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

Abstract

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 <italic>dq</italic>-frame impedance model of the LVSM is first established, and it is found that <inline-formula> <tex-math notation= LaTeX >$Z_{dd}$ </tex-math></inline-formula> exhibits negative resistor impedance within 10 Hz. In addition, the <italic>dq</italic>-frame impedance of the LVSM is approximately inductive above 10 Hz. Then, using the <italic>dq</italic>-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 <inline-formula> <tex-math notation= LaTeX >$J$ </tex-math></inline-formula> and the damping gain <inline-formula> <tex-math notation= LaTeX >$D_{p}$ </tex-math></inline-formula> affect the stability of the LVSM, and the smaller <inline-formula> <tex-math notation= LaTeX >$J$ </tex-math></inline-formula> and <inline-formula> <tex-math notation= LaTeX >$D_{p}$ </tex-math></inline-formula> are, the more stable the LVSM is in weak grid. Finally, simulations and experimental results verify the impedance model and the stability analysis.