Coupling Quantization Among Control Loops of Parallel Grid-Following and Grid-Forming Inverters

The application of grid-forming (GFM) inverters can be an effective way to enhance the stability of power electronics-based power systems. To further analyze the stability of such systems, it is necessary to evaluate the interaction among the power converters using grid-following (GFL) and GFM controls. This paper thus proposes a method to quantitatively analyze the coupling among power loops of hybrid inverters with GFL and GFM controls. By applying the dynamic relative gain array (DRGA) to the power transfer function matrix, the proposed method enables the analysis of the interactive impact among power loops of multiple inverters. Firstly, Full-order state-space models of the inverters with GFL and GFM controls are established. Then, the influence of various control parameters and grid strength on the coupling is explored with the proposed method. It is demonstrated through the exploration that the line impedance and the GFM inverter have a significant impact on the interaction in the low-frequency range, while the current-feedforward control can alleviate the coupling among GFL and GFM inverters. The effectiveness of the proposed method and the accuracy of the analysis are verified through simulations and experimental tests.