Wideband dq-Frame Impedance Modeling of Load-Side Virtual Synchronous Machine and Its Stability Analysis in Comparison With Conventional PWM Rectifier in Weak Grid

The load-side virtual synchronous machine (LVSM) enables the load to actively participate in the grid regulation, but it might still induce oscillations in a weak grid. Considering the dc-link voltage controller, power loops, ac voltage and current loops, the control delay, and sampling filters, the wideband dq -frame impedance model of the LVSM is first established, and it is found that $Z_{dd}$ exhibits negative resistor impedance within 10 Hz. In addition, the dq -frame impedance of the LVSM is approximately inductive above 10 Hz. Then, using the dq -frame impedance-based approach, the comparative study shows that the smaller the proportional gain and integral gain of the dc-link voltage controller are, the more stable the conventional voltage source rectifier (VSR) is in a weak grid. However, the larger the proportional gain is, the smaller the integral gain is, the more stable the LVSM is in a weak grid. Furthermore, the voltage feedforward decreases the stability margin of the VSR in a weak grid, while the virtual moment of inertia $J$ and the damping gain $D_{p}$ affect the stability of the LVSM, and the smaller $J$ and $D_{p}$ are, the more stable the LVSM is in weak grid. Finally, simulations and experimental results verify the impedance model and the stability analysis.