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arxiv: 2504.05557 · v1 · submitted 2025-04-07 · 📡 eess.SY · cs.SY

Enhanced Entropy-Based Metric for Characterization of Delayed Voltage Recovery

Mohammad Almomani , Muhammad Sarwar , Venkataramana Ajjarapu This is my paper

Pith reviewed 2026-05-22 19:54 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords FIDVRvoltage recoveryEVRVIempirical mode decompositionentropy-based indexviolation detectionpower system stabilityNordic system
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The pith

The enhanced voltage recovery violation index (EVRVI) detects and categorizes fault-induced delayed voltage recovery more accurately than traditional entropy measures by applying empirical mode decomposition to voltage signals.

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

Power systems require precise detection of fault-induced delayed voltage recovery events because these can threaten stability and lead to cascading failures. The paper develops EVRVI to improve on entropy-based indices by first applying empirical mode decomposition to isolate relevant features in the voltage waveform, then using those features to quantify both under-voltage and over-voltage conditions during the recovery phase. Extensive testing on the Nordic system model covers more than 245,000 scenarios. Results show EVRVI reduces false negatives in violation detection while adding a reliable method for identifying over-voltages that earlier approaches overlooked. A reader cares because improved violation metrics support safer operation and planning in grids that must handle variable loads and renewable sources.

Core claim

The paper claims that EVRVI provides a comprehensive index for quantifying FIDVR by leveraging EMD to extract key features from the voltage signal for measuring over-voltage and under-voltage events. Simulations involving over 245k scenarios on the Nordic system demonstrate that EVRVI identifies and categorizes voltage recovery issues more effectively than the traditional entropy-based measure, with a significant reduction in false negatives and a new framework for over-voltage detection.

What carries the argument

EVRVI, the enhanced voltage recovery violation index formed by combining empirical mode decomposition of voltage waveforms with entropy quantification to isolate and measure features of delayed recovery including both under- and over-voltage components.

If this is right

  • EVRVI supplies a framework that detects over-voltages during recovery in addition to under-voltage violations.
  • The index reduces false negatives when identifying voltage recovery problems across hundreds of thousands of simulated cases.
  • EVRVI enables more accurate categorization of FIDVR events for power system reliability studies.
  • The approach outperforms standard entropy-based metrics on the Nordic system model under varied fault and load conditions.

Where Pith is reading between the lines

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

  • If the index holds up on other networks, operators could embed it in real-time monitoring to flag recovery problems earlier.
  • The decomposition step opens the possibility of adapting similar feature extraction to other transient monitoring tasks such as frequency stability or harmonic analysis.
  • Testing EVRVI on field data from recorded disturbances would show whether simulation gains translate to practical settings.
  • The reduction in missed violations suggests the method could streamline contingency screening by focusing attention on genuine risks.

Load-bearing premise

Empirical mode decomposition applied to voltage waveforms must produce intrinsic mode functions that cleanly separate true delayed recovery features from normal transients without creating new classification errors.

What would settle it

Apply both EVRVI and the traditional entropy measure to a fresh collection of recorded voltage traces from actual grid faults and verify whether the false-negative rate for violation detection stays lower with EVRVI.

Figures

Figures reproduced from arXiv: 2504.05557 by Mohammad Almomani, Muhammad Sarwar, Venkataramana Ajjarapu.

Figure 1
Figure 1. Figure 1: False Detection cases using KL Divergence [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Comprehensive analysis of delayed voltage recovery signals using the proposed extended index. The figure illustrates two cases: under-voltage (top row) and over-voltage (bottom row). The columns depict (1) voltage signals and stepwise reference criteria, (2) lower and upper envelopes calculated using equations (2) and (3), (3) probability distributions of the envelopes for N segments, and (4) the EVRVI cal… view at source ↗
read the original abstract

Ensuring accurate violation detection in power systems is paramount for operational reliability. This paper introduces an enhanced voltage recovery violation index (EVRVI), a comprehensive index designed to quantify fault-induced delayed voltage recovery (FIDVR). EVRVI enhances traditional entropy-based methods by leveraging Empirical Mode Decomposition (EMD) to extract key features from the voltage signal, which are then used to quantify over-voltage (OV) and under-voltage (UV) events. Our simulations on the Nordic system, involving over 245k scenarios, demonstrate EVRVI's superior ability to identify and categorize voltage recovery issues compared to the traditional entropy-based measure. EVRVI not only significantly reduces false negatives in violation detection but also provides a reliable framework for over-voltage detection, making it an invaluable tool for modern power system studies.

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

3 major / 2 minor

Summary. The manuscript introduces the Enhanced Voltage Recovery Violation Index (EVRVI), which augments traditional entropy-based measures by applying Empirical Mode Decomposition (EMD) to voltage waveforms in order to extract features for quantifying over-voltage (OV) and under-voltage (UV) events associated with fault-induced delayed voltage recovery (FIDVR). Simulations on the Nordic system with more than 245,000 scenarios are presented to show that EVRVI reduces false negatives relative to the baseline entropy index while also enabling reliable OV detection.

Significance. If the performance claims hold after the methodological gaps are closed, the work would supply a practical, simulation-validated index for improved FIDVR monitoring in large-scale power-system studies; the scale of the Nordic-system test set (245k scenarios) constitutes a genuine empirical strength that could support adoption in operational reliability tools.

major comments (3)
  1. [§3] §3 (EMD-based feature extraction): the sifting stopping criterion and IMF selection rule are not stated. Because the central claim of reduced false negatives rests on the assumption that the resulting IMFs cleanly isolate FIDVR dynamics from normal transients, the absence of these parameters prevents assessment of mode-mixing risk and reproducibility.
  2. [§5] §5 (Nordic-system results): the reported superiority on 245k scenarios is presented without error bars, statistical significance tests, or any description of how detection thresholds were chosen or validated. This directly undermines the load-bearing performance comparison to the traditional entropy measure.
  3. [§3–4] Definition of EVRVI (throughout §3–4): no explicit equations or algorithmic pseudocode are supplied for how the OV/UV quantifiers are computed from the EMD IMFs and combined with entropy. Without this, it is impossible to determine whether the index is a genuine enhancement or reduces to a reparameterization of the input data.
minor comments (2)
  1. [§4] Notation for the final EVRVI formula is introduced without a dedicated equation number, making cross-references in the results section difficult to follow.
  2. [Figures 3–5] Figure captions for the voltage-waveform examples do not indicate the specific Nordic-bus locations or fault scenarios used, reducing clarity for readers attempting to replicate the visual comparisons.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments on our manuscript. These observations highlight important aspects of clarity and rigor that we will address in the revision. We respond to each major comment below.

read point-by-point responses

  1. Referee: [§3] §3 (EMD-based feature extraction): the sifting stopping criterion and IMF selection rule are not stated. Because the central claim of reduced false negatives rests on the assumption that the resulting IMFs cleanly isolate FIDVR dynamics from normal transients, the absence of these parameters prevents assessment of mode-mixing risk and reproducibility.

    Authors: We agree that explicit specification of the sifting stopping criterion and IMF selection rule is necessary for reproducibility and to allow evaluation of mode-mixing risks. The manuscript employed the standard Cauchy-type convergence criterion (standard deviation of consecutive sifting results below 0.2) and retained the first three IMFs, whose frequency content aligns with FIDVR recovery timescales as verified on representative waveforms. We will revise §3 to state these choices explicitly, include a brief justification for IMF selection, and add a short note on mode-mixing mitigation. revision: yes

  2. Referee: [§5] §5 (Nordic-system results): the reported superiority on 245k scenarios is presented without error bars, statistical significance tests, or any description of how detection thresholds were chosen or validated. This directly undermines the load-bearing performance comparison to the traditional entropy measure.

    Authors: The referee is correct that the results section lacks error bars, significance testing, and threshold validation details. In the revision we will report standard deviations across scenario batches as error bars, apply paired statistical tests (Wilcoxon signed-rank) to confirm the reduction in false negatives is significant, and describe that thresholds were selected by maximizing the F1 score on a 20 % held-out validation subset before final evaluation on the full set. These additions will strengthen the comparative claims. revision: yes

  3. Referee: [§3–4] Definition of EVRVI (throughout §3–4): no explicit equations or algorithmic pseudocode are supplied for how the OV/UV quantifiers are computed from the EMD IMFs and combined with entropy. Without this, it is impossible to determine whether the index is a genuine enhancement or reduces to a reparameterization of the input data.

    Authors: We acknowledge that the absence of explicit equations and pseudocode in §§3–4 limits the ability to verify the precise construction of EVRVI. The index is formed by applying EMD, computing sample entropy on the retained IMFs, and deriving separate OV and UV quantifiers as the time-integrated normalized deviation of each IMF from the respective voltage limits during the post-fault recovery window; these terms are then linearly combined with entropy to yield the final scalar. We will insert the complete set of defining equations together with a concise algorithmic pseudocode block in the revised manuscript to make the computation fully transparent and to highlight the distinction from the baseline entropy index. revision: yes

Circularity Check

0 steps flagged

EVRVI is a constructive definition with no reduction to inputs by construction

full rationale

The paper defines EVRVI explicitly as an index that applies Empirical Mode Decomposition to voltage waveforms, extracts features, and then computes entropy-based quantifications of over-voltage and under-voltage events. This is a methodological construction rather than a derivation whose output is forced by its own fitted parameters or prior self-citations. The reported performance gain (reduced false negatives on 245k Nordic scenarios versus plain entropy) is an empirical comparison against an independent baseline; it does not reduce to a redefinition of the input data or to a self-citation chain that supplies the uniqueness or ansatz. No equations in the provided text equate a prediction to a fitted quantity by construction, and the central claim remains externally falsifiable via the simulation results. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities beyond the definition of the new index itself.

invented entities (1)
  • EVRVI no independent evidence
    purpose: Composite index that quantifies FIDVR by combining EMD-derived features for over-voltage and under-voltage events
    New metric introduced by the authors; no independent evidence supplied in the abstract

pith-pipeline@v0.9.0 · 5665 in / 1253 out tokens · 65314 ms · 2026-05-22T19:54:00.312210+00:00 · methodology

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Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

  1. [1]

    Fundamental study on the influence of dynamic load and distributed energy resources on power system short-term voltage stability,

    A. Bori ˇci´c, J. L. R. Torres, and M. Popov, “Fundamental study on the influence of dynamic load and distributed energy resources on power system short-term voltage stability,” International Journal of Electrical Power & Energy Systems , vol. 131, p. 107141, 2021

    work page 2021

  2. [2]

    Entropy- based metric for characterization of delayed voltage recovery,

    S. Dasgupta, M. Paramasivam, U. Vaidya, and V . Ajjarapu, “Entropy- based metric for characterization of delayed voltage recovery,” IEEE Transactions on Power Systems , vol. 30, no. 5, pp. 2460–2468, 2014

    work page 2014

  3. [3]

    Quantitative assessments for transient voltage security,

    Y . Xue, T. Xu, B. Liu, and Y . Li, “Quantitative assessments for transient voltage security,” IEEE Transactions on Power Systems , vol. 15, no. 3, pp. 1077–1083, 2000

    work page 2000

  4. [4]

    Optimal allocation of dynamic var support using mixed integer dynamic optimization,

    A. Tiwari and V . Ajjarapu, “Optimal allocation of dynamic var support using mixed integer dynamic optimization,” IEEE Transactions on Power Systems, vol. 26, no. 1, pp. 305–314, 2011

    work page 2011

  5. [5]

    Multi-objective dynamic var planning against short-term voltage instability using a decomposition-based evolutionary algorithm,

    Y . Xu, Z. Y . Dong, K. Meng, W. F. Yao, R. Zhang, and K. P. Wong, “Multi-objective dynamic var planning against short-term voltage instability using a decomposition-based evolutionary algorithm,” IEEE Transactions on Power Systems , vol. 29, no. 6, pp. 2813–2822, 2014

    work page 2014

  6. [6]

    Control of photovoltaic systems for enhanced short-term voltage stability and recovery,

    G. Lammert, D. Premm, L. D. P. Ospina, J. C. Boemer, M. Braun, and T. Van Cutsem, “Control of photovoltaic systems for enhanced short-term voltage stability and recovery,” IEEE Transactions on Energy Conversion, vol. 34, no. 1, pp. 243–254, 2019

    work page 2019

  7. [7]

    A new global index for short term voltage stability assessment,

    A. Alshareef, R. Shah, N. Mithulananthan, and S. Alzahrani, “A new global index for short term voltage stability assessment,” IEEE Access , vol. 9, pp. 36 114–36 124, 2021

    work page 2021

  8. [8]

    A survey of current practices for transient voltage dip/sag criteria related to power system stability,

    D. Shoup, J. Paserba, and C. Taylor, “A survey of current practices for transient voltage dip/sag criteria related to power system stability,” in IEEE PES Power Systems Conference and Exposition, 2004. , 2004, pp. 1140–1147 vol.2

    work page 2004

  9. [9]

    Addressing short term voltage stability problem - part i: Challenges and plausible solution directions,

    A. Tiwari and V . Ajjarapu, “Addressing short term voltage stability problem - part i: Challenges and plausible solution directions,” in 2016 IEEE/PES Transmission and Distribution Conference and Exposition (T&D), 2016, pp. 1–5

    work page 2016

  10. [10]

    Deep reinforcement learning framework for short-term voltage stability improvement,

    M. Sarwar, A. R. R. Matavalam, and V . Ajjarapu, “Deep reinforcement learning framework for short-term voltage stability improvement,” in 2023 IEEE Texas Power and Energy Conference (TPEC) , 2023, pp. 1– 6

    work page 2023

  11. [11]

    Exelon transmission planning criteria,

    PJM, “Exelon transmission planning criteria,” https://www.pjm. com/-/media/planning/planning-criteria/exelon-planning-criteria.ashx, accessed: 2024

    work page 2024

  12. [12]

    The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis,

    N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.- C. Yen, C. C. Tung, and H. H. Liu, “The empirical mode decomposition and the hilbert spectrum for nonlinear and non-stationary time series analysis,” Proceedings of the Royal Society of London. Series A: mathematical, physical and engineering sciences , vol. 454, no. 1971, pp. 903–995, 1998

    work page 1971

  13. [13]

    On intrinsic mode function,

    G. Wang, X.-Y . Chen, F.-L. Qiao, Z. Wu, and N. E. Huang, “On intrinsic mode function,” Advances in Adaptive Data Analysis , vol. 2, no. 03, pp. 277–293, 2010

    work page 2010

  14. [14]

    Test systems for voltage stability studies,

    T. Van Cutsem, M. Glavic, W. Rosehart, C. Canizares, M. Kanatas, L. Lima, F. Milano, L. Papangelis, R. A. Ramos, J. A. dos Santos et al., “Test systems for voltage stability studies,”IEEE Transactions on Power Systems, vol. 35, no. 5, pp. 4078–4087, 2020

    work page 2020