D-Q Small-Signal Impedance Analysis of Improved Virtual Synchronous Generators for Low-frequency Transmission System

With concerns about the decline of the original inertia of power system, virtual synchronous generator (VSG) is introduced and becomes a research hotspot rapidly. To analysis the impedance characteristic of VSG and grid-tied system stability, this paper firstly proposes a novel outer control loop of power for the VSG. Combined with the classical inner-current loop, fast current regulation and over-current protection and vector control can be realized. Afterwards, small-signal impedance models of VSG as well as inner-current and outer-power loops in the synchronous reference (d-q) frame are derived. As the d-axis of the d-q frame of VSG varies with the command reference and doesn't always coincide with the system voltage vector during steady state, an impedance transformation matrix (ITM) is introduced, through which all the impedances can be reconstructed to a unified d-q frame for the sake of comparison and analysis. On the basis of the work above, the impedance characteristics and related influence factors like inertia, damping factor are analyzed. Results show that: 1) Inertia and damping factors have little effects on the impedance characteristic; 2) Compared with PLL-based inverter impedance, the impedance characteristic of VSG-based inverter is much better for system stability; 3) At the unity power factor working point, the resistance part of is positive, being of importance for suppressing sub-synchronous oscillation caused by negative resistance. Finally, simulation of data on MATLAB /Simulink is built to testify the validity of the small-signal impedance models.