It's probably phosphates, not your chlorine.

Your chlorine levels are fine on paper, but something is feeding the algae and using up your chlorine’s power.

Usually that something is phosphates—they come from leaves, lawn fertilizer, even tap water. Algae love phosphates, and if there’s enough of them, your chlorine gets burned up trying to keep up. The test reads normal because you’re adding chlorine, but it’s not actually sanitizing—it’s just reacting to the phosphates. Two other things to check: stabilizer (CYA) and pH. High CYA locks up chlorine so it can’t work, and high pH cuts its effectiveness by a lot.

Grab a phosphate test. If it’s high, use a phosphate remover, then shock the pool. While you’re at it, check your CYA and pH. Fix those three, and the green usually clears up in a day or two.