Interaction Analysis of Virtual Synchronous Machine Control with the AC Grid

Virtual Synchronous Machine (VSM) controllers are regarded as a promising Grid-Forming solution for the largescale integration of renewable generation, due to their ability to emulate the behavior of synchronous machines. Numerous studies have shown that VSM enhance stability in weak grids; however, little attention has been paid to potential instability issues when Virtual Impedance (VI) and multiple control loops are employed under varying grid conditions. This paper analyzes the stability of a VSM with VI using the multiple-input multiple-output (MIMO) transfer function and Singular Value Decomposition (SVD), explicitly considering variations in grid impedance. The study reveals how the interaction between VI and grid impedance can lead to subsynchronous oscillations in weak grids and highfrequency resonances in strong grids. Based on these findings, a guide for tuning the VI is proposed. The validity of the analysis is confirmed through experimental tests in a Control Hardwarein-the-Loop (C-HIL) environment.