A Time-to-Boundary Margin for Transient Stability: Unifying Critical Clearing Time and Operating-Point Drift

Jul 16, 2026

A unified transient-stability margin M is developed to complement the classical critical clearing time (CCT) used at fixed operating points. Whereas the voltage-stability loading margin measures distance to a saddle-node boundary, M measures the time to the synchronism boundary under joint state–parameter motion. M is defined as the first-passage time to the survival boundary and is proven to match CCT exactly for one-machine–infinite-bus, verified on a published benchmark. Under operating-point drift, M provides lead time before faults become unclearable, highlighted using the 28 April 2025 Iberian blackout drift timescale, and recovers CCT within conservative bounds on a New England 39-bus benchmark while critical slowing-down signals proximity.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages10

Reading Time25 min

Introduction

Classical indices and their limitations

Energy-function and data-driven assessment families

Motivation from operating-point drift

A Time-to-Boundary Margin for Transient Stability: Unifying Critical Clearing Time and Operating-Point Drift Marián Mešter arXiv :2607 .02070v1 [ ee ss . SY] 2 Jul 2026 Abstract—The loading margin to voltage collapse—the distance in parameter space to the closest saddle-node bifurcation—is a standard proximity index for voltage stability. This paper develops its transient-stability counterpart: a margin M that measures the time to the synchronism boundary rather than a distance, and that unifies two limits usually treated separately. The critical clearing time (CCT) is the fast, fixed-parameter limit; the slow drift of the operating point toward a static loadability limit is the other. M is defined as the first-passage time of the joint state–parameter motion to the survival boundary. We prove and verify that M equals the CCT exactly on the one-machine–infinite-bus reduction (deviation ≤ 0.01% across loadings on a published benchmark), establishing a certified single-machine pillar. Under operating-point drift, M yields an operational lead time before faults become unclearable; we take the 28 April 2025 Iberian blackout timeline as an illustrative timescale for the drift rate. On the New England 39-bus system, an independent benchmark, the single-machine-equivalent reduction reproduces the CCT within 1.8–6.0%(conservatively), and a critical slowing-down signature flags proximity to the boundary. For the multimachine case we characterize the limits explicitly: the transfer-conductance work is tightly boundable, while the controlling unstable equilibrium is the binding obstruction to a certified margin. Index Terms—Transient stability, critical clearing time, region of attraction, stability margin, operating-point drift, energy function, critical slowing down, early warning. I. INTRODUCTION TRANSIENT stability—the ability of synchronous ma chines to retain synchronism after a large disturbance—remains among the binding constraints on how close to its limits a power system may be operated [1], [2] . Its classical index is the critical clearing time (CCT): the longest a given fault may persist before the post-fault trajectory leaves the region of attraction. The CCT answers a sharp question, but only at a fixed operating point and for a prescribed fault. Voltage stability faced an analogous need and answeredit with a margin. The loading margin to voltage collapse—the distance in load-power space to the closest saddle-node bifurcation—became a standard proximity index because it summarises “how far from the boundary” in one operational number, with sensitivities that guide control, and without requiring the pattern of load increase to be predicted [3] . No equivalent time-based margin exists for transient stability: the CCT is a threshold, not a distance to a moving boundary, and The author is with the Faculty of Electrical Engineering and Informatics, Technical University of Košice, Košice, Slovakia (e-mail: mar[ian.mester@tuke.sk](ian.mester@tuke.sk)) . recent work has extended it mainly through sensitivities of the CCT to parameters [4], [5] or through simulation-free boundson the CCT [6], [7] rather than through a margin that follows the operating point as it drifts. This positions M relative to the established families of transient-stability assessment. Direct energy-function methods and their controlling-unstable-equilibrium and boundarycontrolling-UEP (BCU) refinements [13], [10], [21] certify stability at a fixed operating point by comparing a transient energy to a critical value; Lyapunov-function constructions [16],[22], [23], [25] and network-theoretic synchronisation results [24] estimate the region of attraction or synchronisation conditions directly. All of these return a verdict—stable or unstable—or a region estimate at a frozen operating point; none reports a time remaining to the boundary under a moving operating point, which is the quantity M adds. A second, fastgrowing family replaces analysi

FAQs

What is the proposed margin M in this paper?

M is a time-to-boundary transient-stability margin defined as the first-passage time for the joint state–parameter motion to reach the survival boundary, instead of measuring distance to it.

How does M relate to the critical clearing time (CCT)?

M equals the CCT exactly in the one-machine–infinite-bus reduction, and on a larger benchmark it reproduces CCT within a small, conservatively bounded percentage range.

Why is the operating-point drift important for applying transient stability margins?

Real systems can drift from secure states toward collapse over tens of seconds; a fixed-parameter CCT can fail to indicate risk until the boundary is already reached, while M provides operational lead time under that drift.

Jul 16, 2026

Upload by Ava Thompson