Modelling and analysis of equivalent SISO d-q impedance of grid-connected converters

Small-signal stability of three-phase grid-connected converters can be analysed by using the impedance-based method in d-q frame. Based on this approach, the d-q impedance models of both source and load subsystems are represented with 2-by-2 matrices, and their ratio (known as the return ratio matrix) is used for stability assessment. This, however, requires to apply the generalized Nyquist criterion (GNC), due to the intrinsic multi-input multi-output (MIMO) property of the d-q system. During the process, some complexities are inevitably caused because of the need to calculate the ratio of the impedance matrices, and to obtain the eigenvalues of the return ratio matrix. In this context, this paper presents an equivalent single-input single-output (SISO) model for the d-q impedance of three-phase grid-connected converters, which leads to two scalar impedance ratios of d- and q-axis, instead of the conventional 2-by-2 return ratio matrix. Consequently, the stability of the two SISO systems can be analysed by using the classic Nyquist stability criterion (NC), resulting in a much simpler and more intuitive analysis process than GNC. The equivalence between the original MIMO d-q impedance model and the proposed SISO model in stability assessment is verified by comparing their stability conditions. As an example of applying this approach, the effects of PLL, grid impedance, and power control on a grid-connected converter are investigated. The performed analysis is finally validated by Matlab/Simulink simulations. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.