Evaluation and Comparison of Small-Signal Characteristics of Grid-Forming Converter Systems in Two Different Reference Frames

The increasing penetration of converter-interfaced generation units results in a frequency-weak power system characterized by decreasing system inertia. Consequently, the angular frequency of the power system may deviate from its nominal value, with its dynamics significantly influenced by the various control loops of converters. To accurately conduct small-signal analysis of such power systems, two impedance-based modeling approaches have been proposed in recent years. The first approach derives small-signal models in a synchronously rotating reference frame, also referred to as the dq-frame, which is defined by the power system's nominal angular frequency. This method characterizes individual converter systems using only their dq-domain impedance matrix. The second approach, on the other hand, develops small-signal models in a dq-frame defined by the dynamic angular frequency of the power system. In this case, converter systems are characterized not only by their dq-impedance matrix but also by an additional transfer matrix that relates variations in the output current to variations in the power system's angular frequency. This leads to different closed-loop transfer matrices for the two approaches, which are used to assess small-signal stability. This article shows, using the derived analytical models, that despite the differences in the closed-loop transfer matrices, the two impedance-based modeling approaches are equivalent and lead to the same conclusions regarding the small-signal stability of the overall system. However, the second approach offers better physical insight into the behavior of converter systems during disturbances. Experimental results are provided to validate the theoretical analysis.