I see my cities can build a number of improvements that provide "power": coal, hydro, neucular. The game nor the instructions make it clear that the effects are additive, and there's no indication of how much more productive any of these will make the cities. Are they additive or is one working power plant enough? And how much do these power plants contribute?
The effect of power is slightly confusing because of the way it interacts with the Factory and slightly ambiguous flavor text. Regardless of the source, Power adds +2 unhealthy penalty to any city. According to the city screen, Power itself adds the 50% bonus and the Factory sill only gives 25% It's very odd that the factory flavor text states it gets a +50% bonus from power (which is meant to mean an
additional 50% bonus on top of the base 25% of the factory for 75% total) but the breakdown of hammer modifiers in the city screen suggest that Power add 50% by itself...this is only possible in a city powered remotely by Three Gorges Dam as all 3 power plants
require a factory in place before they can be built.
In any case, Power adds unhealthy, you
only get a hammer bonus with a Factory in place, and the differences between the power plants are what resources/tech they require (Coal, Nuclear) and terrain (Hydro).
Coal Plants are the most accessible and come the earliest along with Factories at Assembly Line, and so are often the easiest option unless you can't get Coal, but add extra unhealthy as their caveat (pollution, I suppose). When coal plants are obsoleted by another source the health penalty goes away, but it can be hard to catch because the city screen tracks their unhealthiness penalty under "from Power" and not "from Buildings" and the city screen is not exactly forthcoming with all of its information tracking anyway.
Nuclear Plants come slightly later at Fission, are cleaner (only the Power itself adds unhealthy) but can randomly meltdown and wreck your city population and a bunch of the buildings in it!
Hydro Plants are also clean and don't need Uranium or Coal but require river spots and Plastics is the longest tech to get of the three.
I think all contribute to late game Global Warming (factories and forges already do) but Nuclear and Coal may do so even more? Not sure about that.
Doesn't that mean that if you have a power plant and if aren't concerned about the side-effects (if there are any) that it's wasteful to build another one?
Yes and no. Most of the time, Coal is accessible and the additional unhealthy penalty isn't a big deal since +50% hammers is powerful and can offset a couple population lost, but you still may opt to build hydros to remove it and let that river city enjoy 4 less unhealthy overall with Fresh Water. You can build Nuke plants if you can't get Coal but do have Uranium, just like building navies with it when you can't get Oil. They are options, not necessarily equal to another, but options nonetheless.
"Wasteful" is relative, but considering the threat of meltdowns with Nuke plants and the odd specificity of hydros (not every city can be on a river....) along with their hammer cost, I just never bother with anything but the Coal Plant and do whatever it takes to secure a source of Coal like with Oil. Even Three Gorges, while it seems like an attractive prospect, is really just fluff at that point of the game.