Neutral wire within multiple power sources system

I am currently using a 5 KW hybrid inverter with 5 12v 200 Ah lead acid batteries and 8 300 watt panels. It has a phase and neutral input from the grid and a second input from the solar panels which are selected as the primary source to be used. Government power grid is poor anyway.
My suspicion is about the neutral coming out from the inverter and gets connected along the process with grid neutral. The inverter takes one phase out of three phases and switches that phase to selected equipment in the houses (frogs, washing machine s, other appliances). Selection has been made in the distribution panel.

Now I am planning to add another hybrid inverter with lithium batteries. It will also be connected to a second phase to switch it to other set of selected equipment (inverter type AC units and other appliances). 

Third phase is directly connected to a third set of selected equipment (all the remaining equipment).

Now I will end up with three neutrals getting connected together at certain times .

I am not happy about that though I am currently having same issue with my old lead acid system without having faced any safety problem so far. 

Any feedback on this issue is much appreciated.

Mohamed