Simulating changing the tap of the OLTC or regulator also changes the impedance of the source as seen by the load. You wouldn't see that by just changing the pu value of the source. That would only change the voltage magnitude. We have tried to model each element closely to how it actually behaves in the power system.
I'm not sure, but I am suspicious it has something to do with the Delta system and the regulator looking at L-N voltages. The Delta voltages get skewed toward one phase (probably phase 1) and changing taps won't get the voltages back to normal. This will happen with one of the IEEE Test Feeders (37-bus??) and the solution was to change the substation transformer from Delta-Delta to Delta-Wye. This puts a ground reference on the circuit. I think this can happen in real circuits. I've heard stories...
I'm not sure why you are having this problem since the COM server comes with the normal Windows installation. Are you running on Windows? There are several installers you can download from here: https://sourceforge.net/projects/electricdss/files/OpenDSS/
As you point out there is no such thing as Z0 or Z1 for a 1-phase line or for anything other than 3-phase lines. The commercial software that I have investigated have modifications in their power flow and short circuit analysis engines to compensate for the modeling errors. OpenDSS has to have physically-realizable models so it can represent n-phase systems just like you would in an EMT program . It doesn't rely on symmetrical component models. So I am not completely sure what fix-up Synergi does...
I know this is an old post, but I just saw it. Did you ever get this to work correctly?
I assure you that the transformer connection is modeled correctly. Are you comparing Line-Line voltages or Line-Neutral? In OpenDSS you may get both depending on which report you are looking at. I generally use Show Voltages LN Nodes. If you are looking for something in the Transformer code that shows the sqrt(3) and 30 degrees, you won't find it. The complete 3-phase transformer is modeled with the windings connected properly just like the transformer is constructed. So the ratios and phase shift...
I haven't had time to look at your regulator model closely, but it is entirely possible that the regulator can continue to work well in the forward direction even if the active power has reversed direction. You can experiment with different levels of reverse power to see what difference it makes.
I think it is simply a reporting quirk. The net power is flowing backwards into the main power source. The losses are divided by the net power to get the percent losses and is reported as negative because the net power is negative. This brings the negative sign into the math. Try the command "Show Losses" and see what it reports for the losses in the individual elements.