Comparative Analysis of Small-Signal Dynamics in Virtual Synchronous Machines and Frequency-Derivative-Based Inertia Emulation

This paper presents a comparison of small-signal dynamics for a current controlled Virtual Synchronous Machine (VSM), a voltage controlled VSM and a df/dt-based control strategy for inertia emulation. The comparison is based on state-space models of the considered control schemes, which are linearized and utilized for eigenvalue-based analysis. Starting from a comparison of the three schemes with manually tuned controller parameters, it is shown that the current controlled VSM can be unstable for strong grid conditions, while the df/dt-based control becomes unstable when the grid impedance is high. Thus, an iterative tuning algorithm based on eigenvalue parametric sensitivities is applied to investigate how much the time-response and damping of the critical modes can be improved. Limitations to the dynamic performance are identified by participation factor analysis of the critical modes. The results demonstrate that all the investigated schemes can be stable for a wide range of operating conditions, but with inherent differences in the inertial response.