A Complex-Coefficient Voltage Control for Virtual Synchronous Generators for Dynamic Enhancement and Power-Voltage Decoupling

TL;DR

This work tackles instability and weak voltage regulation of grid-forming VSGs in decarbonized power systems by introducing a two-fold complex coefficient strategy. It develops a second-order $cSISO$ voltage loop analyzed with a vectorized geometrical pole method and augments it with a complex current feeding gain and a voltage-angle compensator to decouple power and voltage dynamics and suppress $vSSCI$. The key contributions are direct pole-placement and optimization-based tuning of the complex current feeding gain, plus a first-order compensator to mitigate $dq\leftrightarrow 3\phi$-induced power transients; together they yield faster rise times (around 15–20 ms), low overshoot (a few percent), and robust performance across grid variations. Validation through simulations and scale-down experiments demonstrates improved voltage regulation, reduced cross-coupled power transients, and enhanced robustness for VSGs in strong grids, facilitating practical integration of VSG technology in decarbonizing power systems.

Abstract

As electric power systems evolve towards decarbonization, the transition to inverter-based resources (IBRs) presents challenges to grid stability, necessitating innovative control solutions. Virtual synchronous generator (VSG) emerges as a prominent solution. However, conventional VSGs are prone to instability in strong grids, slow voltage regulation, and coupled power-voltage response. To address these issues, this paper introduces an advanced VSG control strategy. A novel analysis of the VSG control dynamics is presented through a second-order closed-loop complex single-input single-output system, employing a vectorized geometrical pole analysis technique for enhanced voltage stability and dynamics. The proposed comprehensive controller design mitigates issues related to control interacted subsynchronous resonance and $dq \leftrightarrow 3φ$ transformation-induced voltage-coupled power transients, achieving improved system robustness and simplified control tuning. Key contributions include a two-fold design: optimized voltage transition characteristics through direct pole placement and transient power overshoot correction via a compensator. Validated by simulation and experiments, the findings offer a pragmatic solution for integrating VSG technology into decarbonizing power systems, ensuring reliability and efficiency.

Figures (26)

• Figure 1: The circuit and control diagram of a VSG in SMIB case. The control loop is formed with mixed real and complex signal flows in Simulink®. The detailed time-domain complex PI implementation is exemplified.
• Figure 2: A closed-loop complex small-signal diagram of a SMIB case VSG.
• Figure 3: Comparison of voltage and active power response to voltage reference perturbation by different tuning methods: (a) The SO $\{k_{vi}, k_{ip}\}=\{22.1,0.796\}$ and (b) the base case with excessive high voltage integral gain $k_{vi} = 800$. (c) The voltage and real power frequency responses to the voltage set-point change with the configurations described in (a) and (b), forming the resonance peak at 2.18 Hz and 30.1 Hz, respectively.
• Figure 4: Complex voltage loop of VSG with grid dynamics. The imaginary part of grid admittance is shaded in green.
• Figure 5: Illustration of the angle dominant part of poles in the complex plane for stability margin identification. Points $C, D$ move from $B, D_0$ respectively when $\mu$ deviates from 0: (a) The stable dominant pole case with a positive $\mu$, (b) The unstable dominant pole case with negative $\mu$.