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arxiv: 2605.23030 · v1 · pith:CTM34SMBnew · submitted 2026-05-21 · 📡 eess.SY · cs.SY

A Methodology for Impedance-based Stability Margin Analysis for Interconnected Offshore Wind Clusters

Germano Rugendo Mugambi , Behnam Nouri , Oscar Sabor\'io-Romano , George Alin Raducu , Nicolaos A. Cutululis This is my paper

Pith reviewed 2026-05-25 05:29 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords impedance-based stabilityoffshore wind clustersstability marginsNyquist criterionpower park modulesHVDC interconnectionsmall-signal analysis
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The pith

A general impedance-based method evaluates stability margins of an existing offshore connection after a new power park module is added and derives the maximum allowable impedance to meet operator requirements.

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

This paper develops a methodology that uses impedance models of offshore wind clusters and HVDC links to assess how adding a new cluster changes the stability margins at the point of connection. It calculates the largest impedance the new connection may have while still satisfying the minimum margin rules set by system operators. The approach augments the generalized Nyquist criterion with new stability regions plotted on the Nyquist diagram that directly indicate margin compliance and remaining headroom. Validation uses vendor-supplied frequency-domain models of two interconnected offshore wind plants. If the method holds, interconnection studies can set explicit impedance limits without exhaustive time-domain checks for every proposed addition.

Core claim

The paper presents a general impedance-based methodology to evaluate the stability margins of an existing connection after a new PPM is integrated and to derive a maximum allowable impedance for the new connection such that the minimum stability margin requirements specified by system operators are satisfied and stable operation is maintained, with new Nyquist-based stability regions introduced to provide analytical indications of margin compliance and headroom.

What carries the argument

Impedance-based stability analysis that combines frequency-domain models of the existing and new systems with the generalized Nyquist criterion plus newly defined stability regions on the Nyquist plot.

If this is right

  • Stability margins of an existing OWPP connection can be quantified after a new PPM is integrated using the combined impedance at the point of connection.
  • A maximum allowable impedance value for the new connection can be calculated to ensure operator-specified minimum margins are met.
  • New stability regions on the Nyquist plot give direct analytical checks for margin compliance and available headroom without additional encirclement counting.
  • The method supports stable operation decisions for interconnected offshore clusters using only frequency-domain data.

Where Pith is reading between the lines

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

  • The same impedance-limit derivation could be applied when adding multiple new clusters in sequence rather than one at a time.
  • System operators could translate the derived impedance bounds into enforceable technical connection requirements for future wind farms.
  • The approach might extend to other converter-dominated networks such as onshore clusters or mixed wind-solar interconnections.

Load-bearing premise

The frequency-domain impedance models of the OWPPs and HVDC system accurately capture the small-signal dynamics at the point of connection.

What would settle it

A time-domain simulation or measurement that shows instability or margin violation when the new connection impedance is set exactly to the derived maximum allowable value.

Figures

Figures reproduced from arXiv: 2605.23030 by Behnam Nouri, George Alin Raducu, Germano Rugendo Mugambi, Nicolaos A. Cutululis, Oscar Sabor\'io-Romano.

Figure 1
Figure 1. Figure 1: Small-signal representation of grid-connected converter [5]. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Wide area network impedance scan setup. then be evaluated independently for each sequence. A further alternative is the reverse impedance-based ap￾proach, which deviates from the standard formulation by assuming the grid remains stable when the IBR is connected. Stability following disconnection can then be assessed using the Nyquist plot of the loop gain. In this framework, stability is evaluated by focus… view at source ↗
Figure 4
Figure 4. Figure 4: Calculation of ∠Lold(jω) at new crossings. B. Calculation of ∠Lold(jω) at New Crossover Frequencies The crossover frequencies appearing in (13) can also be interpreted as a set (or range) of critical frequencies specified by the system operator, such that a minimum phase margin must be guaranteed if a resonance point falls within this range. Therefore, it is important to evaluate the new phase margin using… view at source ↗
Figure 5
Figure 5. Figure 5: Proposed stability regions. The wedges are interpreted at the gain-crossover frequencies (where |L(jω)| = 1), consistent with the definition of phase margin. The critical area corresponds to phase margins below the minimum requirement, i.e., PM < PMmin, indicating noncompliance and reduced stability margins (even if the encirclement condition for stability is still satisfied) which may lead to instability … view at source ↗
Figure 6
Figure 6. Figure 6: Case 1: Study model configuration with a common transformer. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Case 2: Study model configuration with separate transformers. [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of calculated and measured loop gain. [PITH_FULL_IMAGE:figures/full_fig_p006_8.png] view at source ↗
Figure 11
Figure 11. Figure 11: Case 1: Stability margins using frequency-domain model and [PITH_FULL_IMAGE:figures/full_fig_p007_11.png] view at source ↗
Figure 10
Figure 10. Figure 10: Case 1: Stability margins using frequency-domain model and [PITH_FULL_IMAGE:figures/full_fig_p007_10.png] view at source ↗
Figure 13
Figure 13. Figure 13: Case 1: Stability margins using a Thevenin-equivalent grid and ´ positive-sequence impedance when ZOWPP2 > Zlimit. Nyquist plot for ZOWPP2 > Zlimit -1.5 -1 -0.5 0 0.5 1 Re{L(j!)} -1 -0.5 0 0.5 1 Im{L(j !)} 10 508 1.01e+03 1.5e+03 2e+03 2.5e+03 Frequency (Hz) [PITH_FULL_IMAGE:figures/full_fig_p008_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Case 1: Stability margins using frequency-domain model and [PITH_FULL_IMAGE:figures/full_fig_p008_14.png] view at source ↗
read the original abstract

With recent developments in offshore grid architectures, power park modules (PPMs) such as clusters of offshore wind power plants (OWPPs) are increasingly interconnected offshore. Consequently, it is necessary to assess how integrating a new OWPP affects the stability margins of an existing OWPP at the point of connection. Although impedance-based methods are widely used for small-signal stability assessment of interconnected converter-based systems, many studies rely primarily on Nyquist encirclements and do not explicitly quantify stability margins. Thus, this paper proposes a general impedance-based methodology to (i) evaluate the stability margins of an existing connection after a new PPM is integrated and (ii) derive a maximum allowable impedance for the new connection such that the minimum stability margin requirements specified by system operators are satisfied and stable operation is maintained. In addition, new Nyquist-based stability regions are introduced to complement the generalized Nyquist criterion, providing analytical indications of margin compliance and headroom. The proposed method is validated through case studies using vendor-based frequency-domain models of two interconnected OWPPs and HVDC system.

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 proposes a general impedance-based methodology to evaluate the stability margins of an existing offshore wind connection after integrating a new power park module (PPM) and to derive a maximum allowable impedance for the new connection that satisfies system-operator minimum margin requirements. It introduces new Nyquist-based stability regions to provide analytical indications of margin compliance and headroom beyond standard generalized Nyquist encirclement counts. The method is illustrated and validated via case studies that apply vendor-supplied frequency-domain impedance models of two OWPPs and an HVDC link at the point of connection.

Significance. If the central claims hold, the work supplies a practical, frequency-domain tool for planning offshore grid expansions while explicitly enforcing operator-specified stability margins. The use of black-box vendor models is a strength for industrial relevance. The new Nyquist regions, if rigorously justified, could reduce reliance on exhaustive time-domain searches. However, the significance is limited by the purely frequency-domain validation; without cross-checks against EMT simulations, the quantitative margin predictions remain unconfirmed for the claimed operating conditions.

major comments (2)
  1. [Case studies] Case studies section: Validation is performed exclusively with frequency-domain Nyquist plots derived from vendor impedance models. No EMT or time-domain simulations are reported to confirm that the derived maximum allowable impedances actually produce the claimed stability margins or prevent instability under the generalized Nyquist criterion. This directly affects the central claim that the methodology guarantees operator-specified margins and stable operation.
  2. [Methodology for stability regions] Nyquist-based stability regions (introduced to complement the generalized Nyquist criterion): The geometric definitions of the proposed regions must be accompanied by explicit statements of any assumptions on minimum-phase properties, encirclement topology, or right-half-plane pole counts; without these, the analytical margin headroom calculations risk being non-conservative or non-general.
minor comments (2)
  1. [Abstract] Clarify in the abstract and introduction whether the derived impedance limits are intended as hard bounds or as indicative values that still require final EMT verification.
  2. Ensure all impedance magnitude/phase plots include consistent frequency ranges and clearly labeled stability boundaries corresponding to the new regions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment below, indicating where revisions will be made to the manuscript.

read point-by-point responses

  1. Referee: Case studies section: Validation is performed exclusively with frequency-domain Nyquist plots derived from vendor impedance models. No EMT or time-domain simulations are reported to confirm that the derived maximum allowable impedances actually produce the claimed stability margins or prevent instability under the generalized Nyquist criterion. This directly affects the central claim that the methodology guarantees operator-specified margins and stable operation.

    Authors: We acknowledge that the validation relies exclusively on frequency-domain Nyquist analysis using vendor-supplied impedance models. The methodology is specifically developed for black-box frequency-domain data, which is the practical information available from vendors. We agree that the absence of EMT cross-validation means the quantitative margin predictions are not independently confirmed in the time domain. In the revised manuscript, we will add an explicit discussion of this limitation, clarifying the scope of the claims to the frequency-domain framework and noting that additional time-domain verification would require detailed converter models not provided by vendors. revision: partial

  2. Referee: Nyquist-based stability regions (introduced to complement the generalized Nyquist criterion): The geometric definitions of the proposed regions must be accompanied by explicit statements of any assumptions on minimum-phase properties, encirclement topology, or right-half-plane pole counts; without these, the analytical margin headroom calculations risk being non-conservative or non-general.

    Authors: We agree that the assumptions underlying the proposed Nyquist-based stability regions must be stated explicitly. The revised manuscript will include additional text in the methodology section specifying the relevant assumptions, such as the number of right-half-plane poles in the open-loop impedance ratio and any minimum-phase requirements for the geometric margin interpretations to hold. revision: yes

Circularity Check

0 steps flagged

No circularity: methodology built on standard impedance/Nyquist tools without self-referential reduction

full rationale

The abstract and described claims rely on established impedance-based small-signal analysis and the generalized Nyquist criterion, plus newly introduced stability regions. No load-bearing step reduces a prediction or margin result to a fitted parameter defined by the output itself, nor to a self-citation chain. The derivation chain remains independent of the target stability margins; case studies apply vendor models without the paper redefining its inputs via its own results. This is the normal non-circular outcome for papers extending standard frequency-domain methods.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Ledger populated from abstract only; no free parameters, invented entities, or explicit axioms are stated beyond standard domain assumptions in power system stability.

axioms (1)
  • domain assumption Small-signal stability of interconnected converter systems can be assessed via impedance models and the generalized Nyquist criterion.
    Invoked implicitly as the foundation for the proposed margin analysis method.

pith-pipeline@v0.9.0 · 5739 in / 1204 out tokens · 20036 ms · 2026-05-25T05:29:42.617598+00:00 · methodology

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