pith. sign in

arxiv: 2606.17575 · v1 · pith:KPBIREBMnew · submitted 2026-06-16 · 📡 eess.SY · cs.SY

Dynamic Analysis of Centralized Energy Storage Systems -- A Comparison between Grid-following and Grid-forming Controls

Qiang Fu , Siqi Bu , Yang Wang , Mingyu Yan This is my paper

Pith reviewed 2026-06-26 23:18 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords centralized energy storage systemsgrid-following controlgrid-forming controlsmall-signal stabilitybidirectional power flowvirtual damping methodmodal resonance
0
0 comments X

The pith

Grid-forming controls stabilize centralized storage as scale grows but weaken under power reversal, requiring ratio limits in hybrids to avoid resonance.

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

The paper examines small-signal stability in centralized energy storage systems that use either grid-following or grid-forming controls, with attention to bidirectional power flow and multiple units. It applies a virtual damping method to reduce complex control-loop dynamics to the dominant oscillation mode and then tracks how damping changes with the number of storage units. Single-control-type systems show dynamic superimposition: grid-forming damping rises with added units while grid-following damping falls. Grid-forming systems prove more sensitive to flow direction and every control loop, so they suit large installations except when reversal is large; hybrids need a bounded grid-forming share to block modal resonance between the two types.

Core claim

Single-type centralized energy storage systems exhibit dynamic superimposition characteristics. As the number of energy storage systems increases, damping of grid-forming controlled systems improves while damping of grid-following controlled systems decreases. The damping of grid-forming systems is more sensitive to bidirectional power flow and all control loops, whereas grid-following damping is more sensitive to the d-axis control loop. Consequently grid-forming systems are preferred for large-scale integration but are limited under significant power reversal; in hybrid configurations the ratio of grid-forming units must be constrained to prevent instability from modal resonance between th

What carries the argument

Virtual damping method that reduces high-order dynamics of GFL and GFM control loops to the dominant oscillation mode under bidirectional power flow.

If this is right

  • Damping of GFM-CESSs improves while damping of GFL-CESSs decreases as the number of ESS units increases.
  • GFM-CESSs are preferred for large-scale integration except in scenarios with significant power reversal.
  • In hybrid GFL-GFM CESSs the ratio of GFM units must be constrained to avoid instability from modal resonance.
  • GFM-CESS damping is more sensitive to bidirectional power flow and all control loops; GFL-CESS damping is more sensitive to the d-axis loop.

Where Pith is reading between the lines

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

  • Grid operators could use real-time power-flow direction as a trigger to switch control modes or adjust hybrid ratios.
  • The superimposition property suggests that adding identical units of one type may be predictable without re-running full-order models.
  • The findings imply that hybrid CESS designs in grids with frequent reversal would benefit from adaptive rather than fixed ratios.

Load-bearing premise

The virtual damping method that reduces high-order dynamics to the dominant oscillation mode accurately captures the stability behavior of the full-order GFL and GFM control loops under bidirectional power flow and varying ESS counts.

What would settle it

Modal analysis or time-domain simulation of a hybrid CESS in which the grid-forming ratio exceeds the constrained value or power reversal becomes large, showing either unexpected modal resonance or reversed damping trends.

Figures

Figures reproduced from arXiv: 2606.17575 by Mingyu Yan, Qiang Fu, Siqi Bu, Yang Wang.

Figure 1
Figure 1. Figure 1: Configuration of CESSs. In [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: GFL control of the grid-side converter in the k th ESS. The configuration of grid-side control loops of the k th ESS is illustrated in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
read the original abstract

This study investigates the small-signal stability of centralized energy storage systems (CESSs) using grid-following (GFL) and grid-forming (GFM) controls, particularly focusing on bidirectional power flow and multiple energy storage systems (ESSs). To address the issue of complex dynamics in CESSs when comprehensive GFL and GFM control loops are considered, high-order dynamics are simplified using the virtual damping method by focusing on the dominant oscillation mode. Damping analysis verifies that CESSs using a single-type control (either GFL or GFM) have dynamic superimposition characteristics. Specifically, as ESS number increases, the damping of GFM-CESSs improves but that of GFL-CESSs decreases. The damping sensitivity shows that the damping of GFM-CESSs is more sensitive to bidirectional power flow and all control loops, whereas that of GFL-CESSs is more sensitive to d-axis control loop. Consequently, GFM-CESSs are preferred for large-scale integration but are limited in scenarios with significant power reversal. If GFL and GFM controls are hybridized in CESSs, the ratio of GFM-CESSs should be constrained to avoid instability from modal resonance between GFL-CESSs and GFM-CESSs. This highlights that implementing GFM-CESSs necessitates considering scenario limitations rather than pursuing maximal integration under hybrid integration conditions. The conclusions are validated through modal analysis and time-domain simulations.

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

3 major / 2 minor

Summary. The paper examines small-signal stability of centralized energy storage systems (CESSs) employing grid-following (GFL) and grid-forming (GFM) controls, with emphasis on bidirectional power flow and varying numbers of energy storage systems (ESSs). High-order dynamics are reduced via a virtual damping method that isolates the dominant oscillation mode; damping analysis then shows superimposition behavior, with GFM-CESS damping improving and GFL-CESS damping degrading as ESS count rises. Sensitivity results indicate GFM-CESS damping is more affected by bidirectional flow and all control loops while GFL-CESS damping is more sensitive to the d-axis loop. The work concludes that GFM-CESSs are preferable for large-scale integration but constrained under significant power reversal, and that hybrid GFL/GFM ratios must be limited to avoid modal resonance instability. Conclusions are supported by modal analysis and time-domain simulations.

Significance. If the virtual-damping reduction is shown to preserve the relevant stability ordering, the results would supply concrete guidance on control selection and hybrid sizing for CESS deployment. The explicit treatment of bidirectional flow and the scaling with ESS count address a practically relevant regime; the combination of modal analysis with time-domain checks is a positive feature.

major comments (3)
  1. [§3] §3 (virtual damping reduction): the central stability conclusions (damping trends with ESS count, sensitivity ordering under power reversal, and hybrid modal resonance) rest on the claim that the dominant-mode reduction accurately represents the full-order GFL/GFM models. No eigenvalue comparison table, participation-factor verification, or quantitative error bound is supplied for the bidirectional-flow or multi-ESS cases; the method is applied directly without the checks needed to confirm dominance preservation.
  2. [§4.3] §4.3 (hybrid resonance claim): the assertion that modal resonance between GFL-CESSs and GFM-CESSs can cause instability when the GFM ratio is unconstrained is load-bearing for the hybrid recommendation, yet no explicit frequency-matching data, mode-shape plots, or participation factors are shown to demonstrate the resonance mechanism under the reported operating points.
  3. [Table 2 / Fig. 7] Table 2 / Fig. 7 (damping sensitivity to power reversal): the reported ordering that GFM-CESS damping is more sensitive to bidirectional flow than GFL-CESS damping is used to support the preference/limitation conclusion, but the sensitivity coefficients are obtained after the virtual-damping reduction; without an accompanying full-order verification, the ordering cannot be taken as established.
minor comments (2)
  1. [§2] Notation for the virtual damping coefficient and the dominant-mode frequency should be defined once in §2 before first use in the reduction step.
  2. [§5] The time-domain simulation parameters (line impedances, ESS ratings, controller gains) are listed in an appendix but not cross-referenced in the figure captions of §5; adding the reference would improve reproducibility.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive comments, which highlight areas where additional verification will strengthen the manuscript. We address each major comment below and will revise accordingly.

read point-by-point responses

  1. Referee: [§3] §3 (virtual damping reduction): the central stability conclusions (damping trends with ESS count, sensitivity ordering under power reversal, and hybrid modal resonance) rest on the claim that the dominant-mode reduction accurately represents the full-order GFL/GFM models. No eigenvalue comparison table, participation-factor verification, or quantitative error bound is supplied for the bidirectional-flow or multi-ESS cases; the method is applied directly without the checks needed to confirm dominance preservation.

    Authors: We agree that explicit verification of the virtual-damping reduction is required for the bidirectional-flow and multi-ESS cases to support the central conclusions. In the revised manuscript we will add eigenvalue comparison tables between full-order and reduced models, participation-factor verification of dominant-mode preservation, and quantitative error bounds under the reported operating conditions. revision: yes

  2. Referee: [§4.3] §4.3 (hybrid resonance claim): the assertion that modal resonance between GFL-CESSs and GFM-CESSs can cause instability when the GFM ratio is unconstrained is load-bearing for the hybrid recommendation, yet no explicit frequency-matching data, mode-shape plots, or participation factors are shown to demonstrate the resonance mechanism under the reported operating points.

    Authors: The referee is correct that direct evidence of the resonance mechanism would strengthen the hybrid recommendation. We will include frequency-matching data, mode-shape plots, and participation factors in the revised §4.3 to demonstrate the modal interaction between GFL-CESS and GFM-CESS units at the operating points examined. revision: yes

  3. Referee: [Table 2 / Fig. 7] Table 2 / Fig. 7 (damping sensitivity to power reversal): the reported ordering that GFM-CESS damping is more sensitive to bidirectional flow than GFL-CESS damping is used to support the preference/limitation conclusion, but the sensitivity coefficients are obtained after the virtual-damping reduction; without an accompanying full-order verification, the ordering cannot be taken as established.

    Authors: We acknowledge that the sensitivity ordering must be confirmed with the full-order model. In the revision we will add full-order sensitivity coefficients alongside the reduced-model results in Table 2 and Fig. 7 to verify the reported ordering under bidirectional power flow. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses standard linearization and virtual damping reduction without definitional or fitted-input collapse

full rationale

The paper's core chain applies small-signal linearization to GFL/GFM control loops, then invokes the virtual damping method to collapse high-order dynamics onto the dominant mode for damping analysis under bidirectional flow and varying ESS counts. No quoted equation or step shows a reported damping ratio, sensitivity, or stability conclusion being defined in terms of a parameter fitted from the same dataset, nor does any result reduce by construction to its own inputs. The method is presented as a simplification technique rather than a self-referential fit, and conclusions are cross-checked via modal analysis and time-domain simulations. This qualifies as self-contained against external benchmarks with no load-bearing self-citation chain or ansatz smuggling that forces the outcome.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Analysis rests on standard small-signal linearization of inverter controls and the validity of the virtual-damping reduction; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • domain assumption The dominant oscillation mode after virtual damping reduction faithfully represents the stability margins of the full-order system.
    Invoked to justify simplification of high-order GFL/GFM dynamics.
  • domain assumption Dynamic superimposition holds for identical single-type control units.
    Used to predict damping change with increasing ESS number.

pith-pipeline@v0.9.1-grok · 5800 in / 1417 out tokens · 28966 ms · 2026-06-26T23:18:06.901308+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

35 extracted references

  1. [1]

    Energy management of hybrid power ship system using adaptive moth flame optimization based on multi - populations,

    L. Xu, X. Luo, Y. Wen et al., "Energy management of hybrid power ship system using adaptive moth flame optimization based on multi - populations," IEEE Trans. Power Syst., vol. 39, no. 1, pp. 1711–1727, Jan. 2024

    2024

  2. [2]

    A review of modeling, management, and applications of grid -connected Li -ion battery storage systems,

    M. Rouholamini, C. Wang, H. Nehrir et al., "A review of modeling, management, and applications of grid -connected Li -ion battery storage systems," IEEE Trans. Smart Grid, vol. 13, no. 6, pp. 4505 –4524, Nov. 2022

    2022

  3. [3]

    On mitigation of sub-synchronous control interactions in hybrid generation resources,

    F. Salehi, A. Golshani, I. B. M. Matsuo, P. Dehghanian, M. Aghazadeh Tabrizi, W.-J. Lee, "On mitigation of sub-synchronous control interactions in hybrid generation resources," IEEE Trans. Ind. Informat., vol. 18, no. 7, pp. 4372–4382, Jul. 2022

    2022

  4. [4]

    [Online]

    DOE Global Energy Storage Database. [Online]. Available: https://sandia.gov/ess-ssl/gesdb/public/statistics.html [Accessed: Dec. 2024]

    2024

  5. [5]

    Simultaneous provision of dynamic active and reactive power response from utility-scale battery energy storage systems in weak grids,

    M. Ghazavi Dozein, O. Gomis -Bellmunt, P. Mancarella, "Simultaneous provision of dynamic active and reactive power response from utility-scale battery energy storage systems in weak grids," IEEE Trans. Power Syst., vol. 36, no. 6, pp. 5548–5557, Nov. 2021

    2021

  6. [6]

    A single-phase synchronization technique for grid -connected energy storage system under faulty grid conditions,

    K. Saleem, Z. Ali, K. Mehran, "A single-phase synchronization technique for grid -connected energy storage system under faulty grid conditions," IEEE Trans. Power Electron., vol. 36, no. 10, pp. 12019–12032, Oct. 2021

    2021

  7. [7]

    Dynamic analysis and stability enhancement of a weak grid -tied hybrid system integrating PV, full-scale wind turbine, and battery storage,

    M. A. K. Magableh, A. A. A. Radwan, Y. A. -R. I. Mohamed, "Dynamic analysis and stability enhancement of a weak grid -tied hybrid system integrating PV, full-scale wind turbine, and battery storage," IEEE Open J. Ind. Appl., vol. 6, pp. 325–349, 2025

    2025

  8. [8]

    Optimal control strategy on battery storage systems for decoupled active -reactive power control and damping oscillations,

    R. Hemmati, A. Neda, "Optimal control strategy on battery storage systems for decoupled active -reactive power control and damping oscillations," J. Energy Storage, vol. 13, pp. 24–34, Oct. 2017

    2017

  9. [9]

    Stability analysis and parameters optimization of islanded microgrid with both ideal and dynamic constant power loads,

    J. Chen, J. Chen, "Stability analysis and parameters optimization of islanded microgrid with both ideal and dynamic constant power loads," IEEE Trans. Ind. Electron., vol. 65, no. 4, pp. 3263–3274, Apr. 2018

    2018

  10. [10]

    Small -disturbance stability of a wind farm with virtual synchronous generators under the condition of weak grid connection,

    W. Du, W. Dong, Y. Wang, H. Wang, "Small -disturbance stability of a wind farm with virtual synchronous generators under the condition of weak grid connection," IEEE Trans. Power Syst., vol. 36, no. 6, pp. 5500– 5511, Nov. 2021

    2021

  11. [11]

    A novel control approach for virtual synchronous generators to suppress frequency and voltage fluctuations in microgrids,

    Y. Hirase, K. Abe, K. Sugimoto et al., "A novel control approach for virtual synchronous generators to suppress frequency and voltage fluctuations in microgrids," Appl. Energy, vol. 210, pp. 699 –710, Jan. 2018

    2018

  12. [12]

    System strength constrained grid-forming energy storage planning in renewable power systems,

    Y. Liu, Y. Chen, H. Xin et al., "System strength constrained grid-forming energy storage planning in renewable power systems," IEEE Trans. Sustain. Energy, vol. 16, no. 2, pp. 981–994, Apr. 2025

    2025

  13. [13]

    Comparative study of battery -based STATCOM in grid -following and grid -forming modes for stabilization of offshore wind power plant,

    F. Zhao, X. Wang, Z. Zhou, Ł. Kocewiak, J. R. Svensson, “Comparative study of battery -based STATCOM in grid -following and grid -forming modes for stabilization of offshore wind power plant,” Electr. Power Syst. Res., vol. 212, p. 108449, 2022

    2022

  14. [14]

    Generalized impedance model and interaction analysis for multiple grid-forming and grid-following converters,

    S. Jiang, G. Konstantinou, “Generalized impedance model and interaction analysis for multiple grid-forming and grid-following converters,” Electr. Power Syst. Res., vol. 214, pt. B, p. 108912, 2023

    2023

  15. [15]

    Power system stabilization using virtual synchronous generator with alternating moment of inertia,

    J. Alipoor, Y. Miura, T. Ise, "Power system stabilization using virtual synchronous generator with alternating moment of inertia," IEEE J. Emerg. Sel. Topics Power Electron., vol. 3, no. 2, pp. 451–458, Jun. 2015

    2015

  16. [16]

    Stability analysis of grid -following and grid -forming converters based on state -space model,

    X. Gao, D. Zhou, A. Anvari-Moghaddam, F. Blaabjerg, "Stability analysis of grid -following and grid -forming converters based on state -space model," in Proc. IPEC-Himeji 2022 ECCE Asia, Himeji, Japan, 2022, pp. 422–428

    2022

  17. [17]

    Power dynamic decoupling control of grid - forming converter in stiff grid,

    F. Zhao, X. Wang, T. Zhu, "Power dynamic decoupling control of grid - forming converter in stiff grid," IEEE Trans. Power Electron., vol. 37, no. 8, pp. 9073–9088, Aug. 2022

    2022

  18. [18]

    Power system small -signal angular stability affected by virtual synchronous generators,

    W. Du, Q. Fu, H. F. Wang, "Power system small -signal angular stability affected by virtual synchronous generators," IEEE Trans. Power Syst., vol. 34, no. 4, pp. 3209–3219, Jul. 2019

    2019

  19. [19]

    Analysis and active -impedance- based stabilization of voltage-source-rectifier loads in grid-connected and isolated microgrid applications,

    A. A. Radwan, Y. A. -R. I. Mohamed, "Analysis and active -impedance- based stabilization of voltage-source-rectifier loads in grid-connected and isolated microgrid applications," IEEE Trans. Sustain. Energy, vol. 4, no. 3, pp. 563–576, Jul. 2013

    2013

  20. [20]

    Constant -power load system stabilization by passive damping,

    M. Cespedes, L. Xing, J. Sun, "Constant -power load system stabilization by passive damping," IEEE Trans. Power Electron., vol. 26, no. 7, pp. 1832–1836, Jul. 2011

    2011

  21. [21]

    Dynamic analysis of energy storage integrated systems considering bidirectional power flow and different control loops of energy storages,

    Q. Fu, W. Du, X. Chen, H. F. Wang, X. Xiao, "Dynamic analysis of energy storage integrated systems considering bidirectional power flow and different control loops of energy storages," J. Energy Storage, vol. 86, p. 111171, 2024

    2024

  22. [22]

    Grid- synchronization stability of converter -based resources —An overview,

    X. Wang, M. G. Taul, H. Wu, Y. Liao, F. Blaabjerg, L. Harnefors, "Grid- synchronization stability of converter -based resources —An overview," IEEE Open J. Ind. Appl., vol. 1, pp. 115–134, 2020

    2020

  23. [23]

    Unified modeling and analysis of dynamic power coupling for grid -forming converters,

    M. Li, Y. Wang, W. Hu et al., “Unified modeling and analysis of dynamic power coupling for grid -forming converters,” IEEE Trans. Power Electron., vol. 37, no. 2, pp. 2321–2337, Feb. 2022

    2022

  24. [24]

    Control interaction modeling and analysis of grid-forming battery energy storage system for offshore wind power plant,

    F. Zhao, X. Wang, Z. Zhou et al., “Control interaction modeling and analysis of grid-forming battery energy storage system for offshore wind power plant,” IEEE Trans. Power Syst., vol. 37, no. 1, pp. 497 –507, Jan. 2022

    2022

  25. [25]

    Stability analysis of systems with high VSC penetration: Where is the limit?,

    C. Collados -Rodriguez, M. Cheah -Mane, E. Prieto -Araujo, O. Gomis - Bellmunt, "Stability analysis of systems with high VSC penetration: Where is the limit?," IEEE Trans. Power Del., vol. 35, no. 4, pp. 2021 – 2031, Aug. 2020

    2021

  26. [26]

    Power converter interfaces for electrochemical energy storage systems – A review,

    V. Fernã o Pires, E. Romero-Cadaval, D. Vinnikov, I. Roasto, J. F. Martins, "Power converter interfaces for electrochemical energy storage systems – A review, " Energy Convers. Manage., vol. 86, pp. 453–475, 2014

    2014

  27. [27]

    Controls of hybrid energy storage systems in microgrids: Critical review, case study and future trends,

    X. Lin, R. Zamora, "Controls of hybrid energy storage systems in microgrids: Critical review, case study and future trends," J. Energy Storage, vol. 47, p. 103884, 2022

    2022

  28. [28]

    Stability improvement of microgrids in the presence of constant power loads,

    J. Shair, H. Z. Li, J. B. Hu et al., "Stability improvement of microgrids in the presence of constant power loads," Int. J. Electr. Power Energy Syst., vol. 36, pp. 442–456, Mar. 2018. © 2026 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/repu...

    2018

  29. [29]

    Analysis of subsynchronous oscillation caused by multiple VSCs with different dynamics under strong grid connections,

    Q. Fu, W. Du, H. F. Wang, X. Xiao, "Analysis of subsynchronous oscillation caused by multiple VSCs with different dynamics under strong grid connections," IEEE Trans. Sustain. Energy, vol. 14, no. 4, pp. 2364– 2375, Oct. 2023

    2023

  30. [30]

    Integrating power electronics -based energy storages to power systems: A review on dynamic modeling, analysis, and future challenges,

    Q. Fu, C. Dai, S. Bu, C. Y. Chung, "Integrating power electronics -based energy storages to power systems: A review on dynamic modeling, analysis, and future challenges," Renew. Sustain. Energy Rev., vol. 213, p. 115460, 2025

    2025

  31. [31]

    Modeling of grid -connected VSCs for power system small -signal stability analysis in DC -link voltage control timescale,

    H. Yuan, X. Yuan, J. Hu, "Modeling of grid -connected VSCs for power system small -signal stability analysis in DC -link voltage control timescale," IEEE Trans. Power Syst., vol. 32, no. 5, pp. 3981 –3991, Sep. 2017

    2017

  32. [32]

    Damping torque analysis of DC voltage stability of an MTDC network for the wind power delivery,

    W. Du, Q. Fu, H. Wang, "Damping torque analysis of DC voltage stability of an MTDC network for the wind power delivery," IEEE Trans. Power Del., vol. 35, no. 1, pp. 324–338, Feb. 2020

    2020

  33. [33]

    Analysis of harmonic oscillations caused by grid-connected VSCs,

    Q. Fu, W. Du, H. F. Wang, "Analysis of harmonic oscillations caused by grid-connected VSCs," IEEE Trans. Power Del., vol. 36, no. 2, pp. 1202– 1210, Apr. 2021

    2021

  34. [34]

    Open -loop modal coupling analysis for a multi-input multi-output interconnected MTDC/AC power system,

    W. Du, Q. Fu, H. F. Wang, "Open -loop modal coupling analysis for a multi-input multi-output interconnected MTDC/AC power system," IEEE Trans. Power Syst., vol. 34, no. 1, pp. 246–256, Jan. 2019

    2019

  35. [35]

    Average model of a 100-kW grid -connected PV array,

    P. Giroux, G. Sybille, C. Osorio, S. Chandrachood, “Average model of a 100-kW grid -connected PV array,” MathWorks. [Online]. Available: https://ww2.mathworks.cn/help/sps/ug/average-model-of-a-100-kw-grid- connected-pv-array.html. [Accessed: Dec. 2024]

    2024