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arxiv: 2504.06981 · v2 · pith:2SW4G4VGnew · submitted 2025-04-09 · 📡 eess.SY · cs.SY

LCL Resonance Analysis and Damping in Single-Loop Grid-Forming Wind Turbines

Meng Chen , Yufei Xi , Frede Blaabjerg , Lin Cheng , Ioannis Lestas This is my paper

Pith reviewed 2026-05-22 20:24 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords grid-forming controlLCL filteropen-loop stabilitydroop controlactive dampingwind turbinesresonance analysisreactive power control
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The pith

Single-loop grid-forming controls with droop-I reactive power can produce open-loop unstable poles near LCL resonances.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper challenges the standard assumption that grid-forming and grid-following controls remain open-loop stable near high-frequency resonances. It shows that single-loop grid-forming schemes paired with droop-I reactive power control generate unstable open-loop poles around LCL filter resonances. This creates a previously unrecognized instability mechanism that shrinks high-frequency stability margins and robustness. The analysis traces how reactive power and electrical parameters affect the poles and proposes an active damping method designed around the new mechanism. Experiments validate the results and note distinctly different resonance behavior compared with grid-following schemes.

Core claim

Single-loop grid-forming control schemes that incorporate droop-I reactive power control can produce open-loop unstable poles in the vicinity of LCL filter resonances. This finding contradicts the usual premise that such systems are open-loop stable near resonances and directly reduces stability margins and robustness at high frequencies. The paper derives the result from the control structure, examines parameter sensitivity, and supplies an active damping design that accounts for the instability, together with a comparison to grid-following resonance features.

What carries the argument

The droop-I reactive power control loop inside the single-loop grid-forming structure interacting with LCL filter dynamics to place poles in the right half-plane of the open-loop transfer function.

If this is right

  • Stability margins for single-loop GFM systems must be evaluated with possible open-loop unstable poles in view.
  • Active damping designs need to be constructed explicitly around the identified open-loop instability.
  • Resonance features and required damping differ between single-loop GFM and conventional grid-following schemes.
  • The instability depends on both reactive power control gains and electrical parameters of the LCL filter.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Classical loop-shaping methods may require modification when applied to single-loop GFM inverters.
  • The finding could guide selection between single-loop and multi-loop GFM architectures in wind turbine fleets.
  • Similar open-loop instability risks may appear in other converter topologies that combine droop-style power control with LCL filters.

Load-bearing premise

The small-signal model of the single-loop GFM with droop-I control and LCL filter correctly identifies the open-loop poles from the control structure and parameters.

What would settle it

Hardware measurement of the open-loop transfer function on a physical single-loop GFM inverter with droop-I control that shows no right-half-plane poles near the LCL resonance frequency.

Figures

Figures reproduced from arXiv: 2504.06981 by Frede Blaabjerg, Ioannis Lestas, Lin Cheng, Meng Chen, Yufei Xi.

Figure 1
Figure 1. Figure 1: Structure of a PMSG-WT system with LCL filter controlled by SL-GFM control strategy. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Detailed control block diagram of PMSG-WT system with droop-I [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Small-signal block diagram of SL-GFM PMSG-WT system. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Eigenvalues of detailed model of SL-GFM PMSG-WT system. [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Sensitivity evaluating variation of real parts of resonance modes in [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Root loci when kq increases from 4 to 11 with corresponding bandwidth of RAP loop increasing from 6 Hz to 17 Hz [PITH_FULL_IMAGE:figures/full_fig_p004_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Root loci when Lg increases from 0.2 p.u. to 0.5 p.u. -40 -30 -20 -10 -5 0 -5000 0 5000 Imaginary axis Real axis becoming more stable [PITH_FULL_IMAGE:figures/full_fig_p005_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of open-loop Bode plots of RAP loops using simplified [PITH_FULL_IMAGE:figures/full_fig_p005_10.png] view at source ↗
Figure 13
Figure 13. Figure 13: Root loci of SL-GFM converter with voltage control as in Fig. 11(d). [PITH_FULL_IMAGE:figures/full_fig_p006_13.png] view at source ↗
Figure 15
Figure 15. Figure 15: Equivalent virtual resistors of various AD strategies. [PITH_FULL_IMAGE:figures/full_fig_p007_15.png] view at source ↗
Figure 17
Figure 17. Figure 17: Block diagram of AD strategy for SL-GFM converters. [PITH_FULL_IMAGE:figures/full_fig_p007_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Designed eigenvalues based on worst-case scenario. [PITH_FULL_IMAGE:figures/full_fig_p008_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: 14-bus system diagram with SL-GFM controlled PMSG-WT system. [PITH_FULL_IMAGE:figures/full_fig_p009_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Simulation results with parameters in Table I. [PITH_FULL_IMAGE:figures/full_fig_p009_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Simulation results with Lg = 0.62 p.u. controllability, and full-state feedback design,” IEEE Trans. Sustain. Energy, vol. 15, no. 1, pp. 68–80, Jan. 2024. [2] M. Wang and J. V. Milanovic, “Simultaneous assessment of multiple ´ aspects of stability of power systems with renewable generation,” IEEE Trans. Power Syst., vol. 39, no. 1, pp. 97–106, Jan. 2024. [3] F. Blaabjerg, M. Chen, and L. Huang, “Power el… view at source ↗
read the original abstract

A common assumption in both grid-following (GFL) and grid-forming (GFM) control systems is that they are open-loop (OL) stable in the vicinity of high-frequency resonances. Hence classical loop-shaping approaches are often used for establishing stability margins and designing active damping (AD) strategies. This paper shows that single-loop GFM (SL-GFM) control schemes incorporating a widely used class of reactive power (RAP) control, referred to as droop-I control, can lead to OL unstable poles. This finding reveals a novel instability mechanism resulting in a reduced stability margin and robustness at high frequencies. The sensitivity of this phenomenon to both RAP and electrical parameters is analyzed in detail. An AD design that explicitly accounts for the newly identified instability mechanism is proposed. We also provide a comparison between such SL-GFM and well-studied GFL control schemes, highlighting quite different resonance features between them. Validation is performed through experiments.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that single-loop grid-forming (SL-GFM) inverters with a common droop-I reactive power control can produce open-loop unstable poles near LCL-filter resonances, contrary to the standard assumption of open-loop stability at high frequencies. This reduces stability margins and robustness. The work analyzes sensitivity to RAP and electrical parameters, proposes an active-damping design that accounts for the new mechanism, contrasts the resonance behavior with grid-following schemes, and reports experimental validation.

Significance. If the open-loop instability result holds under realistic parameters, the finding identifies a previously under-appreciated limitation of classical loop-shaping for SL-GFM wind-turbine controls and motivates revised active-damping strategies. The experimental validation and explicit comparison with GFL schemes add practical value; the result would be strengthened by reproducible code or parameter-free derivations, neither of which is indicated in the provided material.

major comments (2)
  1. [Small-signal modeling / open-loop pole analysis] The central claim rests on the small-signal model of the droop-I reactive-power path and LCL filter yielding right-half-plane open-loop poles. The derivation of the open-loop characteristic equation (presumably in the modeling section) must be shown explicitly, including the linearization steps, any low-pass filtering on the droop path, reference-frame transformations, and grid-impedance assumptions. Without this, it is impossible to confirm that the RHP roots are not an artifact of modeling choices.
  2. [Validation / experimental results] Table or figure reporting the open-loop pole locations (realistic parameter set) should be added or expanded. The current experimental validation is cited in the abstract, but the manuscript must demonstrate that the observed instability matches the predicted RHP poles rather than closed-loop behavior alone.
minor comments (2)
  1. [Abstract / Introduction] Clarify the acronym RAP on first use in the abstract and introduction; it is not standard in the broader GFM literature.
  2. [Sensitivity analysis figures] Ensure all figures showing frequency responses or root loci include grid-impedance variation or parameter sweeps so readers can judge robustness at high frequencies.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below and will revise the manuscript accordingly to improve clarity and validation.

read point-by-point responses

  1. Referee: [Small-signal modeling / open-loop pole analysis] The central claim rests on the small-signal model of the droop-I reactive-power path and LCL filter yielding right-half-plane open-loop poles. The derivation of the open-loop characteristic equation (presumably in the modeling section) must be shown explicitly, including the linearization steps, any low-pass filtering on the droop path, reference-frame transformations, and grid-impedance assumptions. Without this, it is impossible to confirm that the RHP roots are not an artifact of modeling choices.

    Authors: We agree that the explicit derivation is necessary for independent verification. The revised manuscript will include a dedicated appendix presenting the complete small-signal modeling steps for the droop-I reactive-power path and LCL filter. This will detail the linearization procedure, low-pass filter implementation on the droop path, reference-frame transformations, and grid-impedance assumptions used to obtain the open-loop characteristic equation. revision: yes

  2. Referee: [Validation / experimental results] Table or figure reporting the open-loop pole locations (realistic parameter set) should be added or expanded. The current experimental validation is cited in the abstract, but the manuscript must demonstrate that the observed instability matches the predicted RHP poles rather than closed-loop behavior alone.

    Authors: We will add a table listing the computed open-loop pole locations for the realistic parameter sets employed in the analysis and experiments. The experimental results section will be expanded with additional time-domain waveforms and frequency-response data that directly link the observed high-frequency instability to the predicted RHP poles, including comparisons before and after activation of the proposed active damping. revision: yes

Circularity Check

0 steps flagged

No significant circularity in small-signal model derivation

full rationale

The paper performs standard small-signal linearization of the SL-GFM control structure including droop-I reactive power control and LCL filter dynamics to obtain the open-loop characteristic equation and locate its poles. This is a direct algebraic derivation from the state-space model equations rather than any fitted parameter renamed as a prediction, self-definitional loop, or load-bearing self-citation chain. The resulting claim of possible right-half-plane poles is a consequence of the explicit model (not presupposed by construction), and the paper remains self-contained against external benchmarks such as experimental validation. No steps reduce to their own inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; the paper likely relies on standard modeling assumptions in the field but no specific free parameters or invented entities are identifiable from the provided text.

axioms (1)
  • domain assumption Small-signal linearization of the control system around an operating point is valid for stability analysis.
    Standard in power electronics control papers for deriving transfer functions and poles.

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Reference graph

Works this paper leans on

30 extracted references · 30 canonical work pages

  1. [1]

    M. Chen, D. Zhou, A. Tayyebi, E. Prieto-Araujo, F. D ¨orfler, and F. Blaabjerg, “On power control of grid-forming converters: Modeling, 10 0.9999 1 1.0001 1.0002 0.47 0.5 0.53 0 3 6 9 12 15 18 21 24 27 Time (Second) -0.07 -0.04 -0.01 Output (p.u.) 0.999998 1 1.000002 0.9999 1 1.0001 0.4996 0.5 0.5004 0.47 0.5 0.53 17.5 18 18.5 -0.0396 -0.0392 -0.0388 21.5...

    work page 2024

  2. [2]

    Simultaneous assessment of multiple aspects of stability of power systems with renewable generation,

    M. Wang and J. V . Milanovi ´c, “Simultaneous assessment of multiple aspects of stability of power systems with renewable generation,” IEEE Trans. Power Syst., vol. 39, no. 1, pp. 97–106, Jan. 2024

    work page 2024

  3. [3]

    Power electronics in wind generation systems,

    F. Blaabjerg, M. Chen, and L. Huang, “Power electronics in wind generation systems,” Nat. Rev. Electr. Eng. , vol. 1, pp. 234–250, Apr. 2024

    work page 2024

  4. [4]

    Transient stability of voltage- source converters with grid-forming control: A design-oriented study,

    D. Pan, X. Wang, F. Liu, and R. Shi, “Transient stability of voltage- source converters with grid-forming control: A design-oriented study,” IEEE Trans. Emerg. Sel. Topics Power Electron., vol. 8, no. 2, pp. 1019– 1033, Jun. 2020

    work page 2020

  5. [5]

    Modeling of grid-forming and grid-following inverters for dynamic simulation of large-scale distribution systems,

    W. Du, F. K. Tuffner, K. P. Schneider, R. H. Lasseter, J. Xie, Z. Chen, and B. Bhattarai, “Modeling of grid-forming and grid-following inverters for dynamic simulation of large-scale distribution systems,” IEEE Trans. Power Del., vol. 36, no. 4, pp. 2035–2045, Aug. 2021

    work page 2035

  6. [6]

    Impact of dc-link voltage control on torsional vibrations in grid-forming pmsg wind turbines,

    S. Liu, H. Wu, T. Bosma, and X. Wang, “Impact of dc-link voltage control on torsional vibrations in grid-forming pmsg wind turbines,” IEEE Trans. Energy Convers., vol. 39, no. 4, pp. 2631–2642, Dec. 2024

    work page 2024

  7. [7]

    Frequency stability of synchronous machines and grid-forming power converters,

    A. Tayyebi, D. Gross, A. Anta, F. Kupzog, and F. D ¨orfler, “Frequency stability of synchronous machines and grid-forming power converters,” IEEE Trans. Emerg. Sel. Topics Power Electron., vol. 8, no. 2, pp. 1004– 1018, Jun. 2020

    work page 2020

  8. [8]

    Comparison of dynamic characteristics between virtual synchronous generator and droop control in inverter- based distributed generators,

    J. Liu, Y . Miura, and T. Ise, “Comparison of dynamic characteristics between virtual synchronous generator and droop control in inverter- based distributed generators,” IEEE Trans. Power Electron. , vol. 31, no. 5, pp. 3600–3611, May 2016

    work page 2016

  9. [9]

    A comparative study of two widely used grid-forming droop controls on microgrid small-signal stability,

    W. Du, Z. Chen, K. P. Schneider, R. H. Lasseter, S. Pushpak Nandanoori, F. K. Tuffner, and S. Kundu, “A comparative study of two widely used grid-forming droop controls on microgrid small-signal stability,” IEEE Trans. Emerg. Sel. Topics Power Electron. , vol. 8, no. 2, pp. 963–975, Jun. 2020

    work page 2020

  10. [10]

    H∞-control of grid-connected converters: Design, objectives and decentralized stability certificates,

    L. Huang, H. Xin, and F. D ¨orfler, “ H∞-control of grid-connected converters: Design, objectives and decentralized stability certificates,” IEEE Trans. Smart Grid , vol. 11, no. 5, pp. 3805–3816, Sep. 2020

    work page 2020

  11. [11]

    Generalized multivariable grid-forming control design for power converters,

    M. Chen, D. Zhou, A. Tayyebi, E. Prieto-Araujo, F. D ¨orfler, and F. Blaabjerg, “Generalized multivariable grid-forming control design for power converters,” IEEE Trans. Smart Grid , vol. 13, no. 4, pp. 2873– 2885, Jul. 2022

    work page 2022

  12. [12]

    Stability criterion for near-area grid-forming converters under the weak grid condition,

    P. Wang, J. Ma, R. Zhang, S. Wang, T. Liu, and Y . Yang, “Stability criterion for near-area grid-forming converters under the weak grid condition,” IEEE Trans. Power Electron. , vol. 40, no. 1, pp. 361–374, Jan. 2025

    work page 2025

  13. [13]

    Small-signal modeling and parameters design for virtual synchronous generators,

    H. Wu, X. Ruan, D. Yang, X. Chen, W. Zhao, Z. Lv, and Q.-C. Zhong, “Small-signal modeling and parameters design for virtual synchronous generators,” IEEE Trans. Ind. Electron. , vol. 63, no. 7, pp. 4292–4303, Jul. 2016

    work page 2016

  14. [14]

    Grid- forming converters: Control approaches, grid-synchronization, and future trends—A review,

    R. Rosso, X. Wang, M. Liserre, X. Lu, and S. Engelken, “Grid- forming converters: Control approaches, grid-synchronization, and future trends—A review,” IEEE Open J. Ind. Appl. , vol. 2, pp. 93–109, May 2021

    work page 2021

  15. [15]

    Power system stability with a high penetration of inverter-based resources,

    Y . Gu and T. C. Green, “Power system stability with a high penetration of inverter-based resources,” Proc. IEEE, vol. 111, no. 7, pp. 832–853, Jul. 2023

    work page 2023

  16. [16]

    Multivariable control design for grid-forming inverters with decoupled active and reactive power loops,

    D. B. Rathnayake and B. Bahrani, “Multivariable control design for grid-forming inverters with decoupled active and reactive power loops,” IEEE Trans. Power Electron., vol. 38, no. 2, pp. 1635–1649, Feb. 2023

    work page 2023

  17. [17]

    Parameter constraints for virtual syn- chronous generator considering stability,

    J. Chen and T. O’Donnell, “Parameter constraints for virtual syn- chronous generator considering stability,” IEEE Trans. Power Syst. , vol. 34, no. 3, pp. 2479–2481, May 2019

    work page 2019

  18. [18]

    Analysis and suppression strategy of synchronous frequency resonance for grid- connected converters with power-synchronous control method,

    X. Xiong, Y . Zhou, B. Luo, P. Cheng, and F. Blaabjerg, “Analysis and suppression strategy of synchronous frequency resonance for grid- connected converters with power-synchronous control method,” IEEE Trans. Power Electron., vol. 38, no. 6, pp. 6945–6955, Jun. 2023

    work page 2023

  19. [19]

    A generic voltage control for grid-forming converters with improved power loop dynamics,

    H. Deng, J. Fang, Y . Qi, Y . Tang, and V . Debusschere, “A generic voltage control for grid-forming converters with improved power loop dynamics,” IEEE Trans. Ind. Electron. , vol. 70, no. 4, pp. 3933–3943, Apr. 2023

    work page 2023

  20. [20]

    Generalized LCL-filter design algorithm for grid-connected voltage-source inverter,

    S. Jayalath and M. Hanif, “Generalized LCL-filter design algorithm for grid-connected voltage-source inverter,” IEEE Trans. Ind. Electron. , vol. 64, no. 3, pp. 1905–1915, Mar. 2017

    work page 1905

  21. [21]

    Passivity enhancement for LCL-filtered inverter with grid current control and capacitor current active damping,

    X. Wang, Y . He, D. Pan, H. Zhang, Y . Ma, and X. Ruan, “Passivity enhancement for LCL-filtered inverter with grid current control and capacitor current active damping,” IEEE Trans. Power Electron., vol. 37, no. 4, pp. 3801–3812, Apr. 2022

    work page 2022

  22. [22]

    Regions of active damping control for LCL filters,

    S. G. Parker, B. P. McGrath, and D. G. Holmes, “Regions of active damping control for LCL filters,” IEEE Trans. Ind. Appl., vol. 50, no. 1, pp. 424–432, Jan./Feb. 2014

    work page 2014

  23. [23]

    Grid-current-feedback active damping for LCL resonance in grid-connected voltage-source convert- ers,

    X. Wang, F. Blaabjerg, and P. C. Loh, “Grid-current-feedback active damping for LCL resonance in grid-connected voltage-source convert- ers,” IEEE Trans. Power Electron. , vol. 31, no. 1, pp. 213–223, Jan. 2016

    work page 2016

  24. [24]

    A study of virtual resistor-based active damping alternatives for LCL resonance in grid-connected voltage source inverters,

    T. Liu, J. Liu, Z. Liu, and Z. Liu, “A study of virtual resistor-based active damping alternatives for LCL resonance in grid-connected voltage source inverters,” IEEE Trans. Power Electron., vol. 35, no. 1, pp. 247– 262, Jan. 2020

    work page 2020

  25. [25]

    High penetration of inverter-based power sources with VSG control impact on electromechanical oscillation of power system,

    M. Chen, D. Zhou, and F. Blaabjerg, “High penetration of inverter-based power sources with VSG control impact on electromechanical oscillation of power system,” Int. J. Electr. Power Energy Syst., vol. 142, pp. 1–12, Jun. 2022

    work page 2022

  26. [26]

    Stability analysis and active damping design for grid-forming converters in LC resonant grids,

    S. Liu, H. Wu, X. Wang, T. Bosma, and G. Sauba, “Stability analysis and active damping design for grid-forming converters in LC resonant grids,” IEEE Open J. Ind. Electron. Soc. , vol. 5, pp. 143–154, 2024

    work page 2024

  27. [27]

    Investigation of active damping approaches for pi-based current control of grid- connected pulse width modulation converters with LCL filters,

    J. Dannehl, F. W. Fuchs, S. Hansen, and P. B. Thøgersen, “Investigation of active damping approaches for pi-based current control of grid- connected pulse width modulation converters with LCL filters,” IEEE Trans. Ind. Appl. , vol. 46, no. 4, pp. 1509–1517, Jul./Aug. 2010

    work page 2010

  28. [28]

    M. Chen. [Online]. Available: https://github.com/MengChen-MC/ LCLResonanceAnalysis2025

    work page

  29. [29]

    G. F. Franklin, J. D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems . Pearson, 2019

    work page 2019

  30. [30]

    Milano, Power System Modelling and Scripting

    F. Milano, Power System Modelling and Scripting . Springer, 2010

    work page 2010