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REVIEW 2 major objections 4 minor 14 references

ANN-Based Grid Impedance Estimation for Adaptive Gain Scheduling in VSG Under Dynamic Grid Conditions

T0 review · 2 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that a virtual synchronous generator can keep a fixed 1-second settling time across weak, strong, and stiff grids when a neural network estimates grid impedance online and a Jacobian-based gain-scheduling law retunes the…

desk verdict Useful idea, but the reported gains don't match the derived scheduling law, so the validation is on shaky ground. read the letter →

arxiv 2506.23304 v2 pith:YXTH2MD4 submitted 2025-06-29 eess.SY cs.SY

Quang-Manh Hoang , Van Nam Nguyen , Taehyung Kim , Guilherme Vieira Hollweg , Wencong Su , Van-Hai Bui This is my paper
classification eess.SYcs.SY
keywords virtualsynchronousgeneratorgridimpedanceestimationartificialneuralnetworkgainschedulingweakstabilitysmall-signalanalysisstrengthinvertercontrol
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 tries to establish that the main weakness of virtual synchronous generators, degrading damping as the grid gets stronger, can be removed by retuning the controller gains online using an artificial neural network that estimates grid impedance from one cycle of PCC voltage and current measurements. If true, the same VSG hardware could keep its designed transient response without re-tuning when grid conditions change, because the control parameters would track impedance automatically. The authors support this with a small-signal derivation tying a 1-second settling time and critical damping to the power-flow Jacobian elements, and with a 60-second simulation that steps the grid from weak to strong to stiff while the fixed-gain VSG oscillates and the adaptive VSG does not. The load-bearing premise is that the scheduling formulas can be evaluated online, but the paper does not fully explain how the operating-point voltage and angle are obtained.

What carries the argument

The matching identity that carries the argument is the Jacobian-based gain-scheduling law (10)-(11), derived from the closed-loop transfer functions. The active-power closed loop is a second-order system $G^P_{cl}(s) = K_{ip}A/(s^2 + D_p K_{ip} s + K_{ip} A)$; choosing $\zeta=1$ and $\omega_n=4$ forces $D_p = A/2$ and $K_{ip}=16/A$. The reactive loop is first-order with steady-state error $D_q/(D_q + D)$, giving $D_q=D/100$ and $K_{iq}=4/(D+D_q)$. The ANN supplies the estimated grid resistance and inductance, which enter $A$ and $D$ together with the operating-point quantities $V_{pcc0}$ and $\delta_0$, and the control architecture buffers 200 samples of PCC voltage and current per cycle before feeding the normalized vector to the network.

What would settle it

Run the same 60-second scenario with the gain-scheduling block fed the true grid impedance instead of the ANN estimates; if settling time or overshoot still drifts from the designed 1-second and zero-overshoot targets, the scheduling law itself is the cause. Separately, freeze $V_{pcc0}$ and $\delta_0$ at their initial values while the ANN tracks the actual impedance changes; if the closed-loop response then degrades, the Jacobian's dependence on the operating point is the limiting assumption.

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Extended reading notes

Core claim

The central claim is that online grid-impedance estimates, produced by a feedforward ANN fed with buffered samples of $v_{pcc}$ and $i_{pcc}$, can drive an adaptive gain-scheduling law that keeps the VSG's active- and reactive-power loops at a designated damping ratio and settling time regardless of grid strength. The gains $D_p$, $K_{ip}$, $D_q$, and $K_{iq}$ are recomputed from the Jacobian entries $A=\partial P_{pcc}/\partial\delta$ and $D=\partial Q_{pcc}/\partial V_{pcc}$ evaluated at the current operating point and estimated grid impedance, so that the closed-loop active-power denominator has damping ratio $\zeta=1$ and natural frequency $\omega_n=4$, and the reactive loop has a 1-second settling time with negligible steady-state error. Simulation shows the fixed-gain VSG's phase margin falling from 52.12 degrees to 20.10 degrees as SCR rises from 2 to 20, while the scheduling law holds the response near a 1-second settling time across all three scenarios. The paper also reports that the ANN estimates previously unseen grid strengths with about 0.02 seconds of delay, and notes that a nonzero overshoot remains because active-reactive coupling terms are omitted in the controller design.

Load-bearing premise

The scheduling formulas depend on the steady-state PCC voltage and angle being known and correct at every retune, but the paper never explains how those operating-point values are measured, estimated, or updated online.

Editorial extensions

If this is right

  • A VSG can be tuned once and remain correctly tuned as grid strength changes, because the controller gains follow the estimated impedance.
  • Previously unseen grid strengths can be handled by the estimator with high accuracy and minimal delay, so the training data need not cover every possible operating point.
  • The approach avoids the disturbance and delay of injection-based impedance estimation while still supporting real-time gain scheduling.
  • The active- and reactive-power responses keep the intended 1-second settling time across weak, strong, and stiff grids, whereas fixed-gain operation becomes increasingly oscillatory as SCR increases.

Reading between the lines

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

  • Editorial extension: if $V_{pcc0}$ and $\delta_0$ are tracked online rather than treated as constants, the same scheduling law could also adapt to load changes and operating-point shifts, not just to grid impedance changes.
  • Editorial extension: the transient peak errors the paper reports for previously unseen SCR values could likely be reduced by adding VSG control states or parameters to the ANN input vector, since the paper itself identifies their omission as the cause of those errors.
  • Editorial extension: a hardware-in-the-loop or field test on a scaled inverter would be the natural next verification, because the simulated validation does not exercise measurement noise, converter nonlinearities, or communication delays.
  • Editorial extension: training the ANN over a denser grid-strength range, or augmenting its inputs with physics-derived features, would test whether the claimed generalization to unseen impedance values holds beyond the specific SCR values studied.
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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

2 major / 4 minor

Summary. This paper proposes an adaptive gain-scheduling scheme for a virtual synchronous generator (VSG). A feedforward ANN is trained offline on Simulink-generated data to estimate the fundamental-frequency grid resistance and inductance from one cycle of PCC voltage and current samples. The estimated impedance is then used to recompute the power-flow Jacobian terms A and D, and the VSG power-loop gains are scheduled so that, according to the Appendix, the active loop has a settling time of 1 s with critical damping and the reactive loop uses a first-order time constant of 0.25 s. The scheme is validated in a 60 s Simulink simulation with SCR values of 2, 8, and 20, and is compared with a fixed-gain VSG. The authors report that the adaptive VSG maintains settling time and overshoot across grid conditions while the fixed-gain VSG degrades, and that the ANN estimates previously unseen impedances with small delay.

Significance. If the consistency issues below are resolved, the paper offers a practical engineering contribution: it combines online impedance estimation with analytically derived gain-scheduling rules, and the design targets (Ts=1 s, xi=1) are explicit rather than fitted to the validation outputs. The use of holdout SCR values, the public code link, and the direct comparison against a fixed-gain VSG are strengths. However, the contribution is incremental relative to existing adaptive VSG and ANN impedance-estimation work, the validation is entirely simulation-based, and the current manuscript contains an internal inconsistency between the derived gain law and the tabulated gains that undermines the central claim as written.

major comments (2)
  1. [Section III-B / Table II / Appendix] Equations (10)-(11) and the Appendix are inconsistent with the gains reported in Table II. The Appendix design fixes DpKip=8 and Kiq(D+Dq)=4 regardless of the operating point. With the Table II values Dp=2.087e3 and Kip=0.00767, the active product is 16.0; with Dq=0.687 (so D=68.7), the reactive product Kiq(D+Dq) is 7.98. Section IV-B states that at SCR=2 the adaptive and conventional VSGs use the same four gains, so these are the scheduled gains at the baseline condition. No choice of A or D can reconcile these numbers because the designed products are independent of A and D. Either the implemented scheduler is not the law described by (10)-(11), or the tabulated parameters do not correspond to the simulated system. In both cases the claim that the reported 1 s settling time and critical damping follow from the proposed law is not supported. The authors should correct one side and re-run or re-report the validation.
  2. [Section III-B, Eqs. (4)-(5)] The gain-scheduling law requires online values of the power-flow Jacobian elements A and D, which depend on Vpcc0, delta0, Rg, and Xg. The manuscript states that the Jacobian components are 'first recalculated' after an impedance update, but it never specifies how Vpcc0 and delta0 are obtained or updated during operation. If fixed nominal values are used, the scheduled gains will not realize the intended Ts=1 s and critical damping once the operating point changes; if measured values are used, the measurement and update mechanism should be described. Without this step the scheme cannot be reproduced or assessed under the 'dynamic grid conditions' claimed in the paper.
minor comments (4)
  1. [Section III-B, Eq. (11)] Equation (11) reads 'Dp = D/100', which appears to be a typo for 'Dq = D/100'; as written it reassigns the active droop coefficient instead of the reactive droop coefficient.
  2. [Section IV-B / Fig. 9] SCR=8 is between the trained values 7 and 9.5, so describing it as 'previously unseen' is imprecise; only SCR=20 is an extrapolation outside the training range.
  3. [Section IV-B / Fig. 8] The IAE values in Fig. 8 are not tied to a specific trace; clarify whether they apply to the conventional VSG, the adaptive VSG, or both.
  4. [Section IV-B] The settling-time and overshoot claims are made qualitatively; a table listing settling time and percentage overshoot for each SCR and for both AVSG and CVSG would make the central comparison quantitative and easier to verify.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the adaptive gains are derived analytically from design targets and impedance estimates, and the ANN holdout tests are genuine.

full rationale

The paper's derivation chain is self-contained and does not reduce to its own inputs. The ANN grid-impedance estimator is trained on data at SCR = [2, 4.5, 7, 9.5, 15] and then evaluated at SCR = 8 and 20, which are outside the training set; this is a genuine extrapolation test, not a re-statement of training targets (Sec. III-A and Sec. IV-B). The gain-scheduling law (10)-(11) and the Appendix (13),(16) compute Dp, Kip, Dq, Kiq directly from the estimated Jacobian elements A and D and from explicitly chosen design targets (Ts = 1 s, xi = 1, small steady-state error), rather than fitting the gains to the reported settling times. The subsequent Simulink validation is a full nonlinear simulation that includes the active-reactive coupling terms deliberately omitted in the design phase, so the observed overshoot and settling time are not identical to the design equations by construction. No load-bearing self-citation or imported uniqueness theorem appears: the only self-reference is [1], which supports an LC-filter modeling detail and is not central to the claimed contribution. The internal numerical inconsistency in Table II (Dp*Kip = 16 vs. the design value of 8, and Kiq*(D+Dq) approximately 8 vs. 4) is a correctness/consistency concern rather than a circularity, because it does not make any predicted output equal to its input by definition. Overall, the reported predictions are not forced by the fitted ANN or by the design equations; they are validated against an independent simulation model.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on two pillars: the ANN's ability to estimate grid impedance accurately enough for real-time scheduling, and the small-signal model's fidelity as a basis for gain computation. The ANN introduces a large set of fitted parameters (weights and normalization statistics) that are not disclosed, and its generalization is demonstrated only within the training simulation. The small-signal model relies on a standard linearization and an explicit dismissal of P-Q coupling. No new physical entities are postulated. The gain-scheduling formulas introduce design targets (Ts=1 s, xi=1) that are chosen by hand.

free parameters (3)
  • ANN hidden weights and biases = Not disclosed (approximately 1,626 parameters for a 200-8-2 network)
    The ANN is trained on 5,000 simulation samples to map one cycle of vpcc and ipcc to Rg and Lg. These fitted weights are the core of the impedance estimator and are not disclosed in the paper.
  • ANN input normalization mean and standard deviation (z-score) = From training data (values not reported)
    Input normalization uses the mean and standard deviation from the training phase; these data-derived constants are not given in the paper and are required to reproduce the estimator.
  • Desired settling time Ts and damping ratio xi = Ts = 1 s, xi = 1
    These design targets are chosen by the authors to derive the gain-scheduling formulas in the Appendix. They are not fitted to data but are free design choices that determine the controller behavior.
assumptions (4)
  • domain assumption The small-signal model of the VSG, including the power-flow equations (1)-(2) and the Jacobian linearization (3), is valid for the operating range considered.
    The controller design and the gain-scheduling formulas rely on this model. It is standard in the literature but is an approximation of the nonlinear system.
  • ad hoc to paper Active and reactive power coupling terms B and C can be neglected when designing the controller.
    The paper explicitly ignores these terms in Section II and later acknowledges in Section III-B that this omission causes a mismatch between design and validation. This is an admitted simplification that affects the claimed performance.
  • domain assumption The grid impedance is constant during the one-cycle buffering window used by the ANN.
    The ANN input is one cycle of vpcc and ipcc (20 ms); if the impedance changes within this window, the estimate will be inaccurate. Section III-A states that only steady-state impedance is considered.
  • domain assumption The Levenberg-Marquardt-trained ANN generalizes from training SCR values to unseen values such as 8 and 20.
    The validation of 'previously unseen' grid conditions is the basis for the claim of high accuracy, but generalization is an empirical behavioral property, not a proven guarantee.

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Cite this review

Pith. "Pith review of ANN-Based Grid Impedance Estimation for Adaptive Gain Scheduling in VSG Under Dynamic Grid Conditions." pith.science (2026). https://pith.science/paper/YXTH2MD4

@misc{pith2026250623304,
  author       = {Pith},
  title        = {Pith review of: ANN-Based Grid Impedance Estimation for Adaptive Gain Scheduling in VSG Under Dynamic Grid Conditions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YXTH2MD4}},
  note         = {Machine review of arXiv:2506.23304}
}
read the original abstract

In contrast to grid-following inverters, Virtual Synchronous Generators (VSGs) perform well under weak grid conditions but may become unstable when the grid is strong. Grid strength depends on grid impedance, which unfortunately varies over time. In this paper, we propose a novel adaptive gain-scheduling control scheme for VSGs. First, an Artificial Neural Network (ANN) estimates the fundamental-frequency grid impedance; then these estimates are fed into an adaptive gain-scheduling function to recalculate controller parameters under varying grid conditions. The proposed method is validated in Simulink and compared with a conventional VSG employing fixed controller gains. The results demonstrate that settling times and overshoot percentages remain consistent across different grid conditions. Additionally, previously unseen grid impedance values are estimated with high accuracy and minimal time delay, making the approach well suited for real-time gain-scheduling control.

Figures

Figures reproduced from arXiv: 2506.23304 by the authors.

Figure 1
Figure 1. Configuration of the studied system. There are several VSG topologies in the literature. In this paper, the VSG structure is similar to those proposed in [5], [6] and is shown in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Bode diagram of GP op(s) with fix (upper) and adjustable (lower) parameters. III. PROPOSED ADAPTIVE GAIN-SCHEDULING CONTROL SCHEME FOR VSG [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. , as previous discussed, illustrates the implementation of the proposed method in the Simulink environment. Due to a mismatch between the simulation sampling time (10 µs) and the ANN input sampling rate (200 µs), a rate transition block is used to resolve this issue. Since 200 points per cycle (0.02 s) must be collected before being fed to the ANN model, a buffer block accumulates input data for each estimation, int… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Neural Network Training Error Histogram. [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]
Figure 9
Figure 9. Figure 9: As shown in Fig. 7, the VSG performs well for both [PITH_FULL_IMAGE:figures/full_fig_p005_9.png]
Figure 7
Figure 7. Figure 7: Active power of VSG with and without proposed adaptive control scheme. [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 8
Figure 8. Figure 8: Reactive power of VSG with and without proposed adaptive control scheme. [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 9
Figure 9. Figure 9: ANN-based online grid impedance estimation performance. [PITH_FULL_IMAGE:figures/full_fig_p007_9.png]

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Reference graph

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