Small-Signal Impedance Analysis of the Impact of Grid-Forming Controllers on their DC and AC Dynamics

Grid-forming converters have recently been gaining more interest as a viable alternative to replace bulk synchronous generation for supporting and sustaining medium to low voltage grids. While the ability of grid-connected converters to support bulk generation has been thoroughly investigated, the capacity and behavior of converters that would replace bulk generation are not well defined. In an inverter-dominated system with one or more grid-forming inverters, maintaining dc-link stability is equally, if not more, important as maintaining frequency stability. To this end, and to better understand the behavior of grid-forming converters with different types of controllers, this paper derives the small-signal models for converters with nested and single-loop control structures, and compares their input and output impedance characteristics with and without synchronization. The analysis of input impedance provides insight into the impact of each grid-forming converter controller on upstream (dc) elements such as the dc-link and non-stiff dc sources, while the analysis of output impedance provides insight into the interaction of the controller with downstream (ac) elements of the grid such as the line impedance and loads. The analytical results are verified using simulation and experimental measurements.