Key Takeaways & Executive Findings
- •• • The proposed decentralized transient damping control reduces angular frequency deviations in multi-parallel GFM-VSC systems by introducing supplementary mutual damping torque, directly mitigating power-frequency oscillations that otherwise trigger protection misoperations and cascading disconnections under grid power flow variations or rapid frequency fluctuations. • • Root locus and Bode analyses identify inertia (J), damping (D), and line impedance (X) disparities as the primary oscillation drivers in dual-machine parallel systems, with the characteristic equation denominator as³ + bs² + cs + d where a = ω₀(K₁+K₂)J₁J₂, b = ω₀(K₁+K₂)(D₁J₂+D₂J₁), c = ω₀(K₁+K₂)D₁D₂ + K₁K₂(J₁+J₂), and d = K₁K₂(D₁+D₂), providing explicit parameter sensitivity for industrial tuning. • • Lyapunov function analysis formally proves the control strategy's correctness, establishing a rigorous mathematical foundation for stability guarantees that is often absent in heuristic damping approaches, thereby reducing certification risk for grid-code compliance in renewable integration projects. • • The impedance-based small-signal modeling approach overcomes the flexibility limitations and parameter-variation modeling difficulties of state-space methods for high-dimensional multi-machine systems, enabling scalable extension to multi-area decentralized control architectures without requiring full-system state information.
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Abstract
Parameter disparities in inertia and damping among parallel grid-forming converters (GFM-VSCs) induce power-frequency oscillations under varying operating conditions, potentially triggering protection misoperations and cascading disconnections. This study establishes an impedance-based small-signal model of a multi-parallel GFM-VSC system and identifies the dominant oscillation mechanisms through root locus and Bode analyses. A decentralized transient damping control strategy is proposed based on state feedback theory, incorporating angular frequency compensation and electromagnetic power compensation to enhance individual converter damping and introduce supplementary mutual damping torque. The strategy reduces angular frequency deviations across parallel units and improves system cooperativity. Lyapunov function analysis proves the correctness of the control strategy. Simulation and experimental validation confirm the feasibility and effectiveness of the proposed method. The approach addresses the limitations of centralized state-space modeling for high-dimensional systems and provides a scalable solution for multi-area decentralized control, maintaining steady-state characteristics while regulating transient behavior through parameter optimization.
1. Introduction
Grid-forming converters (GFM-VSCs) emulate synchronous generator inertia and damping characteristics to provide voltage support for renewable-dominated power systems. However, single-unit capacity constraints necessitate parallel operation, where parameter disparities in inertia, damping, and line impedance induce power-frequency oscillations under grid power flow variations or rapid frequency fluctuations. These oscillations trigger protection misoperations and cascading disconnections, undermining the stability that GFM-VSCs are intended to provide. Existing small-signal modeling approaches bifurcate into state-space methods, which suffer from poor flexibility and modeling difficulties under parameter variations for high-dimensional multi-machine systems, and impedance methods, which offer simpler implementation but require further development for decentralized control synthesis.
Current oscillation suppression strategies fall into two categories: damping enhancement through transient electromagnetic power compensation or mutual damping torque, and control parameter optimization via virtual impedance design or quantitative limiter analysis. Neither approach alone fully addresses the coupled dynamics of multi-parallel GFM-VSC systems under parameter disparities. This study establishes an impedance-based small-signal model, identifies oscillation mechanisms through root locus and Bode analyses, and proposes a decentralized transient damping control strategy that combines angular frequency compensation with electromagnetic power compensation. The strategy introduces supplementary mutual damping torque, extends to multi-area decentralized control, and is validated through Lyapunov energy function proof, simulation, and experimental verification.
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MAO Rui, SU Xiaoling, ZHAO Zhengkui, CHEN Laijun, PEI Wei (2026). Oscillation Suppression Strategy for Multi-Parallel Grid-Forming Converter Systems Considering Decentralized Transient Damping. Acta Energiae Solaris Sinica. https://doi.org/10.19912/j.0254-0096.tynxb.202608_9704
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Frequently Asked Questions
What specific parameter disparities drive power-frequency oscillations in multi-parallel GFM-VSC systems, and how does the proposed control address them?
Inertia (J), damping (D), and line impedance (X) disparities are the primary drivers. The dual-machine characteristic equation denominator as³ + bs² + cs + d explicitly contains these parameters: a = ω₀(K₁+K₂)J₁J₂, b = ω₀(K₁+K₂)(D₁J₂+D₂J₁), c = ω₀(K₁+K₂)D₁D₂ + K₁K₂(J₁+J₂), d = K₁K₂(D₁+D₂). The decentralized transient damping control introduces angular frequency compensation and electromagnetic power compensation to enhance individual converter damping and inject supplementary mutual damping torque, reducing angular frequency deviations across parallel units.
How does the impedance-based small-signal model overcome the limitations of state-space methods for high-dimensional multi-machine systems?
State-space methods require establishing differential equations for all system variables, resulting in poor flexibility and severe modeling difficulties under control parameter variations for high-dimensional systems. The impedance-based approach constructs transfer functions between active power and angular frequency, enabling simpler model construction and easier implementation. This study derives the multi-machine parallel system power-frequency oscillation expression ΔPei/ΔPload = (Jiω₀s + Diω₀)Gi / Σⱼ₌₁ⁿ Gj(Jjω₀s + Djω₀), which captures system dynamics without full-state information requirements.
What is the industrial significance of introducing mutual damping torque for multi-area decentralized control?
Mutual damping torque enables the control strategy to extend beyond single-unit damping enhancement to multi-area decentralized architectures. This reduces angular frequency differences between parallel GFM-VSCs, improving system cooperativity without requiring centralized coordination. The approach maintains steady-state characteristics macroscopically while regulating transient behavior microscopically through parameter optimization, addressing the coupled dynamics that cause protection misoperations and cascading disconnections in renewable-dominated grids.
How is the correctness of the proposed control strategy formally verified?
The study employs Lyapunov function analysis to prove the correctness of the decentralized transient damping control strategy. This provides a rigorous mathematical stability guarantee, distinguishing it from heuristic damping approaches that lack formal proof. The Lyapunov energy function demonstrates that the control effectively suppresses oscillations, with simulation and experimental platform validation confirming feasibility and effectiveness.
What are the limitations of existing oscillation suppression methods that this study addresses?
Existing methods bifurcate into damping enhancement (transient electromagnetic power compensation, mutual damping torque, distributed frequency interaction damping) and control parameter optimization (virtual impedance design, limiter analysis). Damping-focused approaches may not fully address parameter disparity coupling in multi-machine systems, while parameter optimization alone cannot guarantee transient stability. This study combines both: macroscopic damping preservation of steady-state characteristics with microscopic parameter optimization for transient regulation, specifically targeting the multi-parallel GFM-VSC oscillation problem under inertia, damping, and impedance disparities.
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