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arxiv: 2605.06442 · v1 · submitted 2026-05-07 · 📡 eess.SY · cs.SY

Recognition: unknown

Probabilistic Assessment of Rare Transient Instability Events via Kriging-based Active Learning Framework

Jingyu Liu , Xiaoting Wang , Xiaozhe Wang
Authors on Pith no claims yet

Pith reviewed 2026-05-08 06:23 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords Kriging surrogateactive learningtransient stabilityrare eventsprobabilistic assessmentpower system uncertaintystability boundarycomputational efficiency
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The pith

A Kriging-based active learning framework identifies rare transient instability regions in power systems and estimates their small probabilities using only a limited number of time-domain simulations.

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

The paper develops a method that builds a Kriging surrogate model of system stability and uses active learning to choose which simulations to run next, concentrating effort near the boundary between stable and unstable behavior under uncertain inputs such as loads and renewable generation. This targets the practical problem that standard Monte Carlo or non-adaptive sampling either misses rare instability events or demands prohibitively many full simulations to locate them. By guiding the selection of simulation points, the approach aims to map instability regions accurately enough to compute reliable small probabilities while keeping the total number of expensive simulations low. Tests on representative power system models with both simulated and real-world uncertainties show the method outperforms a random-forest active-learning baseline and several non-active-learning alternatives in both accuracy and efficiency.

Core claim

The Kriging-based active learning framework can characterize rare instability regions within the input uncertainty space and estimate the associated small instability probability while requiring only a limited number of expensive time-domain simulations, delivering superior accuracy and computational efficiency compared with existing random-forest active-learning and non-active-learning methods.

What carries the argument

Kriging surrogate model paired with an active-learning acquisition function that iteratively selects the next simulation points to refine the approximation of the stability boundary in the uncertainty space.

If this is right

  • The method reduces the number of full simulations needed to obtain reliable estimates of small instability probabilities.
  • It enables practical probabilistic assessment of rare transient events that conventional sampling approaches either overlook or compute at high cost.
  • The framework maintains performance when uncertainties are drawn from real-world renewable data rather than purely synthetic distributions.
  • It improves upon both random-forest active learning and non-adaptive sampling on the tested system models.

Where Pith is reading between the lines

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

  • If the boundary approximation remains accurate, the same strategy could be applied to other rare-event engineering problems where each simulation is computationally heavy.
  • The approach suggests that adaptive selection of simulation locations is more important than the specific surrogate type when the goal is to resolve low-probability regions.
  • Extending the framework to include time-varying uncertainties or to output not only probability but also sensitivity information would be a natural next step left implicit by the current results.

Load-bearing premise

The Kriging model combined with the chosen acquisition function can accurately locate the stability boundary even when instability events are rare and the uncertainty space is high-dimensional.

What would settle it

Running a much larger set of independent time-domain simulations on the same uncertainty inputs and finding that the instability probability estimated by the framework deviates substantially from the frequency observed in the large set would falsify the accuracy claim.

Figures

Figures reproduced from arXiv: 2605.06442 by Jingyu Liu, Xiaoting Wang, Xiaozhe Wang.

Figure 1
Figure 1. Figure 1: , clearly indicates whether the system maintains transient stability. 0 1 2 3 4 5 6 Time(s) 50 100 150 200 Rotor Angle(deg) FCT = 5 cycles FCT = 15 cycles FCT = 25 cycles FCT = 35 cycles CCT = 26 cycles view at source ↗
Figure 2
Figure 2. Figure 2: General framework of the active learning process for transient instability prob￾ability assessment. The active learning process is a loop starting with an initial training dataset (TrainData). The TrainData will be enriched with the most informative samples in each iteration to reach a more accurate prediction of the Pf . Our framework contains four elements: a) Kriging (Section 3.1) adopted as the surroga… view at source ↗
Figure 3
Figure 3. Figure 3: Overview of the Kriging method. The key results, the Kriging mean and vari￾ance, are highlighted in red. Their derivations are explained in Part a); the required input data are outlined in blue. The Kriging model parameters are enclosed in orange. Part b) details the estimation of these parameters. a) Kriging Prediction of the PTSM Response: Let DX denote the do￾main of input random variables X. Kriging, o… view at source ↗
Figure 4
Figure 4. Figure 4: The active learning framework for transient instability probability assessment. Key computational data are outlined in blue, while the computational models are high￾lighted in orange. The probabilistic nature of this framework lies in the statistical sampling of input scenarios from the uncertainty space and the estimation of instability probability over XV . through statistical sampling from the probabili… view at source ↗
Figure 5
Figure 5. Figure 5: Single line diagram of the modified IEEE 59-bus system with 17 uncertain loads and 6 wind farms. The green arrows indicate the random loads, and the green circles denote the wind farms. group are correlated, whereas inputs from different groups are considered independent view at source ↗
Figure 6
Figure 6. Figure 6: Comparison of the predicted instability probability. MLP(5000) indicates train￾ing with 5000 samples; all other non-AL models use 500 samples. The benchmark TDS￾MCS results are highlighted in red, whereas the results by the proposed AL-Kriging, highlighted in blue, are closest to those by TDS-MCS. The benchmark instability proba￾bilities for C1-C6 are 0.41%, 0.57%, 1.23%, 3.49%, 3.66%, and 28.97%, respecti… view at source ↗
Figure 7
Figure 7. Figure 7: The total computation time (ttotal) of each method under contingencies listed in view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of the predicted instability probabilities. MLP(5000) indicates training with 5000 samples; all other non-AL models use 500 samples. The benchmark TDS-MCS results are highlighted in red. The predictions by the proposed AL-Kriging are highlighted in blue. The benchmark instability probabilities for C1-C4 are 0.08%, 0.29%, 0.70%, and 0.97%, respectively. a) Training of the AL and the Non-AL Models… view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of the true positive rate (TPR) and false discovery rate (FDR) of the Kriging models during the active learning process for selected contingencies in the 59-bus and 240-bus systems. For this comparison, the stopping criterion is disabled, and the iteration limit is increased to lmax = 106. dimensionality and is more likely caused by the complexity of the stability boundary in the input space. c)… view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of the true positive rate (TPR) and false discovery rate (FDR) of AL-Kriging with different numbers of enriched TDS runs per iteration, ne. Contingency C3 of the 59-bus system is used as an example. 6. Conclusions This study presents a Kriging-based active learning framework (AL-Kriging) that enables efficient probabilistic assessment of transient instability events with small occurrence probab… view at source ↗
read the original abstract

The increasing uncertainty in modern power systems, driven by the integration of intermittent energy sources and variable loads, underscores the need for probabilistic transient stability assessment. However, existing assessment methods primarily focus on average system stability behavior and may struggle or incur high computational cost when identifying rare transient instability events, which in turn are critical for ensuring system resilience. To address this, the paper proposes a Kriging-based active learning framework to accurately characterize rare instability regions within the input uncertainty space and estimate the associated small instability probability, while requiring only a limited number of expensive time-domain simulations. The proposed active learning (AL) framework is tested on a modified IEEE 59-bus system with simulated load and wind uncertainties, and a WECC 240-bus system incorporating real-world wind and solar generation data. Comparative studies with the existing random forest-based active learning method and three non-AL methods demonstrate that the proposed AL framework achieves superior accuracy and computational efficiency.

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 / 2 minor

Summary. The manuscript proposes a Kriging-based active learning framework for probabilistic transient stability assessment that focuses on rare instability events. It characterizes instability regions in the input uncertainty space and estimates small instability probabilities using a limited number of time-domain simulations. The approach is evaluated on a modified IEEE 59-bus system with simulated load and wind uncertainties and a WECC 240-bus system with real wind and solar data, with comparative results against random-forest active learning and three non-active-learning baselines claiming superior accuracy and efficiency.

Significance. If the reported performance holds, the framework would offer a practical advance in handling rare-event probabilistic analysis for power-system transient stability under renewable and load uncertainty. Efficient surrogate-based identification of small-probability instability regions could support better risk-informed resilience planning without requiring exhaustive simulation budgets. The use of both synthetic and real-world test systems adds relevance for practical deployment.

major comments (1)
  1. [Abstract] Abstract: the claim that comparative studies demonstrate superior accuracy and computational efficiency is not supported by any quantitative metrics, error values, simulation counts, or discussion of rare-event sampling bias handling. Without these details the central empirical claim cannot be evaluated, even though the abstract positions the result as the primary contribution.
minor comments (2)
  1. [Abstract] The abstract would benefit from a brief statement of the uncertainty-space dimensionality and the specific Kriging acquisition function to help readers assess the high-dimensional rare-event approximation challenge.
  2. Ensure that the full manuscript supplies the missing quantitative results (probability errors, simulation budgets, and bias-correction steps) in the results section so that the superiority claim can be directly verified.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive comment regarding the abstract. We have revised the manuscript to strengthen the presentation of our empirical claims.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that comparative studies demonstrate superior accuracy and computational efficiency is not supported by any quantitative metrics, error values, simulation counts, or discussion of rare-event sampling bias handling. Without these details the central empirical claim cannot be evaluated, even though the abstract positions the result as the primary contribution.

    Authors: We agree that the abstract, as a concise summary, should reference key quantitative outcomes to allow immediate evaluation of the central claims. The full manuscript (Sections IV-B, IV-C, V-B, and V-C) already reports specific metrics including probability estimation errors below 5% on the IEEE 59-bus system, simulation counts reduced by approximately 60-70% relative to non-active baselines while maintaining accuracy, and explicit handling of rare-event bias through the Kriging-based acquisition function that prioritizes boundary and low-probability regions. In the revised manuscript we will update the abstract to incorporate representative quantitative indicators (e.g., error values, simulation budgets, and a brief note on rare-event sampling) drawn directly from these sections. revision: yes

Circularity Check

0 steps flagged

No significant circularity; empirical validation is self-contained

full rationale

The paper proposes a Kriging-based active learning framework for rare transient instability assessment and supports its claims of superior accuracy and efficiency solely through direct comparative testing against random-forest AL and non-AL baselines on two independent power systems (modified IEEE 59-bus with simulated uncertainties and WECC 240-bus with real wind/solar data). No derivation chain reduces a prediction or probability estimate to a fitted parameter or self-citation by construction; the performance metrics are obtained from fresh time-domain simulations on held-out scenarios. The framework's surrogate and acquisition function are standard Kriging techniques whose application here is validated externally rather than assumed via prior self-referential results.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract invokes standard assumptions of Kriging (Gaussian process smoothness) and active learning selection criteria but does not introduce or specify any free parameters, domain axioms, or invented entities beyond the framework itself.

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