe they have improved the fuel cladding and this is no longer an issue - but it was a mandatory constraint in my day.
Chuk almost got it to the end. But from the point of view to answer the question, (now that is what I am told) ASME B&PV code restricts heating rate to 30 degrees centigrade per hour. Normal plants works at around 300 degrees centigrade. This will give you minimum theoritical heat up rate of plant. Secondly when a plant is tripped first cause of trip is found and its rectification. To heat secondry side, steam is required for which there are auxilary boilers that are started. Lastly the water chemistry of all plant is restored and this takes time.