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REVIEW 3 major objections 5 minor 18 references

Admittance Identification of Grid-Forming Inverters Using Time and Frequency-Domain Techniques

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Three identification methods agree on grid-forming inverter admittance from 1 to 100 Hz.

desk verdict A useful comparative benchmark of dq admittance identification methods whose central consistency claim is partly enforced by construction; deserves a revised round, not a desk reject. read the letter →

arxiv 2504.17512 v1 pith:IWMX4QKX submitted 2025-04-24 eess.SY cs.SY

Andres Intriago , Alexandros Paspatis , Francesco Liberati , Charalambos Konstantinou This is my paper · ORCID
classification eess.SYcs.SY
keywords admittanceidentificationdq-framegrid-forminginvertersweepfrequencyresponseanalysisstepexcitationmethodeigensystemrealizationalgorithmimpedance-basedstabilitysmall-signal
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to show that three black-box identification techniques -- sweep frequency response analysis, step excitation, and eigensystem realization -- yield consistent estimates of the dq admittance of a grid-forming inverter over 1 Hz to 100 Hz. The stakes are practical: inverter firmware is proprietary, so stability studies often have to build admittance models from external measurements, and a frequency sweep demands many sinusoidal injections, while the two step-based methods need only two perturbations. The paper demonstrates the consistency on a simulated grid-forming inverter by comparing the Bode plots of the four admittance entries, finding that ERA and SEM overlap closely with each other and with SFRA in the low-frequency band. Above 100 Hz the curves diverge, which the paper attributes to the higher signal-to-noise ratio of frequency scanning at high frequencies.

What carries the argument

The operational core is the dq-frame admittance matrix $Y(s)$, defined with a negative sign so that positive current flows from the inverter to the grid, and its entries are extracted from the transfer functions between dq voltage perturbations and dq current responses. For ERA, the key identity is that feeding a step response to the algorithm is equivalent to identifying a discrete-time extended system $W_{ERA}(z)=W_{int}(z)W_{DD}(z)$, where $W_{int}=z/(z-1)$ is a discrete integrator; the continuous plant is then recovered through $P(s)=d2c(W_{ERA}(z))s/g$. This step-to-impulse equivalence lets ERA work with a simple voltage step, from which it builds a Hankel matrix, applies singular-value decomposition, and truncates at a chosen system order (six in this study). SEM fits continuous-time transfer functions directly from the same step-response data with a low-order model (four poles), and SFRA fits a transfer function to the measured frequency-response points; all three feed their estimates into the same $2\times2$ admittance matrix structure.

What would settle it

Run the three identification methods on a different grid-forming inverter (or a hardware testbed with known admittance), choosing ERA's order from a pre-specified criterion such as the drop-off of Hankel singular values rather than by matching SEM/SFRA; if ERA's Bode curves then depart from SFRA inside 1-100 Hz, the paper's consistency claim fails. A simpler check is to compare step-derived transfer functions against a dense sine sweep in a case where the true admittance is known from the controller parameters.

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Extended reading notes

Core claim

The central claim is that the dq admittance matrix of a grid-forming inverter can be identified equivalently in the time domain and the frequency domain, with agreement across methods from 1 Hz to 100 Hz. For each element of the admittance matrix, the inverter is perturbed separately on the d-axis and q-axis voltages: ERA and SEM apply a 1% step change to $v_{gd}$ and then to $v_{gq}$, record the resulting dq currents, and convert those time traces into transfer functions; SFRA instead injects 0.1 V peak-to-peak sinusoids at 100 discrete frequencies, computes phasors with a Fourier transform, and fits a transfer function through the points. The four fitted entries -- $Y_{dd}$, $Y_{dq}$, $Y_{qd}$, and $Y_{qq}$ -- overlap in Bode magnitude and phase within the 1-100 Hz band. The paper treats the divergence above 100 Hz as a regime difference: time-domain step methods lose signal-to-noise ratio at high frequencies, while SFRA's discrete-point excitation maintains accuracy there.

Load-bearing premise

The agreement between ERA and the other two methods rests on the selected system order (six), which the paper chooses iteratively until the Bode plots match, so the consistency is partly built into the comparison rather than independently discovered.

Editorial extensions

If this is right

  • A grid-forming inverter's dq admittance in the 1-100 Hz band can be obtained from two step perturbations instead of a 100-point frequency sweep.
  • Time-domain identification is therefore a faster route to admittance models for low-frequency stability studies, with lower computational demand than frequency scanning.
  • Above 100 Hz, frequency scanning remains the more trustworthy of the three approaches, because it excites each discrete frequency with a strong, narrow-band signal.
  • ERA and SEM produce overlapping results from the same step data, so the choice between them can rest on convenience and noise handling rather than on the physics captured.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An extension the paper does not make: if the 1-100 Hz agreement survives on other inverter topologies and on hardware-in-the-loop testbeds, step-based identification could become the default screening tool for EMT studies, with frequency sweeps reserved for verifying the high-frequency tail.
  • The ERA order (six) is selected iteratively until its Bode plot matches the other two methods; a stronger test of the paper's consistency claim would fix the order in advance by an independent rule, such as the decay of Hankel singular values, and then compare the resulting curves.
  • The discrete-to-continuous conversion used for ERA is itself a candidate source of the high-frequency mismatch; sampling faster or using a different conversion could reveal whether the divergence above 100 Hz is a physical property of step excitation or an artifact of the conversion.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper compares three black-box identification approaches for extracting the dq admittance of a grid-forming inverter in a simulated EMT testbed: SFRA (frequency-domain sinusoidal injection with tfest fitting), SEM (step excitation with tfest fitting), and ERA (step-response Hankel/SVD realization). The authors derive a discrete-to-continuous conversion for ERA, collect step responses from 1% voltage perturbations, fit transfer functions, and report Bode plots of the four admittance elements. The central claim is that all three frameworks give consistent admittance estimates in the 1-100 Hz range, with ERA and SEM providing faster identification than SFRA for low-frequency EMT stability studies.

Significance. If the consistency claim holds, the practical payoff is substantial: two step perturbations could replace dozens of frequency scans for low-frequency admittance characterization, which is valuable when inverter firmware is inaccessible. The paper is clearly organized and provides a useful side-by-side comparison of the three techniques on a realistic GFM testbed, with transparent fit metrics (NRMSE) for SEM and SFRA. However, the evidence for consistency is weakened by the ERA system order being selected so that its Bode plot matches the other frameworks, and by a dimensional inconsistency in Eq. (6). These issues are fixable within the manuscript's scope, so the result is not fatally compromised but the central claim needs stronger support.

major comments (3)
  1. [Section IV, ERA truncation] The ERA model order is selected iteratively 'starting from the lowest order and increasing until the Bode plot of the admittance matrix approximates the results from the other two frameworks,' and the sixth-order model is chosen because it 'best matches the other frameworks.' This makes the ERA-SEM/SFRA agreement in Fig. 7 partly enforced by construction rather than independently discovered. Furthermore, ERA and SEM use the same step-response data, so their mutual overlap in Fig. 7 is expected and provides no additional evidence of consistency. Please choose the ERA order using an independent criterion, such as the singular-value decay of the Hankel matrix or validation on a held-out portion of the step response, and then re-evaluate the comparison.
  2. [Equation (6)] Equation (6) contains a dimensional inconsistency. If the entries i(1)od(s), i(1)oq(s), i(2)od(s), i(2)oq(s) are the identified transfer functions P(s) from Eq. (5), they already have units of admittance, so the extra factor s/g makes the right-hand side dimensionally incorrect. If these entries instead denote Laplace transforms of step responses, then the notation conflicts with Eqs. (7)-(9), where i(s) are transfer functions. Please clarify the meaning of i(s) and correct Eq. (6) accordingly.
  3. [Equations (4)-(5)] The discrete-to-continuous conversion d2c(WERA(z)) = gP(s)/s is exact only under specific sampling and hold assumptions, but the paper does not state which d2c method is used or validate its accuracy over 1-100 Hz. Because the ERA admittance estimate depends directly on this conversion, please report the d2c method and validate it, for example by comparing the identified continuous-time model against an independent SFRA scan or by checking its prediction on a separate time-domain experiment.
minor comments (5)
  1. [Section III.A] The phrase 'Laplace transform as shown in (6)' should refer to Eq. (5), where P(s) is recovered from WERA(z); Eq. (6) is the admittance matrix construction, not a Laplace transform definition.
  2. [Equations (1)-(3)] The notation Z^{-1}[.] applied to a continuous-time function is ambiguous; please define the sampling period and state explicitly that the equality holds at sampling instants under an assumed zero-order hold.
  3. [Figure 7] Please add a shaded vertical band or markers indicating the 1-100 Hz range to which the abstract's consistency claim refers, so that readers can verify the claim directly from the figure.
  4. [Figures 5 and 6] The NRMSE fit percentages are reported without defining the normalization; please state the formula or cite the MATLAB documentation for tfest's fit metric.
  5. [Section IV, SFRA discussion] The text notes that SFRA 'shows a different response' above 100 Hz; please explicitly reconcile this observation with the abstract's 1-100 Hz consistency claim in the conclusions.

Circularity Check

1 steps flagged · score 6.0 of 10

The ERA model order is chosen until its Bode plot matches SEM/SFRA, so the claimed cross-method consistency is partly enforced by construction.

  1. fitted input called prediction [Section IV ('Comparative Analysis'), ERA truncation paragraph, discussion of system order selection]
    "In this paper, we assume a black-box modeling approach in which truncation is performed iteratively, starting from the lowest order and increasing until the Bode plot of the admittance matrix approximates the results from the other two frameworks. In our case, the estimated system order is determined to be sixth order, as it best matches the other frameworks."

    The ERA system order is the key free parameter that determines the ERA transfer functions. The paper sets this parameter by requiring the ERA Bode plot to 'approximate the results from the other two frameworks,' so the ERA curves in Fig. 7 are optimized to agree with SEM and SFRA. The agreement between ERA and the other two methods is therefore an input to the model-selection procedure, not an independent prediction. This makes the abstract's claim that all three approaches are 'consistent' partly circular for the ERA leg of the comparison.

full rationale

The central consistency claim has one legitimately independent leg: SEM and SFRA use different excitation signals (step versus sinusoidal) and select their orders by fit to their own measured data through NRMSE thresholds (Figs. 5 and 6), so their mutual agreement is not enforced by construction. However, the ERA leg is not independent: the order is chosen by iterating until ERA's Bode plot approximates SEM/SFRA, so the ERA-versus-others agreement in Fig. 7 is partly a fitted result rather than a discovered one. In addition, ERA and SEM are both driven by the same step-response data (Figs. 3 and 4), and the paper itself attributes their overlap to 'their shared use of step responses'; this makes the ERA-SEM overlap a common-data consequence rather than an independent cross-check. No load-bearing self-citation or imported uniqueness theorem is present; the cited prior work is external and not used to forbid alternatives. The d2c conversion in Eqs. (4)-(5) and the notation of Eq. (6) are potential correctness risks but are not circularity. Overall, because the ERA free parameter is tuned to the other frameworks, the headline consistency is partially circular, but the SEM-SFRA comparison preserves some independent content, so the score is moderate rather than maximal.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The identification claims rest on standard control-theory tools (z-transform, Laplace transform, SVD-based realization) and on domain assumptions: small-signal linearity of the GFM, steady-state at perturbation time, a representative simulated model, and observability/controllability from the PCC. The model orders for ERA, SEM, and SFRA are fitted/hand-chosen and are the main free parameters affecting the results.

free parameters (4)
  • ERA system order = 6
    Selected iteratively until the ERA Bode plot approximates the SEM/SFRA results (Section IV), making the consistency claim dependent on this choice.
  • SEM transfer function order = 4 poles
    Chosen iteratively in MATLAB tfest until the estimated response matches the measured step response (Section IV).
  • SFRA transfer function order = 4 poles
    Chosen iteratively until NRMSE exceeds 90% over the frequency response (Section IV).
  • Perturbation amplitudes = 1% voltage step (ERA/SEM); 0.1 V peak-to-peak sine (SFRA)
    Hand-chosen; different amplitudes across methods could bias the comparison and no sensitivity study is provided.
assumptions (5)
  • standard math Standard z-transform/Laplace transform and realization theory (ERA) are valid for the step-response setup.
    Used in Section II-B to relate the discrete extended system to the continuous plant P(s).
  • domain assumption The GFM behaves as a linear time-invariant small-signal system around the steady-state operating point.
    Necessary for the dq admittance matrix to be well-defined and for transfer function models to be valid; stated as 'the system is in a steady state at the time of the perturbation' (Section IV).
  • domain assumption The simulated GFM model (Table I) is representative of a real grid-forming inverter with inaccessible firmware.
    The paper motivates black-box identification from manufacturer nondisclosure, but validates only against its own simulation, not against hardware or a vendor model.
  • domain assumption The system is observable and controllable from the point of common coupling.
    Required for the two voltage perturbations to excite all relevant dynamics; the paper states each state is controllable and observable from the measurement point (Section I) but does not verify it for the testbed.
  • domain assumption The discrete-to-continuous conversion (d2c) used in ERA preserves the plant dynamics over the frequency range of interest.
    Eq. (4)-(5) assume d2c(WERA(z)) = gP(s)/s; approximation errors from the conversion are not quantified.

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Cite this review

Pith. "Pith review of Admittance Identification of Grid-Forming Inverters Using Time and Frequency-Domain Techniques." pith.science (2026). https://pith.science/paper/IWMX4QKX

@misc{pith2026250417512,
  author       = {Pith},
  title        = {Pith review of: Admittance Identification of Grid-Forming Inverters Using Time and Frequency-Domain Techniques},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IWMX4QKX}},
  note         = {Machine review of arXiv:2504.17512}
}
read the original abstract

The increasing integration of inverter-based resources (IBRs) into the power grid introduces new challenges, requiring detailed electromagnetic transient (EMT) studies to analyze system interactions. Despite these needs, access to the internal firmware of power electronic devices remains restricted due to stringent nondisclosure agreements enforced by manufacturers. To address this, we explore three system identification techniques: sweep frequency response analysis (SFRA), step excitation method (SEM), and eigensystem realization algorithm (ERA). SFRA employs sinusoidal signals of varying frequencies to measure the system's frequency response, while SEM and ERA utilize step functions to derive time-domain responses and transform them into Laplace-domain transfer functions. All three approaches are shown to provide consistent results in identifying the dq admittance of grid-forming inverters (GFM) over a frequency range of 1 Hz to 100 Hz.

Figures

Figures reproduced from arXiv: 2504.17512 by the authors.

Figure 2
Figure 2. Reference scenario for the ERA experiment. a) Discrete impulse. b) [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Step change of 1% at vgd and resulting effect on iod and ioq. 0.4 0.5 0.6 0.7 0.8 378 380 382 384 Time (sec) Voltage (V) vgd(t) (a) 0.4 0.5 0.6 0.7 0.8 −1 1 3 5 Time (sec) Voltage (V) vgq(t) (b) 0.4 0.5 0.6 0.7 0.8 −8 −4 0 4 Time (sec) Current (A) i (2) od (t) (c) 0.4 0.5 0.6 0.7 0.8 −16 −14 −12 −10 Time (sec) Current (A) i (2) oq (t) (d) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Percentage of accuracy between the measurement time domain data and the estimation employing SEM. )) ) [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figures from the paper (2 more)
Figure 6
Figure 6. Figure 6: Percentage of accuracy between the measurement frequency domain data and the estimation employing SFRA. [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: DQ admittance extraction comparison employing the three frameworks, ERA, SEM, and SFRA. [PITH_FULL_IMAGE:figures/full_fig_p005_7.png]

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