Control system tuning and stability analysis of Virtual Synchronous Machines

Virtual Synchronous Machines (VSMs) have been introduced as a control concept for emulating the behavior of traditional synchronous machines with power electronic converters. This paper analyses a VSM control scheme where an outer loop for inertia emulation provides references for two cascaded voltage and current controllers. This scheme offers several advantages compared to alternative VSM implementations. However, the interactions between the cascaded control loops and the complex functional dependency of the system dynamics with respect to the controller parameters prevents the effective application of classical tuning methods to this scheme at low switching frequencies. Therefore, a tuning approach for the VSM guided by the eigenvalue sensitivity matrix of a linearized system model is proposed in the paper. The method is implemented in the form of an iterative optimization procedure enforcing stability of the system and ensuring that the system eigenvalues are moved away from critical locations. Numerical simulations in the time domain are presented to verify the improvement in dynamic performance of the system when tuned with the presented algorithm compared to the results achieved by a more conventional tuning method.