On the input admittance of a universal power synchronization controller with droop controllers

Recent work has proposed a universal framework that integrates the well-established power synchronization control into vector current control. Using this controller for the parallel operation of grid-forming converters, and/or with loads that have strong voltage magnitude sensitivity, requires additional loops manipulating the voltage magnitude, e.g., $QV$ and $PV$ voltage-power droop controllers. This paper derives the input admittance of the resulting overall scheme. Sensitivity analyses based on the passivity index demonstrate the benefits of the proportional components of $QV$ and $PV$ control. A case study is presented where a grid-forming converter is operated in parallel with a generator.