If you have green hair algae, you have elevated Nitrates and/or phosphates. Thats about it. If your test kits are good or sensitive enough to help locate the issue is a different story. Sometimes its hard to track down. Usually lack of water changes (Over feeding, overstock, etc) or a filter you *think* is clean that needs replaced (not cleaned, replaced). As for your tests, get a second opinion. Algae requires food and its coming from somewhere. As for feeding if your fish are fat and sassy cut back to half of the amount you are feeding them every other day. Over feeding is one of the issues that crop up over time you don't realize until its a problem. I don't like to link to this site for the pop ups, so I apologize, but its as direct and to the point on the algae problem as it gets.
Same question over and over, same answer..Find the source of the excess nutrients and starve off your algae. As for the 'Sun light causes algae' wives tale its not that its not helpful, just not technically accurate so don't waste time breaking down your tank or putting up new blinds. If you have good new quality bulbs, your all set. Find the source and stop it. Always remember that once you correct the condition, it can and probably will take weeks for you to see a difference.