Hi Sarac,
Charging two 12 volt batteries in series would be done
in the same way as a single battery.
The cells in a 12 volt battery are charged in series
anyway. (two 12v batteries in series is a 24v battery)
Below about 10.5 volts would be considered flat,
although barely usable if the battery is otherwise in
good order. (21v for a 24v battery),
full charge would be about 14 to 14.5 volts while on
charge at a low rate. (28 to 29 for a 24v battery)
During heavy discharge usage the terminal voltage can
drop to ten or eleven volts (20 to 22 on a 24v unit)
I would not think that the relatively minor problems
of making a battery charger to suit your needs should
have made you change your designs on the inverter you
intend to build.
Your original intention to use two batteries has much
to recommend it.
500 watts will be quite a draw from a 60 A/h battery.
The choice of transformer is another headache.
With clever circuitry a simple two winding transformer
(primary and secondary) can be used, these are usually
the easiest type of transformer to get hold of.
If a transformer with a halfway split primary can be
found, or if one is winding ones own transformer then
other, easier circuits can be made.
I have made small power supplies myself, but mine have
been oscillators rather than inverters, and only small
scale low power units. I find that the inverters are
ok for electrical items that do not contain any
electronics, but i find that they do have a very
spiky output and put electronic items at risk, unless
they are carefully damped.
In the drawings attached some of the more common
arrangements are shown. The transistors can be 'doubled
up' as you know. Ive never seen capacitor fed output
on inverters or oscillator power supplies, although
it is quite common on medium power audio outputs.
Best of luck with your project,
are you funding it yourself or is this done through a
company or some scheme ?
Regards, John