I have it set up for SBU (solar, battery, utility).
It's getting dark and I'm on battery now. Tomorrow when there is solar power will the unit charge the battery AND produce 120vac or does the battery charge happen first and then the inverter produces 120 vac ?
When in SBU mode (and battery voltage is above the lower threshold setting to switch to utility), PV output first supplies household loads, and then any left over power goes to charge the battery. You cannot provide supplemental charging from the grid in this mode.
I have the charging mode set to utility AND solar ( I did wire up the AC input).
Charging the battery from the utility can only occur when the unit is also powering loads from the utility.
When in utility first mode, the unit will pass through grid power to loads, while any available solar PV will be used to charge the battery (up until the battery is fully charged).
In Utility First mode you may also set the unit to supplement the solar PV charging with extra charge power from the grid. You can set two charge current limits, a total charge current limit - this is to protect the batteries from being charges too fast- and a utility charge current limit - this is to limit how much of the battery's charge comes from the supplemental charge source. The utility charge limit can't override the total charge limit.
I operate my system slightly differently to many. Since I also have grid-tied solar PV, I use Utility First mode during the day. That way my grid-tied PV is powering my loads while the smaller off-grid PV array is dedicated to charging the battery. On some days (e.g. cloudy) the small off-grid array may not being able to fully charge the battery and so I want the system to supplement that charging with power from the grid-tied PV array, but I only do so if my grid-tied array has sufficient excess capacity (I do not want to import power from the grid to charge my battery as daytime power is more expensive than over night power).
Later in the day the system switches over to SBU mode and the battery (and any residual off-grid PV which may still be available) powers the home during the evening peak tariff period and then overnight. Obviously if the battery state of charge gets too low then the system switches back to Utility First mode. It is set to prioritise covering the evening peak tariff period.
The times of day/night when the change over between modes occurs and the switching on/off of any supplemental charging from the utility input is all automated with the aid of Home Assistant (via Solar Assistant).