The role of VSG parameters in shaping small-signal SG dynamics

TL;DR

The paper develops a small-signal transfer-function framework for a VSG–SG–load interconnection, incorporating voltage and reactive power dynamics to analyze how SG behavior responds to VSG parametrization. It derives a complete load-to-SG output transfer function via a block-structured interconnection that includes intermediate bus dynamics, enabling targeted sensitivity analyses across inertia $H_ ext{v}$, governor lag $T_{ ext{p,v}}$, XR-ratio, and related parameters. Key findings show a trade-off where larger $H_ ext{v}$ dampens primary oscillations but can amplify secondary ones unless inertia is matched to the SG, while impedance matching ($X_ ext{v}=X_ ext{s}$) and sufficiently large damper winding constants mitigate secondary dynamics; smaller governor lag generally reduces primary oscillations. The results provide actionable tuning guidelines for VSGs in interconnected grids and emphasize the role of zero locations in the transfer function for predicting oscillatory behavior.

Abstract

We derive a small-signal transfer function for a system comprising a virtual synchronous generator (VSG), a synchronous generator (SG), and a load, capturing voltage and frequency dynamics. Using this model, we analyze the sensitivity of SG dynamics to VSG parameters, highlighting trade-offs in choosing virtual inertia and governor lag, the limited effect of damper-winding emulation, and several others.

Figures (18)

• Figure 1: Diagram of the VSG model.
• Figure 2: Diagram of the interconnected system model.
• Figure 3: Pole-zero plots for inertia constants in the range $H_\mathrm{v} \in \left[2, 8\right]$ s. (Black: base case $H_\mathrm{v}=4$ s, red: $H_\mathrm{v}$ smaller than default, blue: $H_\mathrm{v}$ larger than default. Darker shades refer to parameter values closer to the base case. Crosses refer to poles, circles indicate zeros.)
• Figure 4: Step response plots for inertia constants in the range $H_\mathrm{v} \in \left[2, 8\right]$ s. (Black: base case $H_\mathrm{v}=4$ s, red: $H_\mathrm{v}$ smaller than default, blue: $H_\mathrm{v}$ larger than default. Darker shades refer to parameter values closer to the base case.)
• Figure 5: Bode magnitude plots and step responses of $P\to\omega$ for $T_\mathrm{p,v}\in\left[0.03,1.3\right]$ s. (Black: base case $T_\mathrm{p,v}=1$ s, red: $T_\mathrm{p,v}$ smaller than default, blue: $T_\mathrm{p,v}$ larger than default. Darker shades refer to parameter values closer to the base case.)

Theorems & Definitions (1)

• Remark