Physics-Informed Neural Network Models for EMT Simulators

Benjamin Vilmann; Ignasi Ventura Nadal; Mohammad Kazem Bakhshizadeh; Nicolae Darii; Petros Aristidou; Rahul Nellikkath; Spyros Chatzivasileiadis

REVIEW 4 major objections 5 minor 30 references

Physics-Informed Neural Network Models for EMT Simulators

T0 review · 4 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read By replacing a wind turbine's phase-locked loop with a trained physics-informed neural network, EMT simulations run about 4–6 times faster with negligible error.

desk verdict First credible EMT-solver integration of a PINN surrogate for a closed-loop control block, with a real 4–6x speed-up on a wind-turbine PLL, but the reuse claim is only as good as the training envelope. read the letter →

arxiv 2511.23046 v3 pith:7TZXO7YE submitted 2025-11-28 eess.SY cs.SY

Ignasi Ventura Nadal , Nicolae Darii , Petros Aristidou , Mohammad Kazem Bakhshizadeh , Rahul Nellikkath , Benjamin Vilmann , Spyros Chatzivasileiadis This is my paper · ORCID

classification eess.SYcs.SY

keywords physics-informedneuralnetworkselectromagnetictransientsimulationphase-lockedlooptype-4windturbinesurrogatemodelspowersystemcontrolaccelerationdifferential-algebraicequations

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

This paper claims that the slowest part of an electromagnetic transient (EMT) simulation—the nonlinear closed-loop control blocks that require iterative solvers—can be replaced by a trained physics-informed neural network (PINN) acting as an explicit solver. Using a standardized type-4 wind turbine model, the authors replace the phase-locked loop (PLL) with a PINN and report a 4–6x simulation speedup while keeping current and voltage errors in the 1e-5 to 1e-4 per-unit range and PLL angle errors below 1e-3 radians. The formulation is modular: the PINN has the same inputs and outputs as the control block it replaces, so it plugs into existing EMT solvers without changing their interface. If correct, this offers a practical path to faster transient stability studies for grids with high shares of inverter-based resources, with the added benefit of hiding proprietary control details. The main caveat, acknowledged in the paper, is that accuracy holds only within the PINN's training domain.

What carries the argument

The central object is the explicit PINN update formula: y_t = y_{t-Δt} + Δt * PINN(Δt, x_t, y_{t-Δt}), where Δt is the simulation time step, x_t is the electric-system solution at the current step, and y_{t-Δt} is the control-system solution at the previous step. This treats the PINN as a direct replacement for a nonlinear closed-loop control block, avoiding both the iterative solvers and the artificial time delays used to break algebraic loops. The PINN is trained with a combined loss of data-error and physics-residual terms, and its input domain is deliberately bounded (time step up to a maximum, voltages within ±1.1 per unit of nominal, PLL angle over a full cycle) so that a single traine

What would settle it

Run a scenario with a voltage dip deeper than 20% (outside the ±1.1 per-unit training band) in the hybrid EMT solver and compare the current and voltage trajectories with the conventional solver; if mean current error grows beyond roughly 1e-4 per unit or the PLL angle error exceeds about 1e-2 rad, the case-independent reuse claim fails. A second test is to change the PLL controller gains after training and observe whether accuracy degrades.

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Extended reading notes

Core claim

The central claim is that a PINN can replace a nonlinear closed-loop controller inside an EMT simulation and act as an explicit, non-iterative solver for that control block. The proposed update rule computes the control output at the current time step as the previous value plus the time step times a neural network evaluated on the current electric-system solution, the time step size, and the previous control output. In a type-4 wind turbine EMT model at a 100 microsecond time step, replacing only the PLL with a PINN yields a 4.24x speedup on a single scenario and a 4.87x average speedup over 20 random events, with mean current error of 8.9e-6 per unit, mean voltage error of 4.9e-4 per unit,

Load-bearing premise

The load-bearing assumption is that a PINN trained on a bounded input domain remains accurate for every operating point inside that domain; the paper itself states that outside the trained range its outputs quickly become inaccurate.

Editorial extensions

If this is right

Replacing a single computationally expensive closed-loop control block (e.g., a PLL) with a trained PINN can reduce EMT simulation runtime by roughly 4–6x while maintaining similar accuracy.
The same trained PINN can be reused across different scenarios and systems provided all inputs remain within the training domain, making it case-independent for practical purposes.
The explicit PINN formulation removes the need for iterative solvers and artificial time delays in control loops, which the paper reports as more numerically robust than the delay-based approach.
The modular integration means users can decide before running a simulation whether to deploy PINN acceleration, and the approach is extensible from EMT to RMS simulations and to other device types.
Even when the speed advantage diminishes in large-scale systems where only a few components are replaced, the PINN models still provide numerical stability and protection of proprietary control designs.

Reading between the lines

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

The same explicit formulation could be applied to other nonlinear closed-loop controllers (e.g., current controllers with saturation or anti-windup) if their inputs and outputs are similarly bounded, potentially extending the speedup beyond PLL replacement.
If the PINN's training domain included parameters such as controller gains as additional inputs, the surrogate could be made robust to parameter changes, removing one of the paper's stated limitations without changing the method.
The accuracy degradation outside the training domain suggests a practical safeguard: an online domain checker that falls back to the conventional solver when inputs leave the envelope, which would make the hybrid approach safe for real-world deployment.
The reported speedup, measured on a single component in an aggregated wind-turbine model, may compound when several control loops in a multi-device system are replaced, but the paper's own large-scale caveat implies the net gain depends on the share of replaced components.

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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

Worth a look if you care about accelerating EMT simulations or about the gap between surrogate-model promise and practice. The paper does something genuinely new: it replaces a closed-loop PLL inside an EMT solver with a trained PINN, using an explicit Δt-residual formulation that slips into the existing solver interface. The measured 4.24–4.87x speed-up on a type-4 wind turbine model is concrete, the errors are small in the tested cases, and the source code and in-house solver are public. That is a solid, reproducible contribution, and the PSCAD overlap in the Appendix at least validates the base solver, which is the right frame of reference.

The soft spots are real but not fatal. First, the abstract claims a 40% speed-up over iterative numerical solvers, but the body never shows that comparison — the traditional baseline appears to be the time-delay approach, not an iterative one. That needs fixing. Second, the accuracy benchmark is the same solver that generated the training data, so the error numbers largely measure in-distribution fit. The PSCAD check does not directly validate the hybrid/PINN configuration. Third, there are no error bars or seed variation; the speed-up and errors come from a single training run. Fourth, and most important, the case-independence claim in Section IV-C is overstated. The paper itself concedes in Section IV-F that out-of-range inputs give inaccurate outputs and that verification is essential, but no such verification or fallback is implemented. The 20 random events all stay inside the training envelope, so faults or parameter changes that push voltages above 1.1 Vnom are simply unvalidated. This does not kill the measured speed-up on the tested cases, but it makes the plug-and-play reuse claim conditional on a guarantee the paper does not provide.

For a PSCC submission this is a reasonable conditional accept. The core idea is sound, the demonstration is honest, and the limitations are stated even if the framing oversells reuse. I would send it to peer review and ask for: reconciliation of abstract and body on the iterative-solver comparison, error bars or multiple seeds, and an explicit discussion — or better, a runtime input-domain monitor — for the reuse claim.

Reading group: maybe. It is a good springboard for discussing surrogate validation standards. I would cite it if I were writing on EMT acceleration or PINN-based component modeling.

Referee Report

4 major / 5 minor

Summary. The paper proposes a modular integration of Physics-Informed Neural Networks (PINNs) into Electromagnetic Transient (EMT) simulations, targeting computationally expensive nonlinear closed-loop control blocks. Using a type-4 wind turbine model, the authors replace the Phase-Locked Loop (PLL) with a trained PINN and report a 4–6x simulation speed-up over a conventional solver, with small errors in currents, voltages, and PLL angle (Tables II–IV). The authors also claim that PINNs are more numerically robust than artificial delay methods and that, compared with iterative numerical solvers, their surrogates increase computation speed by 40% on average. The paper includes validation against the commercial PSCAD tool for the base solver and makes the source code publicly available.

Significance. If the central claims hold, this work is a meaningful step toward accelerating EMT simulations by replacing stiff nonlinear control loops with cheap neural surrogates, while also offering intellectual-property protection for vendor control models. The paper's strengths include a clearly formulated explicit PINN architecture (Eq. (5)–(6)), a modular integration concept that preserves existing solver interfaces, concrete speed-up numbers on a realistic type-4 wind turbine benchmark, and public release of the code and in-house solver. These are positive elements that facilitate reproducibility and follow-up research.

major comments (4)

[§V-C/V-D and Eq. (7)] The accuracy comparison is circular. The training targets in Eq. (7) are generated with the same 'traditional' solver that is later used as the accuracy benchmark for the hybrid/PINN simulation (Tables II–IV). Thus the reported errors measure how well the PINN reproduces the training-data generator, not how accurately the hybrid simulation tracks an independent ground truth. The PSCAD validation in the Appendix compares only the developed solver (presumably the traditional configuration) with PSCAD, not the hybrid/PINN configuration. To support the 'validated with PSCAD' claim, please validate the hybrid trajectory directly against PSCAD (or another high-accuracy reference) on a scenario not used for training, and clarify the data-generation process for D_u.
[Abstract and §V] The abstract claims 'Compared with iterative numerical solvers, we show that NN surrogates replacing components with algebraic loops increase computation speed by 40% on average,' but no iterative solver is used anywhere in the experimental section. The only baseline is a 'traditional' PLL solver whose solution method (time-delay or iterative) is never specified. If the traditional baseline already uses the time-delay approach, then the 4–6x speed-up is against the faster of the two conventional methods, making the 40% claim unattributable. Please either add a comparison against an iterative closed-loop solver or remove this claim from the abstract and text.
[§IV-C and §IV-F] The case-independence/reuse claim is not supported. Section IV-C states that a PINN trained on the bounded domain (|v|≤1.1 V_nom, Δt∈[0,Δt_max], θ_PLL∈[0,2π)) becomes 'case-independent and can be repeatedly used,' and Section IV-D extends this to 'any scenario, system, or even software.' However, Section IV-F explicitly concedes that operating points outside the training range lead to quickly inaccurate outputs and that it is 'essential to verify whether the inputs queried fall within the learned range.' No such verification or fallback is implemented, and all 20 random events in Table IV stay within the training envelope. EMT faults routinely produce voltages above 1.1 V_nom (e.g., load rejection, switching overvoltages), so the deployment guarantee is absent. Please implement a runtime input-domain monitor with fallback to the conventional solver, or substantially soften the reuse clai
[Tables II, III, IV] The speed-up numbers, which are central to the paper, are reported as single scalars (4.24x for one event and 4.87x average over 20 events) with no error bars, run-to-run variation, or measurement methodology. Speed-up measurements can be sensitive to hardware, timer granularity, warm-up effects, and whether the same code path is used in both configurations. Please report the number of repeated runs, the confidence interval or min–max range, and the hardware/software measurement setup. Also specify what the 'traditional' baseline does at each time step (time-delay or iterative solve) so the reader can interpret the 4–6x claim.

minor comments (5)

[§V-A and Table I] The simulation time step is given as a set {1–100} μs, but all experiments use Δt=100 μs. If the PINN was trained across the whole range, it would be useful to show results at smaller Δt as well; if not, the table is misleading.
[§IV-E and Eq. (8)] The physics-based loss L_p is introduced but details are missing: how are collocation points (t_j) sampled, what is f(·) for the PLL, and how does α affect training? An ablation of the physics term (data-only vs. physics-informed) would strengthen the 'PINN' claim.
[§V-D and Fig. 7/8] The captions say 'almost 5 times' (Fig. 8) while Table II for the same event reports 4.24x. Please align the reported speed-up values between text, captions, and tables.
[§IV-C and §IV-F] Section IV-F is a sensitivity/robustness analysis but is placed before the numerical results and is not referenced in the experiments. Consider moving it to the discussion or connecting it explicitly to the input-domain verification recommendation.
[Appendix] The PSCAD validation figure (Fig. 9) shows only the traditional solver trajectories. If the hybrid configuration is also intended to be validated, it must be included; otherwise state clearly that PSCAD validates only the developed EMT solver.

Circularity Check

1 steps flagged · score 4.0 of 10

Accuracy claims are partly circular: the PINN is trained on data from the same traditional EMT solver used as its accuracy benchmark; the 4-6x speedup claim is independent.

fitted input called prediction [Sec. IV-E (Eq. 7) vs Sec. V-C/V-D (Tables II-IV)]
"The data-based loss, L u, minimizes the difference between the target values and the PINN predictions using a mean squared error. These targets are provided by a dataset, D u, which contains accurate simulated results for different time step sizes and initial conditions... The traditional solver serves as a benchmark for the hybrid solver, which evaluates the PLL dynamics using a PINN."

The PINN is trained to minimize squared error against the in-house traditional EMT solver's simulated outputs (Eq. 7). The accuracy evaluation in Sec. V-C/D then compares the hybrid/PINN configuration against that exact same solver and reports the resulting errors (Tables II-IV). Thus the small errors primarily demonstrate in-distribution interpolation of the training-target generator, rather than an independent validation of the PINN. The speedup measurement is unaffected because it compares computational cost, not accuracy, so the circularity is partial rather than total.

full rationale

The paper's headline 4-6x speedup is not circular: it compares the hybrid and traditional configurations with identical solver interfaces and the same time step, so the runtime comparison stands independently. The base in-house solver is also externally anchored in the Appendix via a PSCAD comparison, although that comparison validates the traditional solver, not the hybrid/PINN configuration. The circular element is confined to the accuracy claims: Eq. (7) trains the PINN on 'accurate simulated results' from the in-house traditional solver, and Sec. V-C uses that same traditional solver as the benchmark for Tables II-IV. Consequently, the reported current/voltage/PLL errors are largely a measure of how well the PINN reproduces its own training-data generator. Some independent content remains because the 20 random events are not explicitly shown to be training points, and the physics-based loss provides additional constraints; however, Sec. IV-F concedes that out-of-training-range operation degrades quickly, and the tested events stay inside the trained envelope. Self-citations [11,12,14] are contextual and not load-bearing. Overall, the speedup claim is independent and externally meaningful, but the accuracy validation is partially circular, warranting a moderate score of 4.

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

The ledger contains four fitted or hand-chosen numerical ingredients: the trained network itself, the physics/data loss weighting, the training hyperparameters, and the hand-picked input-domain bounds. There are no new physical entities. The most consequential assumption is domain coverage: the reusable-PINN claim depends on the network generalizing inside the training box and never being queried outside it.

free parameters (4)

PINN weights and biases Θ = {W_k, b_k} = not reported (3 hidden layers × 64 neurons, tanh)
Learned via Eq. (9) against solver-generated targets; all accuracy claims in Section V depend on this fitted function.
Loss weighting α in Eq. (9) = not reported
Balances data loss L_u and physics loss L_p; treated as a tunable hyperparameter in training but the value is omitted.
Training hyperparameters (layers, epochs, optimizer, LR schedule) = 3 hidden layers × 64, 1e6 epochs, Adam, decaying LR not specified
Selected empirically in Section V-B; the final trained model is irreproducible without these exact choices.
Input-domain bounds for training = v ∈ [−1.1,1.1] p.u., θ_pll ∈ [0,2π), Δt ∈ [0, Δt_max]
Hand-chosen in Section IV-C to define all possible operating conditions; deployment reliability depends entirely on these bounds.

assumptions (4)

domain assumption The explicit surrogate update y_hat_t = y_{t-Δt} + Δt * PINN(...) (Eq. 6) is an accurate and stable discretization of the PLL dynamics at Δt = 100 µs.
No stability or error analysis is given for the learned map; the method assumes the residual form is a sufficiently accurate explicit integrator over the whole simulation.
domain assumption The traditional solver is the ground truth for PLL dynamics and is used both to generate training targets (Eq. 7) and as the accuracy benchmark (Section V-C).
The Appendix verifies the base solver against PSCAD for one double-setpoint trajectory, but does not directly validate the hybrid/PINN configuration against PSCAD, nor all 20 random events.
domain assumption A neural network trained on bounded input ranges generalizes to all in-range operating points; out-of-range inputs are assumed not to occur.
Section IV-F explicitly warns that out-of-range inputs produce inaccurate outputs; the case-independent and reusable claim in Section IV-C/D relies on this.
standard math The standard partitioned EMT algorithm (Dommel/TACS) separates electrical and control solutions with a one-step interface delay; this framing is accepted as an accurate model of commercial EMT tools.
Section III-C adopts this partition; all comparisons inherit its assumptions, including any numerical delay effects in the baseline.

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Cite this review

Pith. "Pith review of Physics-Informed Neural Network Models for EMT Simulators." pith.science (2026). https://pith.science/paper/7TZXO7YE

@misc{pith2026251123046,
  author       = {Pith},
  title        = {Pith review of: Physics-Informed Neural Network Models for EMT Simulators},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7TZXO7YE}},
  note         = {Machine review of arXiv:2511.23046}
}

read the original abstract

This is the first paper, to the best of our knowledge, to propose a framework that integrates Physics-Informed Neural Network (PINN) models in Electromagnetic Transient (EMT) simulations. Both industry and EMT simulation tools face emerging challenges, as the share of inverter-based resources in power grids rapidly grows. Vendors need to protect the Intellectual Property (IP) of their control design when sharing their component models with customers and system operators. EMT simulation tools need to increase computation speed while maintaining numerical stability. NN surrogates offer numerically stable models with higher degrees of IP protection, as they do not expose the underlying model structure and control parameters. We show that NN surrogates can accurately capture the dynamic behavior of both open-loop and closed-loop controllers, producing identical results in both a validated in-house EMT solver and commercial tools, such as PSCAD. Compared with the artificial delay methods used by commercial solvers, we show that NN surrogates are more numerically robust. Compared with iterative numerical solvers, we show that NN surrogates replacing components with algebraic loops (e.g., closed-loop controllers) increase computation speed by 40\% on average. We demonstrate our methods on PSCAD and the IEEE 39-bus system. Although the speed advantage vanishes when NN surrogates replace only a few components in large scale systems, NN-based models continue to offer enhanced IP protection and numerical stability. Our source code, in-house EMT solver, and the code for seamless integration to PSCAD are made publicly available.

Figures

Figures reproduced from arXiv: 2511.23046 by the authors.

**Figure 2.** Companion circuits of an inductance and a capacitance. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** The two main approaches to solve control systems. [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: Interface overview between the network and control [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

**Figure 6.** Figure 6: Block diagram representation of the wind turbine control systems. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]

**Figure 7.** Figure 7: Traditional vs hybrid algorithms simulation results. Replacing the conventional model of the PLL with a PINN leads to 4.3x speed-up, while maintaining the same accuracy. 0.5 1 1.5 2 2.5 3 3.5 4 0 2 4 6 ·10−2 ˆθpll − θgrid [rad] 0.5 1 1.5 2 2.5 3 3.5 4 0 0.1 0.2 Time t …

**Figure 8.** Figure 8: Simulation results of an active power setpoint change [PITH_FULL_IMAGE:figures/full_fig_p007_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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