When the percentage boost of the power plant is greater than simply adding another factory.  Usually you just dump them on your huge industrial planets, maintanance costs be damned.

Example:  If your plant adds 10% to manufacturing, and a factory adds 10 units, you would build 11 factories, then a power plant would provide 11 units as opposed 10 units from just another factory.  I think I used a power plant one time in a game, just to say i did it.  Everyone else was doing it and peer pressure got to me.

The powerplants can be upgraded, later ones add more cap, but yeah.  Same goes for research coordination centers which I think are a 25% bonus, so I add them when I have 4 or more research centers.

Remember, though, if you have a factory on a tile with a bonus to count that tile the appropriate number of times -- two times for a 100% bonus, 4 for a 300%, 8 for a 700%.

Of course in TA the formula changes a bit if you play a race that has one-per-planet high-production factories/research centers, the spammable improvements tend to not provide as much as the % bonus improvements would.

A good rule of thumb, but the manufacturing points given by the inital colony should be thought of as well and oftentimes far outweigh the choice.  w/o putting much thought into it though, yeah just follow the quoted peice...you won't go gray as soon in life.

The Yor in TA I beleive have one sick one that give 50% increase...them or the Iconians.

When you do the rough calcs to decide whether a power plant is worth the tile, don't forget to include production from your Initial Colony tile. That ususally adds a 'factory' or two to your total, depending on the tech you have & whether it's your homeworld.

The Fusion plant is very rarely useful to me, but I don't play a wide range of game types and I can imagine it providing a helpful sliver of advantage on some maps. Even in TA as the Thalans, I still find Anti-Matter and Quantuum plants useful for serious manufacturing worlds. If a world already has 15-20 factories, that boost can help cut quite a few turns of ship production times.

Stardock should have included an in-game calculator for this.  V2.1 patch? 

Yeah.  To put it in plainer English, take a Tech Capital, on a planet with a moon.  Build a Xeno Lab on it.  You get 8rp * 110% = 16.8.

Take the same planet, 4 labs already there, add an RCC.  RCC only adds 25% to the planet--not 50%.   That's 8rp*4 + 10 (initial colony) = 42rp.  25% of that is 10.5rp.  You come out ahead just building another lab, because RCC didn't get multiplied by the Tech Capital.   P.S. the moon is irrelevant in this calculation, for the same reason.

That's the base production, not what you actually get from a lab on the planet, which is 16.8 after the already-existing bonuses.  The key is that it's a cost of opportunity situation- you can't get everything due to a limited number of land plots, so you need to balance your gains such that you get as much as possible out of the planet.  If we had unlimited land available, then there's no reason not to eventually build every single multiplier building you can, though the order in which you build them would matter.

It's somewhat counter-intuitive, but the more multiplicative bonuses you already have on a planet, the less sense it makes to add more in the place of an expanded base production capacity.  To illustrait, let's take a pair of planets that both have a plot of land to build on, both produce 100 RPs, and only differ in that Planet A is pure production for its 100 RPs (multiplier of 1.0), and planet B has a 100% bonus (multiplier of 2.0) to get it to 100 RP (base of 50).  Now we build a 50% bonus building on that land (adds 0.5 to the multiplier).  Planet A changes to a total of 150 RP (base(100)*1.5).  However, Planet B only goes to 125 RP (base(50)*2.5).  Planet B's already-existing multiplier bonus actually cut the end benefit from the building in half!

Yes, bonus tile output is multiplied by bonus structures. If you have a lab on a 700% tile, it would count as 8 labs in all the formulas betting thrown around in this topic.

The bonus from your example would apply to the 64 RP total output.

I think maintenance could be reasonably factored in, if you're near the break-even point.  But you also have to factor in that building a RCC may take awhile, when you could just build a Xeno Lab now and upgrade it later.  Also, by the time the RCC starts to make sense, you're already paying >60bc in maintenance + paid RP production, so a 7bc difference in maintenance may not matter much to you.  But like I said, near the break-even point you may find you're paying another 7bc in maintenance just to get an extra 0.8rp, and that may be a little expensive.  

BUT--bear in mind--we have not factored in race-wide research bonuses yet.  If you accumulate +100% in racial bonuses (not hard to achieve, if you have multiple purple and/or economic starbases), even that razor-thin difference of 0.8rp now becomes 1.6rp, and 50% of that is free.  Now suddenly you're paying closer to 4bc/1rp, which is starting to make more sense.

Just say, "No".  Civs don't let other civs build Fusion Power Plants.