Is 120V AC power the goal? (Parallel connecting the two inverters)
Listing off some of the appliances that need to be run will help estimate the load draw.
LV6548 says 6,500 Watts and 48 Volts.
Amperes = Watts / Volts
Watts = Volts * Amperes
(Referring to
Ohm's Law)
so
6500 Watts / 48 Volts = 135 Ampere minimum, ignoring any loss from resistance in the wiring and connectors.
Around 15% loss can be assumed for the inverter itself. So around 135A/0.85efficiency = 155 Amps. (1-0.15 = 0.85) per inverter
If you wish to run Two (2) LV6548 devices, then the max load of 6.5kW * 2 might be around 155 A * 2 = 310 Amps @ 48V.
Four 48V batteries (in parallel) are mentioned for the plan, so this ~310 Ampere load would be hopefully spread evenly as ~77 A to each battery.
This would imply that a 100A BMS should suffice, assuming all four batteries are sharing the load somewhat evenly.
Active vs Passive balancing.
The battery is made up of cells. In order to get the most energy in/out of a battery, the cells need to be somewhat balanced.
If any one cell goes too high or low in voltage, the BMS will have to disconnect.
So, a balancer helps keep the cells paced at the same part of the lap to prevent "early" disconnect.
Passive balancers just "burn off" energy by heating up a resistor temporarily connected to the highest voltage cell.
Active balancers actually exchange energy between cells by taking energy from the highest and spreading it back out to slightly recharge other cells.
There's a slight efficiency win with active balancers, but with new cells there's usually little need for balancing at first.
As the cells age and go different ways, the balancing function becomes more valuable.
hope this helps, please ask more questions about anything that didn't make sense.