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arxiv: 2606.28023 · v1 · pith:7JJO7ARYnew · submitted 2026-06-26 · 📡 eess.SY · cs.SY

Decentralized Stability of IBR-dominated Power Grids Using Block Diagonal Dominance

Youhong Chen , Xiaoyu Tan , Muhammad Sharjeel Javaid , David Angeli , Balarko Chaudhuri This is my paper

Pith reviewed 2026-06-29 03:18 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords block diagonal dominancesmall-signal stabilityinverter-based resourcesdecentralized stabilitypower system stabilitydecay rateIBRs
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The pith

A block diagonal dominance criterion certifies decentralized small-signal stability and decay rates in IBR-dominated power grids.

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

This paper develops a block diagonal dominance criterion to assess small-signal stability in power grids with high shares of inverter-based resources. The criterion enables local checks for each IBR connection without needing full network models. It is less conservative than strict diagonal dominance and guarantees not just stability but a minimum decay rate for oscillations. The approach avoids restrictive assumptions on network topology or IBR dynamics, making it practical for large-scale grids.

Core claim

The block diagonal dominance criterion applied to a suitably partitioned system matrix provides a sufficient condition for stability and a prescribed decay rate in IBR-dominated grids, allowing decentralized compliance checks for new IBR connections.

What carries the argument

The block diagonal dominance (BDD) criterion on a partitioned system matrix, which generalizes strict diagonal dominance and certifies stability plus decay rate via dominance conditions on the blocks.

If this is right

  • Each IBR can be evaluated locally against the BDD condition to decide whether it can connect without destabilizing the grid.
  • The criterion guarantees a minimum decay rate, which directly bounds the maximum settling time of IBR-induced oscillations.
  • Stability certification remains valid for arbitrary network topologies and arbitrary internal IBR models.
  • The method scales to large grids because the checks do not require centralized computation or full system knowledge.

Where Pith is reading between the lines

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

  • Operators could embed the BDD test in interconnection standards so new resources are approved or rejected on the basis of local measurements alone.
  • The same partitioning idea might apply to stability assessment in other large-scale networked dynamical systems that possess natural block structure.
  • If the BDD margin can be computed from online data, it could support real-time monitoring of how close a grid is to losing the certified decay rate.

Load-bearing premise

The power grid and IBR dynamics admit a block partitioning of the system matrix such that the block diagonal dominance condition is both applicable and sufficient to certify stability and decay rate.

What would settle it

A concrete counterexample grid where the BDD condition holds for the chosen block partition but the closed-loop eigenvalues include at least one with positive real part.

Figures

Figures reproduced from arXiv: 2606.28023 by Balarko Chaudhuri, David Angeli, Muhammad Sharjeel Javaid, Xiaoyu Tan, Youhong Chen.

Figure 1
Figure 1. Figure 1: Feedback of two subsystems. The quantity on the left-hand side of the previous inequality can be explicitly computed: min µ∈[1,+∞) |µ + Hii| =  Im(Hii) if Re(Hii) ≤ −1 |1 + Hii| if Re(Hii) > −1 . so that the corresponding inequalities ‘only’ need to be verified for all s ∈ ∂C<α, rather than searching the space also with respect to the homotopy parameter k ∈ (0, 1]. When feedback of two subsystems is consi… view at source ↗
Figure 2
Figure 2. Figure 2: Left subfigure: A power system with N upcoming IBR plants to be connected to the rest of the grid (RoG) comprising existing IBR plants, synchronous machines, loads, and the network. The busbars represent the points of interconnection (PoI) of the upcoming IBR plants. Right subfigure: Positive feedback structure with two subsystems - upcoming IBR admittance YI(s) and rest of the grid (RoG) impedance ZG(s) u… view at source ↗
Figure 3
Figure 3. Figure 3: Circuit diagram of single IBR connected to a Thevenin equivalent [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 6
Figure 6. Figure 6: Local SDD margins, δd(jω) (top) and δq(jω) (bottom), for a single IBR connected to a Thevenin grid equivalent with α = −0.8 sec−1 . All traces are color-coded by SCR (grid strength falls from blue to yellow). Dashed red traces highlight operating points that fail the SDD test (here, for SCR ≤ 1.8). margin over the frequency range of interest, minω δ(jω), and the real part of the least-damped sub-synchronou… view at source ↗
Figure 4
Figure 4. Figure 4: Local SDD margins δd(jω) (top) and δq(jω) (bottom), for a single IBR connected to a Thevenin grid equivalent. All traces are color-coded by SCR (grid strength falls from blue to yellow). Dashed red traces highlight operating points that fail the SDD test (here, for SCR ≤ 1.7) [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Left: minimum SDD margin minω δ(jω) over the frequency range of interest (blue, left axis) and the real part of least-damped sub-synchronous (SS) mode max Re(λss) (red, right axis). Blue shaded region denotes guaranteed stable SCR range and red shaded region shows stability range from eigenvalue analysis. Right: closed-loop SS modes for varying SCR from 3 to 1. Blue circles mark eigenvalues at stability gu… view at source ↗
Figure 7
Figure 7. Figure 7: Left: minimum SDD margin minω δ(sα) (blue, left axis) and the dis￾tance of real part of least-damped sub-synchronous (SS) mode max Re(λss) from the prescribed decay rate boundary α = −0.8 sec−1 (red, right axis). Blue shade denotes region with guaranteed decay rate and red shaded region shows region with actual decay rate. Right: closed-loop SS modes for varying SCR from 3 to 1. Blue circles denote eigenva… view at source ↗
Figure 8
Figure 8. Figure 8: A modified IEEE 39-bus system [20], [21] with all machines replaced [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 11
Figure 11. Figure 11: The first three subplots show BDD margins of the upcoming IBRs for [PITH_FULL_IMAGE:figures/full_fig_p008_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: BDD-based compliance assessment and actual closed-loop stability. [PITH_FULL_IMAGE:figures/full_fig_p008_10.png] view at source ↗
Figure 12
Figure 12. Figure 12: Left: effect of location on BDD conservativeness. Right: comparison [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
read the original abstract

The growing penetration of inverter-based resources (IBRs) necessitates stability assessment methods that are scalable, decentralized, and model-agnostic. This paper develops a block diagonal dominance (BDD) criterion for decentralized small-signal stability of IBR-dominated power grids. The proposed approach forms the basis for an enhanced IBR connection compliance condition from a small-signal stability perspective that can be evaluated locally for IBRs to be connected to the grid. The proposed approach is shown to be much less conservative than strict diagonal dominance (SDD). Beyond mere stability, we ensure a minimum decay rate or maximum settling time for IBR-induced oscillation. Crucially, these are achieved without imposing restrictive assumptions on network or IBR models. The framework therefore, offers a practical and theoretically grounded basis for decentralized stability certificate of IBR-dominated power grids.

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 / 0 minor

Summary. The paper develops a block diagonal dominance (BDD) criterion for decentralized small-signal stability assessment of IBR-dominated power grids. It claims this yields an enhanced local IBR connection compliance test that is less conservative than strict diagonal dominance (SDD), guarantees a minimum decay rate (or maximum settling time) for IBR-induced oscillations, and requires no restrictive assumptions on network topology or IBR internal models.

Significance. If the central claims are rigorously established, the work would provide a scalable, topology-independent tool for local stability certification in high-IBR grids, extending beyond conservative SDD methods while also bounding transient performance. This addresses a practical need for decentralized compliance criteria without global model knowledge.

major comments (2)
  1. Abstract: The claims that the BDD criterion 'works', is less conservative than SDD, guarantees decay rates, and requires no restrictive assumptions are asserted without derivation, proof outline, numerical validation, or comparison data. This prevents any evaluation of the mathematical support for the central claim.
  2. The sufficiency of BDD for stability and decay-rate certification (via vertical shift of eigenvalues) relies on a block partitioning of the closed-loop system matrix (presumably one block per IBR plus network) such that row/column sum conditions on off-block norms hold. Standard results (e.g., Feingold-Varga) require these norms to be bounded; for arbitrary network admittance matrices the inter-block terms are dense and topology-dependent, so the local compliance test must explicitly justify why the chosen partitioning remains dominant without global knowledge.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below and indicate where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: Abstract: The claims that the BDD criterion 'works', is less conservative than SDD, guarantees decay rates, and requires no restrictive assumptions are asserted without derivation, proof outline, numerical validation, or comparison data. This prevents any evaluation of the mathematical support for the central claim.

    Authors: We agree the abstract is highly condensed. In the revised version we will expand it to include a one-sentence outline of the derivation (application of the block-diagonal dominance theorem to the closed-loop admittance matrix), a reference to the eigenvalue-shift argument for the decay-rate guarantee, and explicit mention of the numerical comparisons with strict diagonal dominance that appear in Section V. The full proofs remain in Sections III–IV. revision: yes

  2. Referee: The sufficiency of BDD for stability and decay-rate certification (via vertical shift of eigenvalues) relies on a block partitioning of the closed-loop system matrix (presumably one block per IBR plus network) such that row/column sum conditions on off-block norms hold. Standard results (e.g., Feingold-Varga) require these norms to be bounded; for arbitrary network admittance matrices the inter-block terms are dense and topology-dependent, so the local compliance test must explicitly justify why the chosen partitioning remains dominant without global knowledge.

    Authors: The partitioning places each IBR (including its internal states) in its own diagonal block; the network dynamics appear only in the off-block columns. The row-sum dominance condition is expressed using the local IBR transfer function and an upper bound on the network admittance magnitude at the point of connection. This bound is obtained from the Thevenin equivalent impedance seen by the IBR, which can be measured or estimated locally without knowledge of the full topology. We will add a dedicated paragraph in Section IV clarifying this local computation and its independence from global network data. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation applies standard block-diagonal dominance theorems to a partitioned system matrix without reduction to inputs or self-citations.

full rationale

The provided abstract and context present the BDD criterion as derived from properties of the closed-loop system matrix under a block partitioning, with sufficiency for stability and decay rate following from existing dominance results (e.g., generalizations of Feingold-Varga). No equations or steps reduce the claimed local compliance condition to a fitted parameter, a self-referential definition, or a load-bearing self-citation chain. The block-partitioning premise is stated as an assumption on the model class rather than constructed from the stability conclusion itself, leaving the central claim independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Central claim rests on the applicability of block diagonal dominance as a stability certificate for partitioned power-system state matrices. Since only the abstract is available, no free parameters, new entities, or paper-specific axioms are identifiable beyond standard domain assumptions.

axioms (2)
  • domain assumption Small-signal linearization of the power system dynamics around an equilibrium point yields a valid model for stability analysis.
    Standard assumption in small-signal stability studies of power grids.
  • domain assumption The overall system matrix can be partitioned into blocks corresponding to IBRs and network components such that BDD conditions can be checked locally.
    Implicit premise required for the decentralized local evaluation claim in the abstract.

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Reference graph

Works this paper leans on

23 extracted references · 3 canonical work pages · 1 internal anchor

  1. [1]

    Definition and classification of power system stability – revisited & extended,

    N. Hatziargyriou, J. Milanovic, C. Rahmannet al., “Definition and classification of power system stability – revisited & extended,”IEEE Transactions on Power Systems, vol. 36, no. 4, pp. 3271–3281, 2021. A SUBMISSION TO IEEE TPWRS, 2026 10

    2021

  2. [2]

    Real-world subsynchronous oscillation events in power grids with high penetrations of inverter-based resources,

    Y . Cheng, L. Fan, J. Roseet al., “Real-world subsynchronous oscillation events in power grids with high penetrations of inverter-based resources,” IEEE Transactions on Power Systems, vol. 38, no. 1, pp. 316–330, 2023

    2023

  3. [3]

    High inverter-based resource integration: The experience of five system operators,

    N. Modi, M. V . Escudero, K. Aramakiet al., “High inverter-based resource integration: The experience of five system operators,”IEEE Power and Energy Magazine, vol. 22, no. 2, pp. 78–88, 2024

    2024

  4. [4]

    N. W. Miller. (2024) Diagnosis and mitigation of observed oscillations in ibr-dominant power systems: A practical guide. [Online]. Available: https://www.esig.energy/wp-content/uploads/2024/08/ESIG-Oscillation s-Guide-2024.pdf

    2024

  5. [5]

    (2025) Guidance on oscillation assessment for inverter based resources (IBRs) - version 2

    NESO. (2025) Guidance on oscillation assessment for inverter based resources (IBRs) - version 2. [Online]. Available: https: //www.neso.energy/document/368341/download

    2025

  6. [6]

    (2025) Inverter-based resource controller design using frequency scanning techniques

    AEMO. (2025) Inverter-based resource controller design using frequency scanning techniques. [Online]. Available: https://www.aemo.com.au/-/ media/files/initiatives/frequency-scanning/inverter-based-resource-contr oller-design-using-frequency-scanning-techniques--november-2025.pdf

    2025

  7. [7]

    R. A. Horn and C. R. Johnson,Matrix Analysis. Cambridge University Press, 1985

    1985

  8. [8]

    H. H. Rosenbrock,Computer-aided Control System Design. Academic Press, 1974

    1974

  9. [9]

    Dynamic stability analysis and control of power system based on nyquist array theory,

    S. Xu, H. Sun, S. Fanget al., “Dynamic stability analysis and control of power system based on nyquist array theory,” in2020 IEEE Power & Energy Society General Meeting (PESGM), 2020, pp. 1–5

    2020

  10. [10]

    S. Shah. (2023) Grid impedance scan tool (GIST): Software for stability analysis of IBR power systems. [Online]. Available: https://docs.nrel.gov/docs/fy23osti/86112.pdf

    2023

  11. [11]

    Rational approximation of frequency domain responses by vector fitting,

    B. Gustavsen and A. Semlyen, “Rational approximation of frequency domain responses by vector fitting,”IEEE Transactions on Power Delivery, vol. 14, no. 3, pp. 1052–1061, 1999

    1999

  12. [12]

    Gain and phase: Decentralized stability conditions for power electronics-dominated power systems,

    L. Huang, D. Wang, X. Wanget al., “Gain and phase: Decentralized stability conditions for power electronics-dominated power systems,” IEEE Transactions on Power Systems, vol. 39, no. 6, pp. 7240–7256, 2024

    2024

  13. [13]

    Geometric decentralized stability certificate for power systems based on projecting DW shells,

    L. Huang, L. Luo, R. Lenget al., “Geometric decentralized stability certificate for power systems based on projecting DW shells,”arXiv preprint arXiv:2508.17033, 2025. [Online]. Available: https://arxiv.org/abs/2508.17033

    work page arXiv 2025

  14. [14]

    Decentralized Parametric Stability Certificates for Grid-Forming Converter Control

    V . H ¨aberle, X. He, L. Huanget al., “Decentralized parametric stability certificates for grid-forming converter control,”arXiv preprint arXiv:2503.05403, 2025. [Online]. Available: https://arxiv.org/abs/2503 .05403

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  15. [15]

    Decentralized stability rules for microgrids,

    P. V orobev, S. Chevalier, and K. Turitsyn, “Decentralized stability rules for microgrids,” in2019 American Control Conference (ACC), 2019, pp. 2596–2601

    2019

  16. [16]

    Dynamic passivity multipliers for plug-and-play stability certificates of converter- dominated grids,

    A. Gorbunov, Y . Chen, P. V orobevet al., “Dynamic passivity multipliers for plug-and-play stability certificates of converter- dominated grids,”arXiv preprint arXiv:2602.09150, 2026. [Online]. Available: https://arxiv.org/abs/2602.09150

    work page arXiv 2026

  17. [17]

    C. A. Desoer and M. Vidyasagar,Feedback Systems. Society for Industrial and Applied Mathematics, 2009

    2009

  18. [18]

    Block diagonally dominant matrices and generalizations of the gerschgorin circle theorem,

    D. G. Feingold and R. S. Varga, “Block diagonally dominant matrices and generalizations of the gerschgorin circle theorem,”Pacific Journal of Mathematics, vol. 12, no. 4, pp. 1241–1250, 1962

    1962

  19. [19]

    R. S. Varga,Ger ˇsgorin and his circles, ser. Springer Series in Compu- tational Mathematics. Springer Verlag, 2004, vol. 36

    2004

  20. [20]

    Benchmark systems for small-signal stability analysis and control,

    C. Canizares, T. Fernandes, E. Geraldiet al., “Benchmark systems for small-signal stability analysis and control,” IEEE Power and Energy Society (PES) Project Report, 2015, pp. 67–70

    2015

  21. [21]

    EMT−RMS Modeling Trade-Off for IBR-Driven Sub-Synchronous Oscillations,

    M. S. Javaid, B. Chaudhuri, F. Tenget al., “EMT−RMS Modeling Trade-Off for IBR-Driven Sub-Synchronous Oscillations,”IEEE Trans- actions on Power Systems, vol. 41, no. 1, pp. 425–437, 2026

    2026

  22. [22]

    How many grid-forming converters do we need? a perspective from small signal stability and power grid strength,

    H. Xin, C. Liu, X. Chenet al., “How many grid-forming converters do we need? a perspective from small signal stability and power grid strength,”IEEE Transactions on Power Systems, vol. 40, no. 1, pp. 623– 635, 2025

    2025

  23. [23]

    Yazdani and R

    A. Yazdani and R. Iravani,Voltage-sourced converters in power systems : modeling, control, and applications. Hoboken, New Jersey: IEEE Press/John Wiley, 2010. APPENDICES Appendix A: Proof of Theorem 5.By contradiction, assumeMis singular. There exists non-zerov∈C n, such thatM v= 0. Partitionvaccording to the blocks inM, i.e.v ′ = [v ′ 1, v′ 2, . . . , v′...

    2010