Ok, i think you want to do so called on-line UPS, double conversion. In this case, there a comon DC rail of 311V that came from AC/DC converter and use this converter when AC is present; when AC fail, there are a boost converter that boost from 24-36 or any other battery bank voltages to same DC rail of 311V that feed an inverter which provide AC output voltage. PFC is used in AC/DC converter to improve PF. In your case there are too many linked convertes and efficiency is bad. If don't need online UPS, may use a relay to switch UPS output from direct AC line to inverter. Much more simple.