DAB converter With DPS modulation

[BurnedElectron]

I am developing a 1 kW prototype of a DAB converter with DPS modulation and a planar transformer. The DAB has a dual active bridge, with one side having a constant DC bus voltage of 200 V, while the other side varies between 10 V and 50 V. Currently, I am facing two problems:

alpha1, which is the angle between the two H bridges, and alpha2, which is the angle between the arms of the H bridge.
I am unsure which formula to use to calculate the transformer's auxiliary inductor as there are two formulas for calculating inductance. One for when alpha1 < alpha2 and another for alpha1 > alpha2.

My control strategy involves drawing a power curve as a function of alpha1 and directly setting the angle based on the desired power to make the converter faster. Does anyone have advice on how to calculate alpha2 to minimise reactive power? I still don't have a strategy.