Electronic – How to charge an AGM battery fast

The short answer is: No, you don't have to keep a charger connected constantly to keep your battery healthy.

The longer answer is: A naiive timer on the charger may or may not work, depending on a lot of factors. AGM batteries can have a self-discharge of as low as 10% per year (which is quite good). For such cells, a full charge every few months should be adequate to keep your battery charged when you need it. The catch is that you want to make sure that your battery is really fully charged each timer cycle. If the timer turned the charger off prematurely, the battery state of charge could get lower and lower each cycle, leaving you without power when you need it.

For a simple solution (and assuming your charger is appropriately sized), try turning your charger on for several days every 2 or 3 months. This should ensure that the battery is fully charged each cycle, while still allowing you to leave the charger disconnected the majority of the time.

For an EE-centric solution, look for a lead acid battery charge management IC that can give you a reliable indication of the transition from bulk (constant current) to polish (constant voltage) charging, and ideally provide a timer for the duration of constant voltage charging to indicate when the battery can be considered fully charged.

There are really two questions here.

1. To calculate the run time you first need to estimate the amount of current being drawn by the inverter. If you assume an efficiency of 85% (your millage may vary) then you can calculate the current as
   ((120V / 24V) * 7A) / 0.85= 41A. This number is a bit on the high side since the voltage will initially start around 26V and drop down as you discharge the battery. The run time for 50% discharge is then calculate as a) (200 AH/41A) / 50% = 9.7 hrs. In case b) you have double the capacity so the runtime is increased by two.
2. You don't get any more charge discharge cycles by combing batteries in series. However, if you combine them in parallel then you would only be discharging the banks by half as much for a given a given amount of time. So even though your charge/discharge cycles wouldn't change, you would get twice as much work out of the batteries.