Impact of proportional resonant controller parameters of VSC connected to AC grids with variable X/R characteristic on the small signal stability

•A step-by-step procedure is proposed to analyze the stability of VSC-AC system.•Design criteria for PR controller for weak and stiff AC grids with constant X/R is derived.•Design criteria for PR controller for weak and stiff AC grids with variable X/R is derived.•The analysis is verified via EMT simulations. The purpose of this paper is to assess the impact of proportional resonant controller (PR) parameters of a Voltage Source Converter (VSC) and AC grid topology on the small signal stability of a VSC-AC system. Based on this, a small signal model is constructed, step by step, and validated against EMT simulations. Following this validation, several scenarios containing different PR controller gains are proposed and compared by means of trajectory of eigenvalues. A discussion of the best adequacy of PR controller parameters and AC grid strength in combination with inductive-resistive characteristic (X/R) is developed to ensure the stability of the system. The previous eigenvalue analysis is verified in time domain by means of EMT simulations. The analysis performed concludes that, while the AC grid strength in combination with PR controller parameters plays an important role in determination of stability, variations in the inductive-resistive AC grid characteristic need to be included in the analysis, since further instabilities can appear even when the PR controller is well designed for a specific AC grid configuration.