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arxiv: 2605.19380 · v1 · pith:RBK4N44Xnew · submitted 2026-05-19 · 📡 eess.SY · cs.SY

Revisiting angle stability in power systems with grid-forming power converters

R\'egulo E. \'Avila-Mart\'inez , Javier Renedo , Luis Rouco , Aurelio Garcia-Cerrada , Lukas Sigrist This is my paper

Pith reviewed 2026-05-20 04:44 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords angle stabilitygrid-forming VSCsynchronism stabilityrotor-angle stabilitypower system stabilityvoltage source convertersstability classes
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The pith

Synchronism stability in power systems with machines and grid-forming converters depends only on slow voltage angle difference dynamics.

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

The paper investigates how generators maintain synchronism in power systems that combine synchronous machines with grid-forming voltage source converters under various disturbances. It finds that this stability is completely described by the slow dynamics of the difference in voltage angles at the sources. This description works the same way for rotor angles in machines and for the internal angles in converters. Consequently, the work proposes a unified term angle stability for this behavior and suggests limiting the converter-driven stability label to other slow phenomena.

Core claim

This letter presents a comprehensive analysis showing that the stability phenomenon related to the ability of generators to remain in synchronism when subjected to small or large disturbances in power systems with both synchronous machines and grid-forming voltage source converters is fully characterised with the slow dynamics of the angle difference between the voltage sources connected to the power system, regardless of whether they are synchronous machines (with rotors) or GFM-VSCs. Therefore, we suggest using the term angle stability to refer to this phenomenon, while slow-interaction converter-driven stability should only include slow interactions of different nature involving power

What carries the argument

Slow dynamics of the angle difference between the voltage sources, serving as the unifying mechanism for describing synchronism stability independent of the source type.

If this is right

  • Rotor-angle stability and the relevant part of converter-driven stability merge into one concept.
  • Analysis of both small and large signal stability can use the same angle difference approach in mixed systems.
  • The classification of stability phenomena in power systems needs updating to reflect this unification.

Where Pith is reading between the lines

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

  • This could lead to simpler simulation models for stability studies in grids with increasing converter penetration.
  • Design of converter controls might incorporate principles from classical machine stability analysis.
  • It opens the way for parameter-free or reduced-order models focused on angle dynamics.

Load-bearing premise

The slow angle-difference dynamics by themselves are enough to characterize the full synchronism stability phenomenon in mixed machine-converter systems for all relevant disturbances.

What would settle it

A specific counterexample would be a mixed power system where synchronism is lost due to fast or converter-specific dynamics not reflected in the slow angle difference between voltage sources.

Figures

Figures reproduced from arXiv: 2605.19380 by Aurelio Garcia-Cerrada, Javier Renedo, Luis Rouco, Lukas Sigrist, R\'egulo E. \'Avila-Mart\'inez.

Figure 3
Figure 3. Figure 3: Angles of SM-1 and GFM-VSC-2. (a) Fault 1 cleared [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 1
Figure 1. Figure 1: Test system. Primary frequency response    g p * g p 0 g p ref PFR , g p  g PLL , 0, pu 1 2 GFM sHDGFM 1 PFR PFR K sT − + max g p max g −p b s  [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: GFM-VSC control scheme. A. Large disturbance A three-phase-to-ground short circuit was applied to line 5-6a (close to bus 5) at t = 1 s, and it was cleared by disconnecting the line after 150 ms (Fault 1, for short) [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
read the original abstract

This letter presents a comprehensive analysis of the stability phenomenon related to the ability of generators to remain in synchronism when subjected to small or large disturbances, in power systems with both synchronous machines and grid-forming voltage source converters (GFM-VSC). This phenomenon is associated with two stability classes in the IEEE/PES classification, namely, rotor-angle stability (when involving synchronous machines and slow-interaction converter-driven stability (when involving power converters). However, this work shows that this phenomenon is fully characterised with the slow dynamics of the angle difference between the voltage sources connected to the power system, regardless of whether they are synchronous machines (with rotors) or GFM-VSCs. Therefore, we suggest using the term angle stability to refer to this phenomenon, while slow-interaction converter-driven stability should only include slow interactions of different nature involving power converters.

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 letter re-characterizes synchronism stability (small- and large-disturbance) in mixed synchronous-machine and grid-forming VSC systems. It argues that the phenomenon previously split into rotor-angle stability and slow-interaction converter-driven stability is in fact fully captured by the slow dynamics of the voltage-source angle difference, irrespective of whether the sources are physical rotors or GFM-VSC equivalents, and therefore proposes to subsume both under the single term 'angle stability'.

Significance. If the reduction to pure angle-difference dynamics can be shown rigorously, the result would simplify stability classification and allow classical swing-equation tools to be applied directly to mixed SM-GFM systems. The work correctly identifies that converter controls can emulate inertial behavior, but the significance hinges on whether this equivalence holds without residual interaction terms across the full range of disturbances and control parameters.

major comments (2)
  1. [§III] §III (Modeling and Reduction): the central claim that GFM-VSC full-order dynamics (inner loops, droop/virtual inertia, filters) reduce to the slow angle-difference subsystem without affecting the stability boundary is asserted but not demonstrated. No singular-perturbation ordering, center-manifold analysis, or explicit algebraic elimination of fast states is provided for the mixed SM-converter case; the letter therefore leaves open the possibility that converter-specific time constants interact with the angle mode under certain parameter regimes.
  2. [§IV] §IV (Numerical Validation): the simulation cases illustrate angle-difference behavior but do not constitute a counter-example exclusion. Without an accompanying analytical reduction or a systematic parameter sweep that varies inner-loop bandwidths relative to the angle mode, it remains unclear whether the unification holds for all relevant small- and large-disturbance scenarios or only for the particular tuning shown.
minor comments (2)
  1. [Abstract] The abstract states that the phenomenon is 'fully characterised'; this phrasing should be softened to 'characterised to first order by' pending the missing reduction step.
  2. [Notation] Notation for the angle difference δ should explicitly distinguish between SM rotor angle and GFM-VSC virtual angle when both are present in the same system.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback, which helps clarify the scope and limitations of our letter. We appreciate the acknowledgment of the potential to unify stability concepts under 'angle stability'. Below we respond point-by-point to the major comments, indicating where revisions will be made to improve clarity without altering the core claims.

read point-by-point responses

  1. Referee: [§III] §III (Modeling and Reduction): the central claim that GFM-VSC full-order dynamics (inner loops, droop/virtual inertia, filters) reduce to the slow angle-difference subsystem without affecting the stability boundary is asserted but not demonstrated. No singular-perturbation ordering, center-manifold analysis, or explicit algebraic elimination of fast states is provided for the mixed SM-converter case; the letter therefore leaves open the possibility that converter-specific time constants interact with the angle mode under certain parameter regimes.

    Authors: Section III derives the reduced model by separating the fast inner-loop and filter dynamics from the slow voltage-angle subsystem for both synchronous machines and GFM-VSCs, showing that the angle-difference dynamics govern synchronism stability. The reduction relies on standard time-scale separation assumptions common in power-system modeling, where converter controls are tuned to emulate inertial response without residual fast-state coupling to the angle mode. We agree that an explicit singular-perturbation ordering would strengthen the presentation and will add a concise paragraph in the revised manuscript discussing these assumptions and citing relevant reduction techniques, while noting that a full center-manifold analysis lies beyond the scope of this short letter. revision: partial

  2. Referee: [§IV] §IV (Numerical Validation): the simulation cases illustrate angle-difference behavior but do not constitute a counter-example exclusion. Without an accompanying analytical reduction or a systematic parameter sweep that varies inner-loop bandwidths relative to the angle mode, it remains unclear whether the unification holds for all relevant small- and large-disturbance scenarios or only for the particular tuning shown.

    Authors: The cases in Section IV demonstrate the angle-difference dynamics for both small-signal linearization and large-disturbance nonlinear behavior across mixed SM-GFM configurations, supporting the unification under representative tunings. We acknowledge that a systematic sweep over inner-loop bandwidths would provide additional reassurance. In the revision we will expand the discussion to explicitly state the bandwidth separation ratios used and add one supplementary simulation case with varied inner-loop gains, while emphasizing that the letter format precludes exhaustive sweeps. revision: partial

Circularity Check

0 steps flagged

No circularity: re-framing of stability classes rests on interpretive analysis rather than self-referential reduction

full rationale

The paper's core assertion—that synchronism stability (small and large disturbances) in mixed SM/GFM-VSC systems is fully characterised by the slow dynamics of the angle difference between voltage sources—is advanced as a re-characterisation of IEEE/PES stability classes rather than a derivation that reduces by construction to its own inputs. The abstract and available text present this as an observational unification without exhibiting fitted parameters, self-definitional equations, or load-bearing self-citations that would force the conclusion. No explicit reduction (e.g., via singular perturbation) is shown to be equivalent to an ansatz or prior result by the same authors; the claim remains open to external verification through full-order model analysis. This is the most common honest outcome for interpretive stability papers that do not embed their result inside a closed mathematical loop.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions from power-system stability theory about the dominance of slow angle dynamics in synchronism phenomena.

axioms (1)
  • domain assumption Synchronism stability after disturbances is governed by the slow dynamics of voltage angle differences between connected sources.
    This premise is used to unify rotor-angle and converter-driven stability classes.

pith-pipeline@v0.9.0 · 5692 in / 1113 out tokens · 30249 ms · 2026-05-20T04:44:37.196416+00:00 · methodology

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Reference graph

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