Ahh, one of the most common mistakes a new player can make. Always see a thread like this every two or so months.
As the others said, each time you build a power plant it replaces the original plant and adds no production whatsoever. I'd just stick with the hydro plant because it has the same production as the coal plant and it produces no pollution.
When you get up to nuclear plants, you can build a nuclear plant without replacing the previous power plants. I.E nuclear plants do not replace the existing power plant in the city and still add +100% production. Same applies with the Iron Works and Manufacturing Plant. So to sum it up:
Plants that you can only have one of in the same city:
Hydro plant (50%)
Nuclear Plant (100%)
Coal Plant (50%)
Solar Plant (50%)
Plants that do not replace the existing plants:
Iron Works (100%)
Manufacturing Plant (50%)
EDIT: The () beside the plant means how much production it increases the city by.
So by combining the Iron Works, Nuclear Plant, Manufacturing Plant and one power plant, your city's production can be increased to a massive 250%, but it is unlikely that you will get Iron Works.
Also, the power plants: hydro, coal and solar don't actually increases the city's production by 50% as you may think. What it does, is increases the production the factory produces by 50%, not the whole city. However, the rest of the plants increase the whole city's production, not just the factory's production.