Analyzing Low-frequency Oscillation in Virtual Synchronous Generators Using Vector Motion

Nabil Bakar^*
*Correspondence: Nabil Bakar, Department of Mathematical, Leiden University, Leiden, Netherlands, Email:

Introduction

Low-Frequency Oscillation (LFO) is a critical issue in power systems, especially with the integration of Virtual Synchronous Generators (VSGs). These oscillations can lead to system instability, reduced efficiency, and potential failures if not properly analyzed and mitigated. Understanding the mechanisms behind LFOs from a vector motion perspective provides valuable insights into their behavior and potential control strategies. Virtual synchronous generators are an advanced control strategy used in inverter-based renewable energy sources to emulate the behavior of traditional synchronous generators. By mimicking inertia and damping characteristics, VSGs enhance grid stability and frequency regulation. However, due to their control dynamics, they can also introduce low-frequency oscillations under certain operating conditions. These oscillations result from interactions between the VSG control loops, grid impedance, and load variations, making it crucial to analyze their root causes and effects.

Description

Vector motion analysis provides a powerful tool for understanding the dynamics of LFOs in VSGs. In traditional synchronous machines, oscillations arise due to the rotorâ??s inertia and the electromechanical interactions between generators and the grid. Similarly, in VSGs, these oscillations are influenced by virtual inertia and damping coefficients programmed into the inverter control. The vector representation of voltage and current phasors helps visualize these interactions and track the evolution of oscillatory behavior. One of the primary sources of LFOs in VSGs is the interaction between the Phase-Locked Loop (PLL) and power control loops. The PLL is responsible for synchronizing the inverter with the grid by tracking the phase angle of the grid voltage. However, under weak grid conditions or sudden load changes, the PLL can introduce phase delays and oscillations, which, when coupled with the VSG's virtual inertia response, can create sustained low-frequency oscillations. By representing these dynamics in a vector space, it is possible to observe the phase trajectory deviations and their impact on system stability. Another contributing factor to LFOs is the power-sharing mechanism in multi-VSG systems. When multiple VSGs operate in parallel, their active and reactive power-sharing characteristics affect system stability. If the control parameters are not properly tuned, resonance conditions can develop, leading to oscillations. A vector-based approach allows for tracking power angle deviations and phase shifts, which can help in designing robust droop control and damping strategies [1-3].

Damping plays a crucial role in mitigating LFOs in VSGs. Unlike traditional synchronous generators that have inherent mechanical damping, VSGs rely on control-based damping mechanisms. Virtual damping coefficients must be carefully selected to counteract oscillatory tendencies without compromising the dynamic response of the inverter. Using vector motion analysis, it is possible to evaluate the effects of different damping strategies, such as derivative-based damping, adaptive damping, and supplementary damping controllers. The impact of grid impedance on LFOs must also be considered. Grid-connected VSGs interact with the impedance of transmission and distribution networks, which can affect the stability of the entire system. Weak grid conditions with high impedance can exacerbate oscillatory behavior, as seen in vector plots where voltage and current phasors exhibit increased oscillation amplitudes. Implementing impedance-matching techniques and grid-forming control strategies can help stabilize the system and reduce LFO risks. Simulation and experimental studies confirm the significance of vector motion analysis in understanding LFOs in VSGs. Time-domain simulations using MATLAB/Simulink or PSCAD can illustrate how voltage and current phasors evolve over time under different operating conditions. Frequency-domain analysis using small-signal modeling provides additional insights into resonance frequencies and damping ratios. Experimental verification with hardware-in-the-loop (HIL) setups further validates theoretical findings and helps in developing practical mitigation strategies [4,5].

Conclusion

Advanced control techniques, such as Model Predictive Control (MPC) and reinforcement learning, offer promising solutions for addressing LFOs in VSGs. MPC allows for real-time optimization of control parameters, improving transient response and stability. Reinforcement learning algorithms can adaptively tune VSG parameters based on grid conditions, providing a dynamic approach to mitigating oscillations. These techniques can be analyzed using vector motion representations to assess their effectiveness in stabilizing the system. Future research directions in LFO analysis for VSGs include exploring hybrid energy storage integration, multi-agent control frameworks, and wide-area monitoring systems. Hybrid energy storage, such as battery-supercapacitor combinations, can provide fast-response damping support for oscillations. Multi-agent control enables coordinated operation of multiple VSGs, improving overall system resilience. Wide-area monitoring systems utilizing Phasor Measurement Units (PMUs) can offer real-time vector motion tracking for proactive oscillation detection and mitigation. In conclusion, analyzing low-frequency oscillations in virtual synchronous generators using vector motion provides a comprehensive understanding of their behavior and control challenges. By visualizing phase trajectories, power angle deviations, and damping effects, engineers can design more robust VSG control strategies to enhance grid stability. As renewable energy penetration increases, effective LFO mitigation will be essential for ensuring reliable and efficient power system operation.

Acknowledgement

None.

Conflict of Interest

None.

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