Inverters convert DC voltage to AC voltage. They have a battery system which provide adequate backup time to provide continuous power in the home. The inverter system then converts the battery voltage to AC voltage through electronic circuitry. The inverter system also has some charging system that charges the battery during utility power.
To determine the power back time of your Inverter Battery System during the power outage with your running appliances, lets do the calculations. Here is the formula: Battery Backup Time (Hours) = Battery capacity (Ah Rating)*Input Voltage (12 Voltage) / Total Loads (Watts)
After the battery is charged, you want to keep the battery "full", despite loads. So the inverter targets a lower constant battery voltage, this is the float voltage. When the battery voltage dips below the float voltage, current flows back into the battery to keep the battery full. Most of it will actually flow to the load.
To keep the battery near to fully charged, you need a constant voltage target for the inverter's charger. That voltage is called the "float" voltage, for historical lead-acid reasons. Perhaps you don't "need" it for chemical reasons as you might for lead-acid, but really it's the same situation, so why not call it the float voltage.
The input voltage of the inverter should match the battery voltage. (For example 12v battery for 12v inverter, 24v battery for 24v inverter and 48v battery for 48v inverter
Let’s say that a battery can produce 300 DC amps for 30 seconds, while maintaining 7.2V. While this is great for starting a cold engine, it is not for running an inverter. An inverter usually shuts down around 10-10.5V, so you can see that 3V is a substantial difference on a 12V system.