Reference Frame Selection on Impedance Modeling of VSCs with Fundamental Frequency Dynamics

The fundamental frequency of ac power-electronic-based power systems may deviate from its nominal value, and it is highly affected by converter control dynamics. To capture the dynamics of fundamental frequency, two impedance modeling methods for voltage-source converters (VSCs) are reported, with respect to the selection of system reference frame. The first method is to model VSCs in a reference frame with the nominal frequency, while the second method models VSCs in a reference frame with varying fundamental frequency, and hence, the fundamental frequency is represented as an additional terminal variable in the impedance model. This article mathematically proves that the two impedance models are essentially equivalent, provided that the frequency dynamics is accounted in the modeling of control delay and power stage of VSCs in the second method. This equivalence is demonstrated for both grid-following (GFL) and grid-forming (GFM) VSCs. Stability predictions based on two methods are further compared based on an interconnected GFM and GFL VSC system. The results are also found to be identical. Finally, experiments validate the correctness of the theoretical analysis.