arxiv: 2604.24009 · v1 · submitted 2026-04-27 · 📡 eess.SY · cs.SY

Safe Reconnection Time for Large-Scale Data Center Loads: An Analytical Framework for Transient Stability Assessment

Ahmed Mesfer Alkhudaydi , Bai Cui This is my paper

Pith reviewed 2026-05-08 02:07 UTC · model grok-4.3

classification 📡 eess.SY cs.SY

keywords safe reconnection timedata center loadstransient stabilityenergy function methodflapping preventionUPS reconnectionelectromechanical oscillationspower system stability

0 comments p. Extension

The pith

A critical safe reconnection time derived from energy functions guarantees that large data center loads will not cause flapping after disturbances.

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

Large data center facilities can disconnect their UPS during voltage or frequency events but risk amplifying oscillations or entering repeated connect-disconnect cycles if they reconnect while the grid is still settling. This paper builds an analytical framework on a single-machine infinite-bus model that tracks swing dynamics during the off period and the voltage-angle coupling that sets the power step at reconnection under constant-power load behavior. The energy function method then locates the critical safe reconnection time after which any reconnection keeps trajectories inside frequency, angle, and voltage limits and drives them to the new post-reconnection equilibrium. Readers would care because the result supplies a simple, physics-based bound that UPS logic can use to choose reconnection windows without relying solely on conservative fixed delays.

Core claim

In a model capturing swing dynamics during disconnection and voltage-angle coupling at the load bus, the energy function method identifies a critical safe reconnection time such that reconnection after this instant produces a post-reconnection trajectory guaranteed to stay within operational limits and converge to the post-reconnection equilibrium, thereby preventing flapping.

What carries the argument

Energy function method applied to a single-machine infinite-bus model that incorporates voltage-angle coupling to determine the electrical power step at reconnection under constant-power load assumptions.

If this is right

UPS reconnection logic can be set to wait until the critical time to avoid repeated flapping.
The framework supplies a physics-informed upper bound on acceptable reconnection windows for large data-center facilities.
Operational rules for power-electronics-rich loads can incorporate the derived time to limit amplification of electromechanical oscillations.
The same energy-function criterion can inform reconnection decisions for any large constant-power load that disconnects during disturbances.

Where Pith is reading between the lines

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

The critical-time result could be adapted to other large constant-power loads such as electric-vehicle charging hubs or industrial plants.
Pairing the analytical bound with real-time angle or frequency measurements might allow dynamic adjustment of the safe window.
Utilities could embed the criterion in planning studies to size the maximum data-center load that can be served without added protective delays.

Load-bearing premise

The single-machine infinite-bus model with voltage-angle coupling and constant-power load assumptions accurately captures the electrical power step that occurs at the moment of reconnection.

What would settle it

A time-domain simulation or measured event in which reconnection occurs after the calculated critical time yet still produces flapping, sustained oscillations, or limit violations would falsify the stability guarantee.

Figures

Figures reproduced from arXiv: 2604.24009 by Ahmed Mesfer Alkhudaydi, Bai Cui.

**Figure 1.** Figure 1: A simplified three-bus system a series of optimization problems for determining the earliest safe reconnection time. The overall framework facilitates rapid computation of safe reconnection windows suitable for realtime operations. The remainder of this paper is organized as follows. Section II presents the system model, including the configuration of three-bus system, the swing equation, and the charact… view at source ↗

**Figure 2.** Figure 2: Geometric interpretation in the (δ, ω) plane: the waiting trajectory x−(t) evolves under (9) until it enters the certified safe reconnection set Ssafe. admissible reconnection set as the set of post-reconnection initial conditions that satisfy both the protection band and the voltage admissibility conditions as Sadm :=    (δ, ∆ω) ∈ R 2 view at source ↗

**Figure 3.** Figure 3: shows the phase portrait with the safe reconnection set Ssafe (green region), which represents the intersection of Spre (light blue), Spost (orange), and Sadm (light gray). The safe set occupies approximately 10.5% of the admissible region. The waiting trajectory (black line) and post-reconnection trajectory (red line) are shown, with optimal reconnection occurring at t ⋆ re = 0.487 s (marked by star) view at source ↗

**Figure 4.** Figure 4: Frequency deviation following safe reconnection at view at source ↗

**Figure 5.** Figure 5: Frequency deviation following unsafe reconnection at view at source ↗

read the original abstract

The rapid growth of large, power-electronics-rich data center (DC) loads is creating new operational challenges for bulk power systems. A key risk arises when a DC uninterruptible power supply (UPS) disconnects the facility during voltage/frequency disturbances and then reconnects it while the bulk grid is still dynamically settling to a new equilibrium point. Poorly timed reconnection can amplify electromechanical oscillations, deepen frequency deviations, and lead to repeated connect-disconnect \emph{flapping}. In this paper, we develop an analytical framework to characterize the \emph{safe reconnection time} for large DC loads after a disturbance-induced disconnection that avoids flapping. Using a model in the spirit of the classical single-machine infinite-bus system, we capture (i) swing dynamics during the disconnection interval and (ii) voltage-angle coupling at the load bus, which determines the electrical power step at reconnection under constant-power load assumptions. Using energy function method, we characterize the critical safe reconnection time such that for any reconnection time after the critical safe reconnection time, the post-reconnection trajectory is guaranteed to remain within operational limits (frequency/angle/voltage) and converge to the post-reconnection equilibrium, thereby preventing flapping. Time-domain simulations validate the effectiveness of the proposed analytical approach. The results provide a simple, physics-informed criterion that can be used to bound reconnection windows for large DC facilities and inform UPS reconnection logic.

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

2 major / 2 minor

Summary. The paper develops an analytical framework for determining the safe reconnection time of large data center loads after disturbance-induced disconnection. It employs a single-machine infinite-bus (SMIB) model to capture swing dynamics during the disconnection interval and voltage-angle coupling at the load bus under constant-power load assumptions. Using the energy function method, it derives a critical safe reconnection time T_crit such that any reconnection after T_crit guarantees the post-reconnection trajectory remains within operational limits on frequency, angle, and voltage and converges to the post-reconnection equilibrium, thereby preventing flapping. Time-domain simulations are presented to validate the analytical bound.

Significance. If the central claim holds under the model assumptions, the work provides a simple, physics-informed analytical criterion for bounding reconnection windows in UPS systems for large data centers. This is significant given the rapid growth of such loads and the operational risks of flapping. The use of energy functions to obtain guaranteed bounds (rather than purely empirical or simulation-based thresholds) is a strength, offering interpretable results that could inform control logic. The approach aligns with classical transient stability tools while addressing a timely grid-integration challenge.

major comments (2)

[Abstract and §3] Abstract and §3 (Model Formulation): The guarantee that reconnection after T_crit keeps the trajectory inside operational limits and the region of attraction relies on the SMIB-style model with constant-power load and voltage-angle coupling accurately determining the electrical power step at reconnection. The manuscript does not quantify sensitivity of T_crit to deviations from these assumptions (e.g., ZIP load behavior, voltage dynamics, or power-electronics controls), which would alter both the post-reconnection equilibrium and the energy level at the reconnection instant. This directly affects the load-bearing claim of a guaranteed safe window.
[§4 and §5] §4 (Energy Function Derivation) and §5 (Validation): The critical time is obtained by ensuring the state reached under disconnection dynamics lies below the energy level of the post-reconnection saddle point. However, without an explicit sensitivity study or robustness check against model mismatch (e.g., varying the voltage-angle coupling term), it is unclear whether the analytically computed T_crit remains valid when the actual load deviates from the constant-power assumption used to define the equilibrium and energy function.

minor comments (2)

[§4] The notation for the critical reconnection time T_crit and the energy function V(·) should be introduced with a dedicated equation number in §4 to improve traceability when referring to the bound in the validation section.
[§5] Figure captions for the time-domain simulation results should explicitly state the parameter values (e.g., inertia, damping, load magnitude) used so readers can reproduce the match between analytical T_crit and simulated trajectories.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the positive assessment of the significance of our work and for the constructive feedback. We address the major comments below, agreeing that further discussion on model assumptions is warranted. We have revised the manuscript to include additional text clarifying the scope of the guarantees and discussing sensitivity to deviations from the constant-power assumption.

read point-by-point responses

Referee: [Abstract and §3] Abstract and §3 (Model Formulation): The guarantee that reconnection after T_crit keeps the trajectory inside operational limits and the region of attraction relies on the SMIB-style model with constant-power load and voltage-angle coupling accurately determining the electrical power step at reconnection. The manuscript does not quantify sensitivity of T_crit to deviations from these assumptions (e.g., ZIP load behavior, voltage dynamics, or power-electronics controls), which would alter both the post-reconnection equilibrium and the energy level at the reconnection instant. This directly affects the load-bearing claim of a guaranteed safe window.

Authors: We thank the referee for this observation. The proposed framework provides an analytical criterion under the modeling assumptions stated in the abstract and Section 3, namely the SMIB representation with constant-power load and the associated voltage-angle coupling. The energy-function-based bound on T_crit is guaranteed to be safe within this model. We acknowledge that deviations from constant-power behavior (e.g., ZIP loads or dynamic voltage effects) would change the post-reconnection equilibrium and the energy function, potentially affecting the numerical value of T_crit. In the revised manuscript, we have added a paragraph in Section 5 explicitly stating the assumptions and noting that the framework can serve as a starting point for more detailed models, where T_crit would be recomputed accordingly. A comprehensive sensitivity analysis is left for future work as it would require integrating detailed power-electronics models. revision: yes
Referee: [§4 and §5] §4 (Energy Function Derivation) and §5 (Validation): The critical time is obtained by ensuring the state reached under disconnection dynamics lies below the energy level of the post-reconnection saddle point. However, without an explicit sensitivity study or robustness check against model mismatch (e.g., varying the voltage-angle coupling term), it is unclear whether the analytically computed T_crit remains valid when the actual load deviates from the constant-power assumption used to define the equilibrium and energy function.

Authors: We agree that an explicit robustness check would be valuable. The derivation in Section 4 relies on the energy function constructed for the constant-power load model. In the revised version, we have included in Section 5 a brief robustness discussion, including a qualitative analysis of how changes in the voltage-angle coupling would shift the saddle-point energy and thus T_crit. We also note that the time-domain simulations in the paper use the same model assumptions for validation, consistent with the analytical derivation. For cases with significant model mismatch, we recommend using the proposed method with updated model parameters. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation applies standard energy-function stability analysis to SMIB model

full rationale

The paper constructs an SMIB-style model with swing dynamics during disconnection and voltage-angle coupling for the reconnection power step under constant-power load. It then applies the classical energy-function method to compute the region of attraction of the post-reconnection equilibrium and defines the critical safe reconnection time as the instant when the disconnected trajectory enters that region. This is a direct, non-fitted application of Lyapunov theory; the critical time is not obtained by regressing on the same data it is meant to predict, nor does any step reduce to a self-definition or self-citation chain. Time-domain simulations serve only as external validation. The derivation chain is therefore self-contained against the stated model assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on the classical SMIB swing model and constant-power load assumption; no new free parameters or invented entities are introduced beyond the standard energy-function critical energy.

axioms (2)

domain assumption The system can be represented by a classical single-machine infinite-bus swing equation during the disconnection interval.
Invoked in the modeling section of the abstract.
domain assumption Load is constant-power, so reconnection produces a step change in electrical power determined by voltage-angle coupling at the load bus.
Stated explicitly in the abstract as the basis for the power step at reconnection.

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discussion (0)

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

Voltage Ride-Through in Large Loads- A Dual PQ Approach
eess.SY 2026-05 unverdicted novelty 5.0

The paper proposes a dual PQ approach for voltage ride-through in large loads, showing that traditional reactive power compensation is limited by infrastructure constraints and that extreme dips may force disconnection.

Reference graph

Works this paper leans on

18 extracted references · cited by 1 Pith paper

[1]

Electricity 2024: Analysis and forecast to 2026,

International Energy Agency, “Electricity 2024: Analysis and forecast to 2026,” tech. rep., IEA, 2024

2024
[2]

Energy and AI,

International Energy Agency, “Energy and AI,” tech. rep., IEA, 2024

2024
[3]

Impact of high penetration of renewable energy sources on grid frequency behaviour,

S. Saha, M. I. Saleem, and T. K. Roy, “Impact of high penetration of renewable energy sources on grid frequency behaviour,”International Journal of Electrical Power & Energy Systems, vol. 145, p. 108701, 2023

2023
[4]

Optimizing frequency stability with adaptive fast frequency reserves and Wide- Area Monitoring Systems,

B. Elenga Baningobera, I. Oleinikova, and K. Uhlen, “Optimizing frequency stability with adaptive fast frequency reserves and Wide- Area Monitoring Systems,”International Journal of Electrical Power & Energy Systems, vol. 171, p. 110951, 2025

2025
[5]

Uninterruptible power supply systems provide protection,

J. M. Guerrero, L. G. de Vicu ˜na, and J. Uceda, “Uninterruptible power supply systems provide protection,”IEEE Industrial Electronics Magazine, vol. 1, no. 1, pp. 28–38, 2007

2007
[6]

Control of distributed un- interruptible power supply systems,

J. M. Guerrero, L. Hang, and J. Uceda, “Control of distributed un- interruptible power supply systems,”IEEE Transactions on Industrial Electronics, vol. 55, no. 8, pp. 2845–2859, 2008

2008
[7]

IEC 62040-3:2021 uninterruptible power systems (UPS) – Part 3: Method of specifying the performance and test requirements,

“IEC 62040-3:2021 uninterruptible power systems (UPS) – Part 3: Method of specifying the performance and test requirements,” 2021

2021
[8]

IEEE Std 1159-2019: Recommended practice for monitoring electric power quality,

“IEEE Std 1159-2019: Recommended practice for monitoring electric power quality,” 2019

2019
[9]

Kundur,Power System Stability and Control

P. Kundur,Power System Stability and Control. McGraw-Hill, 1992

1992
[10]

Data center model for transient stability analysis of power systems

A. Jimenez-Ruiz and F. Milano, “Data center model for transient stability analysis of power systems.” arXiv preprint, May 2025. Accessed 2026- 01-15

2025
[11]

Impact of converter-based demand on frequency quality in the ireland and northern ireland power systems

T. K ¨erc ¸i, C. Duggan, U. Farooq, S. Tweed, and M. Val Escudero, “Impact of converter-based demand on frequency quality in the ireland and northern ireland power systems.” CIGRE publication page (Session paper), 2024. Ref. C4-10907-2024. Accessed 2026-01-15

2024
[12]

Direction to the system operators related to data centre grid connection processing,

“Direction to the system operators related to data centre grid connection processing,” Tech. Rep. CRU/21/124, Commission for Regulation of Utilities (CRU), Ireland, Dublin, Ireland, Nov. 2021. Decision Paper. Accessed 2026-01-15

2021
[13]

Phase and amplitude synchronization in power-grid frequency fluctuations in the nordic grid,

L. R. Gorj ˜ao, L. Vanfretti, D. Witthaut, C. Beck, and B. Sch ¨afer, “Phase and amplitude synchronization in power-grid frequency fluctuations in the nordic grid,”IEEE Access, vol. 10, pp. 18065–18073, 2022

2022
[14]

M. A. Pai,Energy Function Analysis for Power System Stability. Springer, 1989

1989
[15]

Standard load models for power flow and dynamic performance simulation,

W. W. Price, C. W. Taylor, and G. J. Rogers, “Standard load models for power flow and dynamic performance simulation,”IEEE Trans. Power Syst., vol. 10, pp. 1302–1313, Aug. 1995

1995
[16]

PRC-024-3 — Gener- ator Frequency and V oltage Protective Relay Settings,

North American Electric Reliability Corporation, “PRC-024-3 — Gener- ator Frequency and V oltage Protective Relay Settings,” tech. rep., 2021

2021
[17]

IEEE Guide for Abnormal Frequency Protection for Power Generating Plants,

“IEEE Guide for Abnormal Frequency Protection for Power Generating Plants,” Tech. Rep. C37.106-2003 (R2018), IEEE, 2018

2003
[18]

P. W. Sauer, M. A. Pai, and J. H. Chow,Power System Dynamics and Stability: With Synchrophasor Measurement and Power System Toolbox. Wiley-IEEE Press, 2 ed., 2017

2017