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arxiv: 2607.00116 · v1 · pith:2OA6H6YB · submitted 2026-06-30 · eess.SY · cs.SY

A Shallow Recurrent Decoder for Dynamic State Estimation with a Limited Number of PMUs in Power Systems

Andrea Pomarico , Alberto Berizzi , J. Nathan Kutz This is my paper

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classification eess.SY cs.SY
keywords dynamic state estimationPMU measurementsshallow recurrent decoderpower systemssparse measurementsIEEE 39-bus systemnonlinear conditions
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The pith

The SHRED decoder reconstructs the full state of a power system from sparse PMU measurements without relying on an accurate physical model.

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

The paper introduces SHRED, a shallow recurrent decoder for dynamic state estimation in power systems. It aims to reconstruct the full system state from only a small number of phasor measurement units, bypassing the need for an accurate physical model that Kalman filter methods require. The approach is tested on the IEEE 39-bus system during short-circuit events and shows better accuracy than a standard shallow decoder when measurements are sparse. It also proves largely unaffected by where the PMUs are placed and handles measurement noise well.

Core claim

The SHRED architecture reconstructs the complete dynamic state of a power system from sparse PMU measurements. Unlike model-based methods, it does not require an accurate physical model and maintains performance under strongly nonlinear conditions such as short-circuit disturbances on the IEEE 39-bus system. It consistently outperforms a state-of-the-art shallow decoder benchmark in sparse-measurement scenarios and remains insensitive to PMU placement while showing robustness to measurement noise.

What carries the argument

The SHallow REcurrent Decoder (SHRED) architecture, a machine learning model that uses recurrent layers to map sparse measurements to the full system state vector.

If this is right

  • Full state reconstruction is possible with fewer PMUs than traditionally required.
  • The method works without an accurate physical model of the power system.
  • Performance holds under strongly nonlinear operating conditions like short circuits.
  • Accuracy is largely independent of the specific locations of the PMUs.
  • High reconstruction accuracy persists even with added measurement noise.

Where Pith is reading between the lines

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

  • SHRED could lower the cost of wide area measurement systems by requiring fewer sensors.
  • Similar architectures might apply to state estimation in other complex dynamical systems with limited sensors.
  • Further tests on larger or real-world grids would confirm scalability beyond the IEEE 39-bus case.

Load-bearing premise

Training data from simulations sufficiently prepares the decoder to handle real-world nonlinear disturbances without needing the underlying physical equations.

What would settle it

If reconstruction error on the IEEE 39-bus system during short-circuit faults with three PMUs exceeds the error of the benchmark shallow decoder, the performance advantage claim would fail.

Figures

Figures reproduced from arXiv: 2607.00116 by Alberto Berizzi, Andrea Pomarico, J. Nathan Kutz.

Figure 1
Figure 1. Figure 1: SHRED architecture applied to power systems. A limited number of PMUs are used to measure voltage and frequency signals. These sensor time [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: IEEE 39-Bus power system III. NUMERICAL RESULTS This section presents a comprehensive analysis of SHRED applied to power system. All the analysis have been carried out on IEEE 39-Bus system, shown in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Short-circuit power at all the 39 buses ability to reconstruct power system dynamics, all tests were carried out using fault scenarios that were not included in the training or validation datasets, thereby assessing the model capability to generalize to unseen dynamics [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Reconstructed V , f and θ at buses 12, 16, 28, and 39, and generator state variables ω, δ, ψ1d, ψ1q, ψ2q, and ψexc for G01 and G05 under a short-circuit test for all case studies with varying numbers of PMUs listed in Table II. SHRED demonstrates very high accuracy for case studies A1 through A6, with a slight decrease in reconstruction performance for case studies A7 and A8. V f 1d 1q 2q exc A1 A2 A3 A4 A… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the mean ℓ2,rel[%] values between SHRED and SDN for all the case studies in Tab. II. the mapping from measurements to the state space is less challenging. However, as the number of PMUs decreases, the performance of SDN degrades, whereas SHRED main￾tains higher accuracy. This behavior can be attributed to the LSTM-based temporal encoder in SHRED, which exploits the temporal history of the mea… view at source ↗
Figure 7
Figure 7. Figure 7: Reconstructed V , f, and θ at buses 12, 16, 28, and 39, along with the generator state variables ω, δ, ψ1d, ψ1q, ψ2q, and ψexc for generators G01 and G05 under a short-circuit test for all case studies with varying PMU placements, as listed in Table IV. SHRED achieves consistent reconstruction performance across all clusters, with the mean reconstruction over all clusters exhibiting higher robustness and a… view at source ↗
Figure 8
Figure 8. Figure 8: ℓ2,rel[%] values for each variable class across the case studies listed in Table IV. As can be observed, all the considered clusters are able to accurately reconstruct the power system dynamics, including both V , f, and θ at the buses and the dynamic state variables ω, δ, ψ1d, ψ1q, ψ2q, and ψexc of the generators. Interestingly, the mean reconstruction obtained across all clusters exhibits better performa… view at source ↗
Figure 9
Figure 9. Figure 9: Reconstructed V , f, and θ at buses 12, 16, 28, and 39, along with the generator state variables ω, δ, ψ1d, ψ1q, ψ2q, and ψexc for generators G01 and G05 under a short-circuit test for case studies B1, B2 and B3, listed in Table IV, adding measurement noise to the PMUs. SHRED achieves consistent reconstruction performance across all clusters even in presence of measurement noise. V f 1d 1q 2q exc B1 B2 B3 … view at source ↗
Figure 10
Figure 10. Figure 10: ℓ2,rel[%] values for each variable class across the case studies B1, B2 and B3, listed in Table IV, with measurements noise. machine learning techniques. However, Kalman-based meth￾ods often suffer from high computational complexity, sensitiv￾ity to model inaccuracies, and performance degradation under strongly nonlinear operating conditions. Furthermore, their effectiveness critically depends on measurem… view at source ↗
read the original abstract

Dynamic State Estimation (DSE) will play a fundamental role in future power system operation by providing real-time estimates of the system state and enabling enhanced situational awareness. Existing DSE approaches are primarily based on Kalman filter variants or Machine Learning (ML) techniques. However, Kalman-based methods often suffer from high computational complexity, sensitivity to model inaccuracies, and performance degradation under strongly nonlinear operating conditions. Moreover, their effectiveness critically depends on the number and placement of measurements, since suboptimal PMU locations can reduce observability and even render state estimation infeasible. Machine learning approaches alleviate some of these limitations but typically require large amounts of training data and may struggle to generalize. To address these challenges, this paper proposes a SHallow REcurrent Decoder (SHRED) architecture for full-state reconstruction of power systems from sparse measurements. Unlike conventional model-based estimators, the proposed approach does not rely on an accurate physical model and is largely insensitive to PMU placement, making it particularly attractive for practical deployment in existing Wide Area Measurement Systems (WAMS). The method is validated on the IEEE 39-bus system under strongly nonlinear conditions, including short-circuit disturbances. The results demonstrate that SHRED can accurately reconstruct the complete system state using only a limited number of PMU measurements, consistently outperforming a state-of-the-art shallow decoder benchmark in sparse-measurement scenarios. Furthermore, the proposed framework exhibits strong robustness to measurement noise and maintains high reconstruction accuracy even under severe disturbances, highlighting its potential as a scalable and reliable alternative to conventional DSE techniques.

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

1 major / 1 minor

Summary. The paper proposes a SHallow REcurrent Decoder (SHRED) architecture for dynamic state estimation (DSE) from sparse PMU measurements in power systems. It claims that SHRED reconstructs the full system state without relying on an accurate physical model at inference time, is largely insensitive to PMU placement, outperforms a state-of-the-art shallow decoder benchmark in sparse-measurement scenarios, and maintains high accuracy under short-circuit disturbances and measurement noise on the IEEE 39-bus system.

Significance. If the generalization and robustness claims are substantiated with held-out test conditions, the approach could offer a practical data-driven alternative to Kalman-filter-based DSE methods that degrade under strong nonlinearities or suboptimal sensor placement.

major comments (1)
  1. [Experimental results section] Experimental results section: the manuscript provides no information on whether the short-circuit fault locations, clearing times, load/generation profiles, or operating conditions in the reported test cases were strictly excluded from the training trajectories. This detail is load-bearing for the central claim that performance reflects generalization to unseen strongly nonlinear conditions rather than interpolation within the training distribution.
minor comments (1)
  1. [Abstract] Abstract: the claims of consistent outperformance and robustness are stated without any quantitative metrics, error bars, or specific numerical results, which reduces the ability to assess the strength of the evidence from the abstract alone.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment on the experimental design. We address the point below and will revise the manuscript to strengthen the presentation of the generalization claims.

read point-by-point responses

  1. Referee: Experimental results section: the manuscript provides no information on whether the short-circuit fault locations, clearing times, load/generation profiles, or operating conditions in the reported test cases were strictly excluded from the training trajectories. This detail is load-bearing for the central claim that performance reflects generalization to unseen strongly nonlinear conditions rather than interpolation within the training distribution.

    Authors: We agree that explicit confirmation of held-out test conditions is necessary to support the generalization claims. The manuscript does not currently provide this information. In the revised manuscript we will expand the Experimental Results section to state that training trajectories were generated exclusively from normal operating conditions (varying load/generation profiles without short-circuit events), while all reported test cases use short-circuit fault locations, clearing times, and operating conditions that were strictly excluded from the training set. This clarification will be added with a brief description of the data-generation protocol to demonstrate that the reported performance reflects generalization to unseen nonlinear disturbances. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical ML validation independent of fitted inputs or self-citations

full rationale

The paper introduces the SHRED architecture for DSE from sparse PMUs and validates it empirically on the IEEE 39-bus system under short-circuit disturbances, claiming superior reconstruction without reliance on an accurate physical model. No equations, parameter-fitting procedures, or derivation steps are presented that reduce outputs to inputs by construction. No self-citations, uniqueness theorems, or ansatzes are invoked in the provided text to support central claims. The performance claims rest on held-out testing rather than tautological re-labeling of training data or model fits, making the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities can be identified from the provided text.

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