Analysis of transforming dq impedances of different converters to a common reference frame in complex converter networks

DQ impedance-based method has been widely used to study the stability of three-phase converter systems. As the dq impedance model of each converter depends on its local dq reference frame, the dq impedance modeling of complex converter networks gets complicated. Because the reference frames of different converters might not fully align, depending on the structure. Thus, in order to find an accurate impedance model of a complex network for stability analysis, converting the impedances of different converters into a common reference frame is required. This paper presents a comprehensive investigation on the transformation of dq impedances to a common reference frame in complex converter networks. Four different methods are introduced and analyzed in a systematic way. Moreover, a rigorous comparison among these approaches is carried out, where the method with the simplest transformation procedure is finally suggested for the modeling of complex converter networks. The performed analysis is verified by injecting two independent small-signal perturbations into the d and the q axis, and doing a point-by-point impedance measurement.