Unified Sequence Impedance Models of Synchronous Generator-and Virtual Oscillator-Based Grid-Forming Converters

Synchronous generators and, more recently, virtual oscillators have inspired the grid-forming (GFm) control of power electronic converters. This paper provides a unified harmonic linearization-based sequence impedance model that characterizes both the synchronous generator- and virtual oscillator-based multi-loop GFm converters. The proposed model is validated for six different GFm control algorithms: droop control, power synchronization control, virtual synchronous generator, matching control, dispatchable virtual oscillator control, and Andronov-Hopf virtual oscillator control. The reasons for impedance behavior agreements and disagreements are highlighted, and the conditions under which the six topologies would share the same sequence impedance profile are discussed. It is found that the six approaches exhibit similar impedance behavior when designed to provide the same steady-state drooping characteristics, regardless of their conceptual and structural differences. Small deviations are depicted in inertial topologies around the synchronous frequency. While the small impact of virtual inertia constant on the sequence impedance of the virtual synchronous generator is known in the literature, it is shown that it deteriorates the converter stability with increasing grid strength compared to non-inertial topologies. MATLAB simulations and real-time simulation tests justify the accuracy of the analytical analysis under different grid conditions.