Neat video. The calculation for run time is nice but probably a little longer than what you would really get with the UPS. There are inefficiencies with the inverter going from 12VDC to 120VAC output, and that really cuts back how long they can run in my experience. Impressive to see the data on the LiFePO4. I've been running small (under 1KVA) UPS on PCs since a brown out in 2002 burned up a power supply and therefore the drives in my desktop. I also use (or try to) automated shutdowns if the UPS reports low battery so the file system of my server gets closed and doesn't corrupt. Changing batteries ever few years isn't too bad, but getting more expensive . Still cheaper than buying new systems due to power issues.
Nice video. Nice ideas. I like the concept. I think that it is good to point out that there are UPS modes of operation. What you have here is essentially a "Bypass mode" UPS, in that there is no protection from most forms of power line "noise". It simply switches from A to B. If it always drew from the inverter after the batteries, the power would be heavily conditioned, with the converter electronics and batteries taking the brunt of any power disturbances before sensitive electronics. There is a big difference in losses with "Double Conversion mode", and the batteries will wear out faster being floated all the time. Lead acid, however is ideal for double conversion, as it is happy in float mode and staying at 99 to 100% SOC for its useful life. In an area with clean municipal power, i would opt for the bypass mode (as you have) with a point of use mini surge protection after service entrance surge protection. Neither will probably do any good with a prolonged power sag or frequency disturbance however, but those are quite rare events here.
