We need to work on a process of elimination of things to find the problem, it could also be a combination of things.
The first impulse of experienced marine aquarium keepers is to say that tap water is bad. Depending on your municipal water treatment plant your water can contain many things that are bad for your tank like, Nitrates, phosphates, heavy metals, chlorine, chloramine...just to name a few. Nitrates and Phosphates are the major food for algea that can turn your water green, grow hair algea the list goes on. If you have either the Nitrates or Phosphates then you need to do water changes combined with a phosphate remover in the canister filter, as well as running fresh carbon.
The best way to help prevent unwanted compounds in your water is to do waterchanges and top off's with RO/DI water.
Mix your waterchange water for at least 24 hours, with powerhead,heater, and aeriate it, before use. Match the temp and salinity before adding to the main tank.
Lighting - if your bulbs spectrum goes below 5000k you are giving the algea a perfect enviroment to grow. If your bulbs are old then it may be the cause of your green algea and it may be time to replace them.
Good to see you have a skimmer. could you tell me what kind it is and how well it is working? The skimmer will help oxygenate the water and remove DOC's. The DOC's can also be used by algea as food.
Overfeeding can cause problems as well, any uneaten food can decay and windup sending the nitrates up giving the algea something to feed on.
Questions for you: Please answer them
What type of substrate do you have?
Once again exactly what did you test for? I'm going to be point blank here as you did not answer the question. Stating that your tests are fine or at 0 does not say what you tested for, nor does it give us any clues to help you.
If you have green water than I can tell you for a fact there is something wrong with your chemistry. Now it may be that your reading for Nitrates are at 0, however the algea present in your tank may be using the nitrates as fast as they are produced as well as feeding off of the phosphates. It could be that your test is wrong and the test kit is outdated. They do go bad.
So please give us the tests that you can test for and tell me what type of test kit you are using. We will go from there.
Thomas