The experiments with the 800 watt inverter and a Delco Voyager
80 amp hour deep cycle battery make it fairly clear lead-acid
chemistry has a very slow recharge. It seems to take at least
24 hours of trickle charge to bring the deep cycle battery back
near full charge status. The current drawn is tiny, half an amp
toward the end, but the long time required makes it clear that
lead-acid batteries are not a good choice if the inverter is
to be used as a UPS for generator backup. If using solar or
wind it might be less bad, but lead-acid isn't good for capturing
energy in a timely way.  

Lithium iron phosphate is claimed to be much quicker to reach
a usable state of charge and is of course not subject to the
effects of sulfation, though chronic undercharge will damage
any battery if continued long-term. 

This discovery shattered my initial goal; that of having one
battery type be usable both for the inverter and, in a pinch, 
starting a car or generator. LiFePO4 batteries that can start 
an engine do exist, but they're in the ~$600 class, a bit much 
for insurance against a "what if?" hazard.

A LiFePO4 that's suitable for the inverter but not for starting
is roughly half the cost. 

Initial experiments with a "Power Queen" 100 amp hour LiFePO4
12 volt battery are more encouraging than those obtained with
the Delco Voyager. Recharge is faster and when charge is complete
the standby power consumption of the Ampinvt inverter is only
about 8.5 watts with the inverter idling, much less than observed
with the Delco Voyager. Running the fridge overnight seems to
deplete the LiFePO4 battery to about 40% of full charge, which
suggests the Voyager was somewhat undersized for the job. 

It's worth noting that apparent battery cost is strongly influenced
by rating methods. Lead-acid acid batteries should usually be
de-rated by at least a factor of two for comparison to LiFePO4
and even lithium batteries have to be derated some to allow for
reduced performance near the end of a charge cycle. That's a
major issue for high-peak, cyclic loads like refrigerators. A
1kWh battery should run my fridge for 24 hours. In practice,
hitting a defrost cycle after 12 hours triggers undervoltage
warnings. If those progress to faults the system goes into a
state of instability leading quicky to total shutdown. 
 
20230806