pith. sign in

arxiv: 2604.06624 · v1 · submitted 2026-04-08 · 📡 eess.SY · cs.SY

Dynamic Modeling of Data-Center Power Delivery for Power System Resonance Analysis

Xingyu Zhao , Junbo Zhao This is my paper

Pith reviewed 2026-05-10 18:27 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords data centerpower system dynamicsresonance analysisdynamic modelingpositive-sequence modeloscillation propagationpower electronicsgrid stability
0
0 comments X

The pith

An explicit dynamic model of data-center power delivery shows how server load fluctuations excite coupled control modes and propagate oscillations in mixed-resource grids.

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

This paper derives a component-level dynamic model of the full power-delivery chain inside data centers so that its interactions with the surrounding power system can be studied analytically. The model keeps the details of each stage's power electronics and controls while converting everything into a time-invariant positive-sequence form that plugs directly into standard phasor-domain grid simulators. A sympathetic reader would care because the derivation identifies concrete frequencies at which realistic server-load changes can drive resonance, amplification, and propagation through grids that contain both synchronous machines and inverter resources. The work therefore supplies a practical tool for predicting when data-center growth will create new stability problems.

Core claim

The paper derives an explicit, component-informed dynamic model of data-center power-delivery chains that preserves component-level fidelity and captures inter-stage control interactions. Formulated as a time-invariant representation in the positive-sequence domain, the model integrates with phasor-domain power-system dynamic models and reveals that realistic server-load fluctuations at specific frequencies excite coupled control modes, inducing oscillation amplification and propagation in power grids that contain heterogeneous dynamic resources including synchronous machines and grid-forming or grid-following inverters.

What carries the argument

The time-invariant positive-sequence domain representation of the data-center power-delivery chain, which assembles component dynamics and control loops into a single grid-integratable model.

If this is right

  • The model integrates directly with existing phasor-domain simulators to perform system-wide resonance analysis.
  • Server-load fluctuations at particular frequencies are shown to excite specific coupled control modes inside the delivery chain.
  • Oscillation amplification and propagation occur in grids containing both synchronous machines and grid-forming or grid-following inverters.
  • Case studies using realistic data-center measurements on test systems confirm that the derived model reproduces the expected dynamic behavior.

Where Pith is reading between the lines

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

  • Grid planners could use the frequency-specific signatures identified by the model to set monitoring thresholds for data-center sites.
  • The same component-by-component assembly method might be applied to other large power-electronic loads whose internal controls are currently treated as black boxes.
  • Validation against electromagnetic-transient simulations at the same operating points would test whether the positive-sequence reduction preserves the critical resonance paths.

Load-bearing premise

The time-invariant positive-sequence domain representation accurately captures the multi-timescale dynamics and inter-stage control interactions of the data-center power delivery chain without significant loss of fidelity for resonance analysis.

What would settle it

A side-by-side comparison in which measured resonance frequencies and amplification factors in a real grid with operating data centers fail to match the frequencies and gains predicted by the model at the observed bands of server-load fluctuation.

Figures

Figures reproduced from arXiv: 2604.06624 by Junbo Zhao, Xingyu Zhao.

Figure 1
Figure 1. Figure 1: The modern data-center power-delivery system operating in online (double-conversion) mode [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: The control and circuit diagram of a three-phase PWM VSI [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: The control and circuit diagram of per-phase downstream DC–DC [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Comparison between the full-order three-phase model and the reduced model under a step change in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Applying participation-factor analysis, we identify the [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) POA factor as a function of frequency, with a peak at 5.54 Hz. (b) Time-domain POA simulation under sinusoidal server-load variations. [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Top-6 eigenvalue trajectories (top row) and corresponding POA curves (bottom row) under varying system conditions: (a),(d) VSI voltage-controller [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Realistic GPU-induced PCC power profile: (a) time-domain simulation. (b) single-sided frequency spectrum from FFT for [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Modified 3-machine 9-bus system. at several frequencies, with the POA factor in [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Eigenvalue map with coupling visualization of the modified 3-machine 9-bus system [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: POA from server load to SM, GFM, GFL, and data center port [PITH_FULL_IMAGE:figures/full_fig_p010_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Realistic GPU-induced PCC active power of the multi-machine case [PITH_FULL_IMAGE:figures/full_fig_p010_14.png] view at source ↗
read the original abstract

The rapid proliferation of data centers is reshaping modern power system dynamics. Unlike legacy industrial loads, data centers have power-electronic interfaces whose multi-timescale dynamics can interact strongly with the grid, inducing oscillatory behavior. However, analytical models that are grid-integratable for revealing the underlying resonance mechanisms remain largely unexplored. To fill this research gap, this paper derives an explicit, component-informed dynamic model of data-center power-delivery chains, which preserves component-level fidelity and captures inter-stage control interactions. This model is formulated as a time-invariant representation in the positive-sequence domain, enabling seamless integration with the phasor (or RMS) domain power-system dynamic models. The analytical derivation reveals how realistic server-load fluctuations at specific frequencies can excite coupled control modes, thereby inducing oscillation amplification and propagation in power grids with heterogeneous dynamic resources, including synchronous machines and grid-forming/following inverters. Case studies on test systems with some realistic data center data demonstrate the effectiveness of the proposed solutions.

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 / 1 minor

Summary. The paper derives an explicit, component-informed dynamic model of data-center power-delivery chains formulated as a time-invariant representation in the positive-sequence domain. This enables integration with phasor-domain power-system models and is used to show how realistic server-load fluctuations at specific frequencies can excite coupled control modes, leading to oscillation amplification and propagation in grids containing synchronous machines and grid-forming/following inverters. Effectiveness is illustrated through case studies on test systems incorporating realistic data-center data.

Significance. If the positive-sequence model retains sufficient fidelity, the work provides a practical bridge between detailed power-electronic component dynamics and grid-level resonance analysis, addressing an increasingly relevant class of loads. The explicit derivation and focus on inter-stage control interactions represent a clear advance over purely numerical or black-box approaches.

major comments (2)
  1. [Model derivation (positive-sequence transformation)] The central modeling step that converts multi-timescale power-electronic and control dynamics into a time-invariant positive-sequence form is load-bearing for the resonance claim, yet the manuscript supplies no quantitative error bound or comparison against a full three-phase time-domain reference that retains harmonics and unbalanced currents. Server loads routinely generate switching harmonics and negative-sequence components; without an explicit assessment of how these are averaged out or neglected, it remains unclear whether the derived equations understate or miss actual resonance paths.
  2. [Case studies] The case-study section reports that the model 'demonstrates effectiveness' but provides no validation metrics (e.g., resonance-frequency error, damping-ratio match, or amplification-factor comparison against detailed EMT simulation). Without these numbers or an accompanying sensitivity study on the balanced-operation assumption, the claim that load fluctuations at specific frequencies induce observable mode coupling cannot be rigorously evaluated.
minor comments (1)
  1. [Abstract] The abstract refers to 'some realistic data center data' without identifying the source, sampling rate, or statistical properties of the load fluctuations; adding this information would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. The points raised regarding model validation and case-study metrics are well taken, and we will incorporate revisions to strengthen these aspects. Below we respond point by point to the major comments.

read point-by-point responses

  1. Referee: [Model derivation (positive-sequence transformation)] The central modeling step that converts multi-timescale power-electronic and control dynamics into a time-invariant positive-sequence form is load-bearing for the resonance claim, yet the manuscript supplies no quantitative error bound or comparison against a full three-phase time-domain reference that retains harmonics and unbalanced currents. Server loads routinely generate switching harmonics and negative-sequence components; without an explicit assessment of how these are averaged out or neglected, it remains unclear whether the derived equations understate or miss actual resonance paths.

    Authors: We acknowledge that the manuscript lacks a quantitative error assessment for the positive-sequence transformation. In the revised version we will add a validation subsection that compares the derived model against a detailed three-phase EMT simulation of a representative data-center power-delivery chain under balanced conditions. This will report resonance-frequency deviation and damping-ratio error. We will also clarify that the positive-sequence formulation follows standard practice for fundamental-frequency resonance studies, where switching harmonics are attenuated by filters and negative-sequence components are assumed negligible under balanced operation; the model targets inter-stage control interactions at the frequencies of interest for grid resonance. revision: yes

  2. Referee: [Case studies] The case-study section reports that the model 'demonstrates effectiveness' but provides no validation metrics (e.g., resonance-frequency error, damping-ratio match, or amplification-factor comparison against detailed EMT simulation). Without these numbers or an accompanying sensitivity study on the balanced-operation assumption, the claim that load fluctuations at specific frequencies induce observable mode coupling cannot be rigorously evaluated.

    Authors: We agree that explicit quantitative metrics and sensitivity analysis are required. We will revise the case-study section to include direct EMT comparisons, reporting resonance-frequency error, damping-ratio match, and amplification-factor values. A sensitivity study on the balanced-operation assumption will be added to quantify the impact of small unbalances on the observed mode-coupling behavior. revision: yes

Circularity Check

0 steps flagged

Derivation from component models to positive-sequence form is self-contained with no circular reductions

full rationale

The paper states it derives an explicit dynamic model starting from component-level models of the data-center power-delivery chain, then transforms them into a time-invariant positive-sequence representation. No equations or steps in the abstract or description reduce by construction to fitted parameters, self-definitions, or load-bearing self-citations; the resonance analysis follows directly from applying the derived model to load fluctuations. This matches the default case of a non-circular modeling derivation that preserves independent content from first-principles components.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard power-electronics component models and the domain assumption that positive-sequence phasor representation suffices for the targeted resonance phenomena; no free parameters or invented entities are identifiable from the abstract.

axioms (1)
  • domain assumption Positive-sequence domain representation is sufficient to capture the relevant multi-timescale dynamics and resonance mechanisms
    Invoked to enable seamless integration with phasor-domain power-system models.

pith-pipeline@v0.9.0 · 5460 in / 1172 out tokens · 64260 ms · 2026-05-10T18:27:39.996638+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages · 1 internal anchor

  1. [1]

    Paris, France, Apr

    IEA,Energy and AI. Paris, France, Apr. 2025

    work page 2025

  2. [2]

    Forced oscillations in power systems induced by AI workloads in data centers,

    G. Valverde, G. Pierrou, J. Krajacic, and G. Hug, “Forced oscillations in power systems induced by AI workloads in data centers,” TechRxiv, Oct. 2025

    work page 2025

  3. [3]

    NERC,Reliability Guideline: Risk Mitigation for Emerging Large Loads, May 2026

    work page 2026

  4. [4]

    Understanding the inception of 14.7 Hz oscillations emerging from a data center,

    C. Mishra, L. Vanfretti, J. Delaree Jr., T. J. Purcell, and K. D. Jones, “Understanding the inception of 14.7 Hz oscillations emerging from a data center,”Sustainable Energy, Grids and Networks, vol. 43, Art. no. 101735, Sep. 2025

    work page 2025

  5. [5]

    Wide-Area Power System Oscillations from Large-Scale AI Workloads

    M.-S. Ko and H. Zhu, “Wide-area power system oscillations from large- scale AI workloads,” arXiv preprint arXiv:2508.16457, 2025

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  6. [6]

    Data center power system stability—Part I: Power supply impedance modeling,

    J. Sun, M. Xu, M. Cespedes, and M. Kauffman, “Data center power system stability—Part I: Power supply impedance modeling,”CSEE J. Power Energy Syst., vol. 8, no. 2, pp. 403–419, Mar. 2022

    work page 2022

  7. [7]

    Data center power system stability—Part II: System modeling and analysis,

    J. Sun, M. Mihret, M. Cespedes, D. Wong, and M. Kauffman, “Data center power system stability—Part II: System modeling and analysis,” CSEE J. Power Energy Syst., vol. 8, no. 2, pp. 420–438, Mar. 2022

    work page 2022

  8. [8]

    Data center model for transient stability analysis of power systems,

    A. Jim ´enez-Ruiz and F. Milano, “Data center model for transient stability analysis of power systems,”arXiv preprint, arXiv:2505.16575, May 2025

    work page arXiv 2025

  9. [9]

    Dynamic modeling of a data center for power system stability studies,

    P. P. Gyang, P. Chakraborty, L. G. Meegahapola, and X. Yu, “Dynamic modeling of a data center for power system stability studies,”IEEE Trans. Power Syst., 2025

    work page 2025

  10. [10]

    Dynamic model and converter-based emulator of a data center power distribution system,

    J. Sun, S. Wang, J. Wang, and L. M. Tolbert, “Dynamic model and converter-based emulator of a data center power distribution system,” IEEE Trans. Power Electron., vol. 37, no. 7, pp. 8420–8432, Jul. 2022

    work page 2022

  11. [11]

    B. A. Ross and J. D. Follum,Electromagnetic Transient Modeling of Large Data Centers for Grid-Level Studies (Alpha Release). Richland, W A, USA: Pacific Northwest National Laboratory, Rep. PNNL-38817, Dec. 2025

    work page 2025

  12. [12]

    MIT Supercloud Dataset,

    MIT AI Accelerator, “MIT Supercloud Dataset,” [Online]. Available: https://github.com/MIT-AI-Accelerator/MIT-Supercloud-Dataset

    work page

  13. [13]

    Investigation of AI Data Center Load Impact on Power System Fre- quency Using Real-World Datasets,

    C. Aghadinuno, S. Ahmed, M. Alamaniotis, B. Wang, and N. Gatsis, “Investigation of AI Data Center Load Impact on Power System Fre- quency Using Real-World Datasets,” inProc. 18th Annual IEEE Green Technologies Conference (GreenTech), Boulder, CO, USA, 2026. SUBMITTED TO IEEE TRANSACTIONS ON POWER SYSTEMS 1 Supplementary Material for “Dynamic Modeling of D...

    work page 2026

  14. [14]

    Synchronous Machine with Exciter and Governor: Differential Eqs. 1 ωb dδ dt =ω−ω s (S4a) 2H dω dt =τm −τe −D(ω−ω s)(S4b) T ′ d0 de′ q dt =−e′ q −(xd −x′ d)id+ef d (S4c) T ′ q0 de′ d dt =−e′ d+(xq −x′ q)iq (S4d) Te def d dt =− ke+se(ef d) ef d+vr (S4e) Tf dvf dt =−vf + kf Te vr − kf Te ke+se(ef d) ef d (S4f) Ta dvr dt =−vr+ka(vref −vf −vt)(S4g) Tsv dpsv dt...

    work page

  15. [15]

    Grid-Forming Inverter: Differential Eqs. 1 ωb dθgfm oc dt =ωgfm oc −ωs (S5a) 1 ωgfm z dpoc,gfm dt =pf,gfm −poc,gfm (S5b) 1 ωgfm f dqoc,gfm dt =qf,gfm −qoc,gfm (S5c) dξgfm dt =vgfm vi −vgfm f (S5d) dγgfm dt =igfm ref −igfm cv (S5e) ℓgfm f ωb digfm cv dt =vgfm cv −vgfm f −rgfm f igfm cv −ωgfm oc ℓgfm f J igfm cv (S5f) cgfm f ωb dvgfm f dt =igfm cv −igfm g −...

    work page

  16. [16]

    Grid-Following Inverter: Differential Eqs. 1 ωb dθgfl pll dt =ωgfl pll −ωs (S6a) 1 ωgfl lp dvgfl q,pll dt =vf,gfl q −vgfl q,pll (S6b) dϵgfl dt =vgfl q,pll (S6c) dσgfl p dt =pref,gfl −pm (S6d) 1 ωgfl z dpm dt =(vgfl f )⊤igfl g −pm (S6e) dσgfl q dt =qref,gfl −qm (S6f) 1 ωgfl f dqm dt =(vgfl f )⊤J igfl g −qm (S6g) dγgfl dt =igfl ref −igfl cv (S6h) ℓgfl f ωb ...

    work page