Here's the short version.
New pool in 2007. Original installer put a SWG cell that was undersized(SC36) on it. Went to a bigger cell (SC48). No significant changes. Time span-2 years.
Ran that size cell(SC48) for about 3 years. Liner failed eventually and pool sat unkept for most over a year.
New liner last year. New Cell again. This time SC52 (formerly SC60). Should produce MORE THAN ENOUGH Chlorine for this 28,000 gallon pool.
I'm a student of TFP and BBB method. All testing done with a TFT-100 test kit.
I've followed all of the Shock (now SLAM) methods and they always remove the algae and I have may pool back...for about 10 days to 2 weeks.
No matter what I do, algae always returns.
Search for my user name here on TFT if you want to look back at the old threads regarding this issue.
The only things that are not "by the book"
Alkalinity - My fill water is above 200. My pool water is routinely in the 140-180 range.
Calcium Hardness - I do not correct for CH based on the common advice here on TFP that it is unnecessary in a vinyl pool (despite the pool store's strong objection, that they can't justify).
The only other variable (that I can think of) is inadequate circulation. My pump is currently set to run 23hrs/day but that's only been in the last week. Prior to that, it was 18hrs/day.
Discussions here and elsewhere lead me to believe that my 1-HP pump and 1.5" return lines were adequate. Those are about the only things I haven't changed.