Dear reader, I have a question about a single-phase auto transformer which is connected to a three-phase electricity grid. The windings of the auto transformer are on a common iron package.
The circuit is planned to be used in a solar power wall of a house. In normal operation, figure A applies, see below. If the grid fails then the inverter of the power wall takes over and will supply energy from batteries and then figure B applies.
Figure A shows how the auto-transformer is connected to the three-phase grid. The auto-transformer gives a 2:1 centertap and divides the L1-L3 phase voltage of 220(380) volts into two. This type of transformer is also called a SplitPhase transformer. I need to connect the centre tap of the auto-transformer to the neutral of the three-phase grid or star point.I have included the values of the voltages for 127V and 220V grids in drawing A.
Figure B shows how the hybrid inverter takes over from the power grid when it fails. The grid is then isolated from the Inverter and the house using an Auto-Tranfer-Switch (ATS) and the Inverter then starts supplying power to a part of the house.
Here is my question en doubt: When I connect the center tap of the auto-transformer to the neutral of the three-phase grid I have a problem explaining the voltages. The three-phase grid tells me that between the neutral and L1 there should be a voltage of 127 (220) volts, but according to the operation of the auto-transformer I would expect 110 (190) volts there.If the voltage were to follow the phases then in the winding the magnetic flux should differ in phase but this cannot be done in a common iron package.What mistake am I making here or am I blowing up an auto transformer here.
I hope someone can explain to me what is happening here and hopefully explain me that nothing is going wrong.

(sorry the picture is in Dutch but i assume it will explain it self.
"Driefasen net met auto transformator" means: Three Phase grid with auto Transformer
"Inverter als energie bron met de auto transformator" means: Inverter as energy source with auto transformer.)