The old posts still hold true. Search for mine... they are what I use today....
1) battery hooked to charger and to an inverter. Charger keeps battery charged, pit runs off inverter. If site power goes out battery wont charge but pit stays running. For most, cooks you can get a big enough battery that if it's fully charged you can run a FEC for a long time...
2) use a device like a TripLite. This is a charger/converter with auto switch. So hook up a battery, and plug into site power. Pit runs off site power unless power goes out, then it's auto switched to battery power. This switch occurrs fast enough the FEC does not reset.
I personally run #2 and it's worked quite well since 2012. There are posts on here documenting that build.
On my current trailer I used a under bed truck tool box to house the Triplite and batteries on the porch of my trailer. Works like a charm.