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Note: this is for deep cycle lead chemistries only! Lithium batteries should not be held at full voltage.
“As long as… you cycle the battery daily, you could set float voltage to [Vabs] too without worry. Only when you stop cycling the battery do you need to return float voltage to more regular 13.2v levels.” – sternwake1)
In off-grid solar charging scenarios batteries are most often damaged by chronic undercharging. Specifically, not holding the manufacturer's recommended Absorption voltage (Vabs), and not holding that voltage long enough2) for acceptance to drop to endAmps.
Causes of insufficient Absorption:
Some controllers/chargers have a “restart Absorption” option allows one to override Float and get more time at Vabs. Best use of this feature would be to look at the controller display a few minutes before the Absorption timer is due to expire. If acceptance is good let it go. If acceptance is too high give the bank another round of Absorption.
If those approaches are insufficient, Eternal Absorption approach completely forgoes Float stage, forcing the controller to stay in Absorption by setting Vfloat to Vabs. This addresses the controller issues above. It will not address the insolation problem on a given day, but extended Absorption will help reduce damage from previous days of poor harvest.
PWM (and shunt) controllers make more power from panels when battery voltage (Vbatt) is higher.
Eternal Absorption may make timing opportunity loads simpler.