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arxiv: 2504.05556 · v1 · submitted 2025-04-07 · 📡 eess.SY · cs.SY

Novel Data-Driven Indices for Early Detection and Quantification of Short-Term Voltage Instability from Voltage Trajectories

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

Pith reviewed 2026-05-22 19:59 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords short-term voltage stabilityLyapunov exponentempirical mode decompositionvoltage trajectorydata-driven indexpower system stabilityOEL activationLVRT relay
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The pith

A data-driven index decomposes voltage trajectories with EMD and Lyapunov entropy to detect and measure short-term instability early.

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

The paper introduces a Short-Term Voltage Stability Index that processes raw voltage measurements to spot instability triggered by over-excitation limiters or low-voltage ride-through tripping. It splits each voltage trace into a slow residual that flags delayed recovery and an oscillatory part that captures swings, then scores the residual with an entropy measure based on the largest Lyapunov exponent. If the index works as described, operators could identify emerging voltage problems from local measurements alone, before full system models or state estimators react. This matters because modern grids with many inverter resources experience fast voltage collapses that traditional steady-state tools miss. The simulations show the index both flags the issue and gives a sense of how severe it is.

Core claim

STVSI uses Empirical Mode Decomposition on measured voltage trajectories to isolate a residual component that signals delayed recovery after OEL activation or LVRT relay action, while the oscillatory component reflects short-term swings; an entropy metric computed on the Lyapunov exponent of the residual then quantifies proximity to instability, allowing both detection and qualitative grading of the stability margin.

What carries the argument

The STVSI metric formed by applying an entropy calculation to the Lyapunov exponent of the EMD residual component extracted from voltage time series.

If this is right

  • Operators obtain an early warning of short-term voltage instability directly from phasor or waveform measurements.
  • The same decomposition distinguishes stable oscillatory behavior from unstable recovery trajectories.
  • The index supplies a continuous score that reflects how far the system sits from the instability boundary.
  • Both synchronous-generator and inverter-based resource contingencies become detectable within the same framework.

Where Pith is reading between the lines

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

  • Real-time control rooms could embed the index in existing PMU streams to trigger remedial actions before voltage collapse propagates.
  • The method might extend to other measurement types such as frequency or current trajectories for broader instability monitoring.
  • Because it is purely data-driven, the index could serve as a model-free benchmark against which full-order dynamic simulations are validated.

Load-bearing premise

The EMD residual reliably isolates only the delayed-recovery effect caused by OEL or LVRT action and is not contaminated by ordinary post-fault transients.

What would settle it

A test case in which the index produces high instability scores during stable post-fault voltage recovery without OEL or LVRT activation.

Figures

Figures reproduced from arXiv: 2504.05556 by Mohammad Almomani, Muhammad Sarwar, Venkataramana Ajjarapu.

Figure 1
Figure 1. Figure 1: Relationship between residual signals s1 and s2 and the tripping characteristic T of OEL or LVRT. high penetration of Motor D, comparing an unstable signal (dynamic load (DL) percentage = 80%) and a close-to-stable signal (DL = 75%). The system is simulated for 50 seconds to identify the critical signal based on the voltage trajectory, with instability occurring at DL = 80%. The second column shows the EMD… view at source ↗
Figure 2
Figure 2. Figure 2: Step-by-step calculation of the proposed stability index for two scenarios: the upper row illustrates a recovery case for Motor D with dynamic load levels of 80% (unstable due to OEL triggering) and 75% (stable), while the lower row presents an oscillatory stable case for Motor A. Each row includes the original voltage signal (V), EMD decomposition into residual (R) and IMFs, corresponding Lyapunov Exponen… view at source ↗
read the original abstract

This paper presents a novel Short-Term Voltage Stability Index (STVSI), which leverages Lyapunov Exponent-based detection to assess and quantify short-term stability triggered by Over Excitation Limiters (OELs) or undamped oscillations in voltage. The proposed method is measurement-based and decomposes the voltage trajectory into two key components using Empirical Mode Decomposition (EMD): a residual part, which indicates delayed voltage recovery, and an oscillatory part, which captures oscillations. The residual component is critical, as it can detect activation of OELs in synchronous generators or Low Voltage Ride-Through (LVRT) relays in inverter-based resources, potentially leading to instability within the quasisteady-state time frame. Meanwhile, the oscillatory component may indicate either a stable or unstable state in the short term. To accurately assess stability, STVSI employs an entropy-based metric to measure the proximity of the system to instability, with specific indices for short-term voltage stability based on oscillations and recovery. Simulations on the Nordic power system demonstrate that STVSI effectively identifies and categorizes voltage stability issues. Moreover, STVSI not only detects voltage stability conditions but also qualitatively assesses the extent of stability, providing a nuanced measure of stability.

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 / 0 minor

Summary. The paper proposes a novel Short-Term Voltage Stability Index (STVSI) that applies Empirical Mode Decomposition (EMD) to voltage trajectories, separating them into a residual component (claimed to indicate delayed recovery from OEL activation or LVRT relay tripping) and an oscillatory component, then uses an entropy metric on the Lyapunov exponent of the oscillatory part to quantify proximity to short-term voltage instability. Simulations on the Nordic power system are presented to show that STVSI can identify, categorize, and qualitatively assess voltage stability issues in a measurement-based manner.

Significance. If the EMD decomposition reliably isolates the claimed physical mechanisms and the entropy-based metric provides robust quantification with low false positives, the index could contribute a practical data-driven tool for real-time monitoring of short-term voltage stability, especially in systems with growing inverter-based resources where model-based methods are limited.

major comments (3)
  1. [Abstract] Abstract: The central claim that the residual component after EMD 'can detect activation' of OELs or LVRT relays is not supported by any correlation analysis, ablation (OEL enabled vs. disabled), or false-positive evaluation against normal post-fault recovery trajectories in the Nordic simulations.
  2. [Abstract] Abstract and results: No quantitative performance metrics, error bars, or comparisons to established indices are reported for the categorization and quantification claims on the Nordic system, leaving the effectiveness assertion unquantified.
  3. The entropy threshold and EMD stopping criteria are free parameters whose selection could introduce hidden fitting; without independent validation on held-out cases, the claimed parameter-light nature of STVSI is not demonstrated.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments on our manuscript. We address each major comment point by point below, providing clarifications based on the existing simulations and outlining revisions where the concerns identify areas for strengthening the presentation of results.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the residual component after EMD 'can detect activation' of OELs or LVRT relays is not supported by any correlation analysis, ablation (OEL enabled vs. disabled), or false-positive evaluation against normal post-fault recovery trajectories in the Nordic simulations.

    Authors: We agree that the abstract claim would benefit from stronger quantitative backing. The Nordic system simulations in the manuscript show delayed voltage recovery in the residual component coinciding with OEL activation or LVRT relay tripping in the presented cases, distinguished from faster recoveries. However, explicit correlation coefficients, ablation studies (OEL on/off), and false-positive rates against normal post-fault trajectories are not included. We will add these analyses in the revision, including tabulated comparisons across multiple fault scenarios to support the detection claim. revision: yes

  2. Referee: [Abstract] Abstract and results: No quantitative performance metrics, error bars, or comparisons to established indices are reported for the categorization and quantification claims on the Nordic system, leaving the effectiveness assertion unquantified.

    Authors: The manuscript currently demonstrates effectiveness through qualitative trajectory examples and STVSI values across Nordic cases for categorization into stable/unstable and grading severity. We acknowledge the absence of numerical metrics such as accuracy, precision, or comparisons to indices like the short-term voltage stability index from prior literature. In the revised version, we will report quantitative metrics with error bars from repeated simulations and include benchmark comparisons to quantify the claims. revision: yes

  3. Referee: [—] The entropy threshold and EMD stopping criteria are free parameters whose selection could introduce hidden fitting; without independent validation on held-out cases, the claimed parameter-light nature of STVSI is not demonstrated.

    Authors: The EMD stopping criteria adhere to standard Hilbert-Huang transform conventions, and the entropy threshold is derived from the observed distribution of Lyapunov exponent entropy values separating stable and unstable regimes in the Nordic simulations. We recognize that without explicit sensitivity tests or held-out validation, robustness is not fully shown. We will add parameter sensitivity analysis and results on held-out simulation cases in the revision to substantiate the parameter-light property. revision: partial

Circularity Check

0 steps flagged

STVSI derivation is self-contained with no reduction to inputs by construction

full rationale

The paper defines STVSI via direct application of EMD to decompose measured voltage trajectories into a residual component (for delayed recovery) and an oscillatory component, followed by computation of the Lyapunov exponent and an entropy metric on those components. No equations or steps in the abstract or described chain show the index being fitted to stability outcomes, self-defined in terms of its own predictions, or justified solely by overlapping-author citations that themselves assume the result. The interpretive mapping from residual shape to OEL/LVRT activation is presented as a post-decomposition observation rather than a tautological input, and the Nordic simulations are treated as external demonstration rather than the source of the metric itself. This keeps the central derivation independent of the target claims.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The index construction assumes that EMD cleanly separates physically meaningful residual recovery from oscillatory content and that the largest Lyapunov exponent entropy is a monotonic proxy for distance to instability; these steps rest on standard signal-processing assumptions plus domain-specific claims about OEL/LVRT behavior that are not independently derived in the abstract.

free parameters (2)
  • EMD stopping criteria and number of modes
    Chosen to isolate residual versus oscillatory parts; values not stated in abstract but required for reproducibility.
  • Entropy threshold or scaling for STVSI
    Determines the final stability score; appears fitted or tuned on simulation cases.
axioms (2)
  • domain assumption The residual component after EMD directly indicates activation of OELs or LVRT relays leading to quasisteady-state instability.
    Invoked to interpret the residual part as a stability precursor.
  • domain assumption Lyapunov-exponent entropy quantifies proximity to short-term voltage instability.
    Central mapping from decomposed trajectory to stability index.

pith-pipeline@v0.9.0 · 5757 in / 1598 out tokens · 46598 ms · 2026-05-22T19:59:53.874911+00:00 · methodology

discussion (0)

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Reference graph

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