Neural Network Predictive Controller for Grid-Connected Virtual Synchronous Generator

Donald C. Wunsch; Mehdi Ferdowsi; Mohammad Saleh Sanjarinia; Pourya Shamsi; Sepehr Saadatmand

REVIEW 4 major objections 5 minor 14 references

Neural Network Predictive Controller for Grid-Connected Virtual Synchronous Generator

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read A neural network predictive controller can regulate active and reactive power from virtual synchronous generators on both inductive and resistive grid lines, adapting to any impedance angle where conventional PI-based VSGs fail.

desk verdict A plausible narrow result on NN predictive control for a VSG voltage loop, wrapped in an overbroad 'any grid impedance angle' claim the evidence does not support. read the letter →

arxiv 1908.05199 v1 pith:MHKSQCTC submitted 2019-08-14 cs.NE cs.SYeess.SY

Sepehr Saadatmand , Mohammad Saleh Sanjarinia , Pourya Shamsi , Mehdi Ferdowsi , Donald C. Wunsch This is my paper · ORCID

classification cs.NEcs.SYeess.SY

keywords virtualsynchronousgeneratorneuralnetworkpredictivecontrollergrid-connectedinverteractivepowerregulationreactiveresistivegridmodelcontrolinertia

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

Inverters that mimic synchronous generators — virtual synchronous generators (VSGs) — normally set their voltage magnitude with a PI voltage-droop controller that assumes the grid line is inductive. This paper proposes replacing that droop block with a neural network predictive controller (NNPC) that learns the plant's input-output behavior offline and, at each control step, chooses the inverter voltage magnitude that minimizes a one-second-horizon cost on active- and reactive-power tracking. In simulations on one inductive line and one resistive line, the NNPC tracks active and reactive power with smaller overshoot and faster settling than the conventional PI-based VSG and a tuned PI-based VSG. The authors conclude that a well-trained network can adapt to any grid impedance angle, so the voltage controller does not need to be redesigned for non-inductive grids.

What carries the argument

The central object is the neural network predictive controller (NNPC), which combines a two-hidden-layer feedforward network with seven nodes per layer and an optimization block that minimizes the predictive cost $J(k)=\sum_{i=1}^{N_H}\|R(k+i)-Y(k+i)\|^2 + \gamma\sum_{i=1}^{N_H}\|\Delta U(k+i-1)\|^2$ over a one-second horizon with one-millisecond steps. The network is trained in batch mode by backpropagation on input-output data collected while the plant runs under the conventional PI-based VSG, then used in place of the state-space model that ordinary model predictive control requires. The optimization block chooses the inverter voltage magnitude from the discrete set $\{-5,-1,-0.2,-0.04,0,0.04,0.2,1,5\}$, while the virtual inertia swing equation still computes the phase angle. The learned network carries the argument because it captures the coupling between voltage magnitude and both active and reactive power that the inductive-line decoupling approximation neglects.

What would settle it

Evaluate the trained NNPC from this paper across a sweep of line impedance angles, keeping the same offline-trained weights, and measure overshoot and settling time for active and reactive power at each angle; if performance degrades sharply or the loop becomes unstable at intermediate or untrained angles, the 'any grid impedance angle' claim fails. A minimal version is to train on an inductive line only, test on a resistive line, and compare against a network retrained with resistive-line data.

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Extended reading notes

Core claim

The paper's central claim is that the poor behavior of conventional VSGs on resistive grids is not a fundamental limit of virtual inertia but an artifact of the PI voltage-droop controller's implicit assumption that active power depends only on phase angle and reactive power only on voltage magnitude. The proposed controller keeps the swing equation for phase angle and replaces the integral reactive-power droop with a neural network predictive controller whose input includes active power, reactive power, both power errors, frequency error, and phase angle, and whose output is the inverter voltage magnitude. The network is trained by backpropagation on 1000 s of data collected while the plant runs under the conventional PI-based VSG, and it serves as the prediction model inside a model predictive controller that searches a nine-level voltage-step set over a one-second horizon. In the reported simulations the NNPC has the smallest overshoot and fastest settling time among PI-VSG, tuned PI-VSG, and NNPC in the resistive case, and less accumulated tracking error in the inductive case. From these results the paper concludes that a well-trained NNPC can adapt to any grid impedance angle, removing the need to redesign the voltage control block for non-inductive grids.

Load-bearing premise

The load-bearing premise is that a network trained offline on data collected while a PI-based VSG operates on a particular grid will keep performing when the grid impedance angle changes to values not represented in the training data; the paper's evaluation covers only one inductive and one resistive line.

Editorial extensions

If this is right

A single NNPC-based VSG voltage controller can operate on both inductive and resistive grid connections, so the voltage droop block no longer has to be redesigned when the line becomes non-inductive.
On resistive grids, the NNPC gives smaller overshoot and faster settling for active and reactive power than both a conventional PI-based VSG and a tuned PI-based VSG.
The virtual inertia swing equation remains unchanged, so the frequency-supporting and inertial behavior of the VSG is preserved while the voltage magnitude is produced by the learned predictive controller.
Because the same trained controller is claimed to work for any grid impedance angle, VSG-style inverters could be deployed on weak or resistive feeders without a separate control design per feeder.
In inductive grids, the NNPC also tracks the references with less accumulated error over the control horizon than the PI-based VSG.

Reading between the lines

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

A natural extension is to train the network on data from several impedance angles and test interpolation across the resistance-to-reactance ratio plane; if the network generalizes, a single NNPC could serve feeders with mixed line types without re-tuning.
The reported simulations do not include time-varying line impedance, so 'adapt to any grid impedance angle' in a deployment sense would require online weight updates or retraining when the grid is reconfigured.
Because the optimization block searches only a small discrete set of voltage steps, the smoothness of the response is bounded by that quantization; a continuous optimizer or finer step set would likely reduce steady-state ripple, though the paper does not test this.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: the paper does one thing passably and then claims much more. The useful piece is a simulation study showing that replacing the PI voltage-droop block in a VSG with an offline-trained neural network predictive controller reduces overshoot and settling time in one inductive-grid and one resistive-grid case. That narrow result is credible. The overreach is the abstract and conclusion statement that a 'well-trained' NNPC 'can adapt to any grid impedance angle.' The network has no impedance-angle input, there is no sweep, and only two line conditions are tested. The stress-test note is right: the 'any' quantifier is not established even in principle.

What is new: the specific combination—NNPC in the voltage-magnitude loop of a VSG, evaluated against PI and tuned-PI baselines on a resistive line—does not appear in the cited prior work, as far as the text shows. The authors explain the classical VSG limitation on non-inductive lines clearly, and they are honest that the conventional controller struggles there. The simulation plots are consistent with that narrative.

Where it is soft, in rough order: - The central generalization claim. The network is trained offline from data collected while the plant runs under the PI-based VSG; the model input is current outputs plus the control input (voltage magnitude), with no line-impedance feature. Two test cases cannot support 'any grid impedance angle.' Restricting the claim to 'the tested inductive and resistive cases' would align it with the evidence. - Reproducibility. No code, model weights, or data. No quantitative performance tables, error bars, repeated trials, or sensitivity analysis. The paper reports only plots. - Training details are incomplete. The 'random changes' during 1000 s of data collection are not specified; the reader cannot tell whether the training set covers the resistive operating region, where the PI controller is least informative. - Minor: figure numbering is duplicated (two Figure 7s), acronyms slip ('NNMP'/'NNPD'), and the candidate voltage set has only nine values. That last point is a limited but acceptable brute-force optimization for a 1 ms step.

On balance, the narrow claim holds up and the broad claim does not. I would not cite the 'any impedance angle' statement, but I might cite the specific application if I worked on VSG control and could verify the simulation myself. This is an honest, modest piece of engineering simulation. It deserves a serious referee because the idea is real and the fix is clear: restrict the claim, add an impedance-angle sweep, share artifacts, and give quantitative results. As-is, I would not accept it, but I would engage.

Referee Report

4 major / 5 minor

Summary. The paper proposes replacing the voltage-magnitude loop of a virtual synchronous generator (VSG) with a neural network predictive controller (NNPC). Section II derives the VSG swing equation and power-flow equations and argues that conventional PI-based VSGs are inadequate for non-inductive grids because active and reactive power are coupled. Section III describes an offline-trained two-hidden-layer neural network that predicts the next-step output vector (active power, reactive power, errors, frequency, phase angle) from the current output vector and the inverter voltage magnitude, and an optimizer that evaluates a quadratic tracking cost over a finite set of voltage increments. Section IV reports simulations on one inductive and one resistive line, comparing the NNPC with a conventional PI-VSG and a tuned PI-VSG. The abstract and conclusion claim that a well-trained NNPC can adapt to any grid impedance angle.

Significance. If the central claim were fully supported, the result would be practically relevant: it would allow VSG-based inverters to operate in low-voltage resistive grids without redesigning the voltage droop law, and it would offer a data-driven alternative to model-based predictive control under line-impedance uncertainty. The paper's strengths are a clear formulation of the non-inductive-grid limitation and a plausible NNPC architecture with a finite-horizon cost. However, the manuscript provides no quantitative performance tables, no repeated trials, no training or validation error analysis, and no code or data; the evidence is a small set of simulation curves. The skeptic's concern is valid: the paper is best read as a proof-of-concept study, and the evidence currently supports only a narrow claim about the two tested line conditions, not the universal 'any grid impedance angle' claim in the abstract.

major comments (4)

[Abstract; Section IV] The central claim that a well-trained NNPC 'can adapt to any grid impedance angle' is not supported by the experimental design. The network input vector is stated to be the current output vector and the control vector (Section III.B, Figure 5), and the control input is only the inverter voltage magnitude; line impedance or impedance angle is not an input. Training data are collected over 1000 s while the plant operates under the conventional PI-based VSG (Section IV), but the line impedance used during data collection is not specified. Evaluation is limited to one inductive line (Section IV.A) and one resistive line (Section IV.B), with no sweep over impedance angle or R/X ratio. The universal quantifier in the abstract and conclusion is therefore an overstatement; a more defensible claim would be limited to the tested inductive and resistive cases, or supported by a systematic sweep and an impedance-aware training or input design.
[Section IV; Figures 7 and 8] The performance comparison is entirely qualitative. The text states that the NNPC has smaller overshoot and faster settling time than the PI-VSG and tuned PI-VSG, but no numerical values, error metrics, confidence intervals, or repeated trials are reported. Given that the power references are changed randomly during training and evaluation (Section IV), the plotted responses could be a single favorable realization. Numerical tables of overshoot, settling time, and tracking error for all three controllers, ideally over several runs, are needed to substantiate the comparative claim. The tuned-PI and conventional-PI gains used in the comparison are also not listed, so the simulation is not reproducible.
[Section II.B; Section III.B] The controller is described in Section II.B as 'an adaptive dynamic controller capable of adjusting its parameters,' but the NNPC described in Section III.B is trained offline in batch mode and no online weight-adaptation mechanism is presented. This is not merely a wording issue: the 'adaptation to any grid impedance angle' claim requires either online adaptation to a changed line impedance or training and testing across the full intended impedance range. Neither is demonstrated. Additionally, no training or validation error of the neural network model is reported, so it is unclear how well the learned model represents the plant at the test conditions, especially in the resistive case where the PI-based training-data-generating controller is said to perform poorly.
[Section III.B; Section IV] The optimization procedure is underspecified. The paper states that the prediction horizon is one second with a one-millisecond time step (i.e., 1000 samples) and that voltage changes are chosen from the finite set I_Nset = {-5, -1, -0.2, -0.04, 0, 0.04, 0.2, 1, 5}, but it does not explain how the optimizer handles the future control moves over the horizon when evaluating J(k) for each candidate. Exhaustive enumeration over 9^1000 sequences is clearly not intended, yet no alternative search strategy (e.g., a one-step greedy rule, a reduced candidate horizon, or a numerical optimizer with the set as a discretization) is described. The control weight factor gamma is set to zero in Table I, and the effect of this choice is not discussed. Without this detail, the reported results cannot be reproduced, and the term 'optimal control' is stronger than what is demonstrated.

minor comments (5)

[Throughout] The paper contains inconsistent acronyms for the proposed controller (NNPC, NNMP, NNPD) and several typographical errors ('neural ne twork', 'predicative', 'discontinuous domain' instead of 'discrete domain'); these should be corrected.
[Section IV; Figure captions] Figure numbering is duplicated for Figure 7: the block diagram is labeled Figure 7 and the inductive-grid performance plots are also labeled Figure 7. Please renumber the figures and update the in-text references accordingly.
[Section II.A, Eq. (2)] The frequency notation is inconsistent: the text defines w_i = theta-dot and later uses omega_i; please use a single symbol for angular velocity throughout.
[Table I] Table I lists filter and line inductances and resistances but does not give the resulting line impedance angles for the inductive and resistive cases; adding R/X ratios and impedance angles would make the experimental conditions easier to interpret.
[Section II.B, Eqs. (3)-(6)] The factor of 1/2 in the power-flow equations suggests that peak values are used, but this is not stated explicitly. Clarify the RMS-versus-peak convention so that equations (3)-(6) can be checked.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the neural network is trained as a plant model, not fitted to the claimed performance, and no self-citation chain or equation-level reduction is present.

full rationale

The derivation chain is self-contained. The neural network model is trained on input/output data collected while the plant operates under the conventional PI-based VSG (Section III.B), and the trained model is then used as the predictor inside the model-predictive optimization block (Section III, Fig. 6). This is a system-identification step, not a circular fit: the network is not trained to match the reported overshoot, settling time, or comparison outcomes, and the Section IV results are obtained from closed-loop simulation rather than read back from a fitted parameter. No equation in the paper makes the claimed improvement equal to a training target, and there is no load-bearing self-citation, no imported uniqueness theorem, and no ansatz smuggled in via citation. The abstract's broad statement that the controller 'can adapt to any grid impedance angle' is not established by the two test cases and the network's lack of an impedance input, but that is a generalization and correctness concern, not a circularity. Under the hard rule that circularity must be exhibited by quoting a specific reduction, no such reduction exists here.

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

The paper introduces no new physical entities. Its central claim depends on trained neural-network weights, hand-chosen hyperparameters, and the modeling assumptions listed above, none of which are independently validated outside the simulation.

free parameters (5)

Neural network weights = Not reported
Trained by backpropagation on 1000 seconds of simulation data collected under the PI-based VSG controller; final weights are not provided, so the learned model cannot be reproduced.
Tuned PI controller gains = Not reported
Section IV.B compares against a 'tuned PI' controller, but the tuning gains are not listed, making the baseline comparison hard to verify.
Candidate voltage step set I_Nset = {-5, -1, -0.2, -0.04, 0, 0.04, 0.2, 1, 5}
The optimizer chooses voltage magnitude changes only from this hand-chosen discrete set; the optimality of the result is relative to this finite action space.
Control weight factor gamma = 0
The cost function in Section III.A includes a weight on control effort, and Table I sets it to zero, so the controller does not penalize voltage changes. This is a design choice, not a fitted value.
NN architecture and prediction horizon = 2 hidden layers, 7 nodes per layer; 1 s horizon, 1 ms step
These hyperparameters are chosen by hand without sensitivity analysis, and the reported performance may depend on them.

assumptions (5)

domain assumption The averaged circuit model with equivalent impedance Z_eq = jX_eq + R_eq represents the grid-connected inverter.
Invoked in Section II.B and Figure 3; the power flow equations and all simulation conclusions rest on this averaged model rather than a detailed switched model.
domain assumption The synchronous generator swing equation (1)-(2) governs the virtual inertia dynamics.
Used in Section II.A to compute the inverter phase angle from power balance, a standard but nontrivial VSG modeling assumption.
standard math Small-angle approximations sin(delta) approximately delta and cos(delta) approximately 1 are valid.
Used in Section II.B to derive the inductive-grid decoupling of active and reactive power; it may fail for large phase steps.
ad hoc to paper Training data collected from the PI-based VSG is representative of plant behavior for all tested and claimed impedance angles.
Section III.B states data is collected while the plant operates under the conventional PI controller; generalization to untested impedance angles is assumed without evidence.
ad hoc to paper The finite discrete action set for voltage magnitude is rich enough to contain the optimal control.
Section IV defines I_Nset with nine values; the claimed performance is optimal only within this set, not over the continuous voltage range.

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Cite this review

Pith. "Pith review of Neural Network Predictive Controller for Grid-Connected Virtual Synchronous Generator." pith.science (2026). https://pith.science/paper/MHKSQCTC

@misc{pith2026190805199,
  author       = {Pith},
  title        = {Pith review of: Neural Network Predictive Controller for Grid-Connected Virtual Synchronous Generator},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MHKSQCTC}},
  note         = {Machine review of arXiv:1908.05199}
}

read the original abstract

In this paper, a neural network predictive controller is proposed to regulate the active and the reactive power delivered to the grid generated by a three-phase virtual inertia-based inverter. The concept of the conventional virtual synchronous generator (VSG) is discussed, and it is shown that when the inverter is connected to non-inductive grids, the conventional PI-based VSGs are unable to perform acceptable tracking. The concept of the neural network predictive controller is also discussed to replace the traditional VSGs. This replacement enables inverters to perform in both inductive and non-inductive grids. The simulation results confirm that a well-trained neural network predictive controller illustrates can adapt to any grid impedance angle, compared to the traditional PI-based virtual inertia controllers.

Discussion (0). Continue with ORCID to comment.

Reference graph

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Enabling Extreme Fast Charging with Energy Storage

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