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

This repository contains the supplementary MATLAB code for the manuscript:

Xingyu Zhao and Junbo Zhao, "Dynamic Modeling of Data-Center Power Delivery for Power System Resonance Analysis," arXiv:2604.06624v1, 2026.
Manuscript: https://arxiv.org/html/2604.06624v1

The code implements the numerical studies associated with the paper's component-informed data-center power-delivery model and its integration into positive-sequence power-system dynamic analysis. The repository is code-only: generated figures, generated CSV outputs, MATLAB autosave files, and raw workload traces were intentionally removed.

Paper context

The paper develops a dynamic model of the online, double-conversion data-center power-delivery chain and uses it for power-system oscillation studies. The modeled chain includes:

1. an active front-end (AFE) rectifier connected to the grid-side point of common coupling (PCC),
2. a UPS DC-link capacitor,
3. a voltage-source inverter (VSI),
4. an aggregated PSU-array equivalent, and
5. a downstream DC-DC/load equivalent representing server-side CPU/GPU demand.

The model is formulated as a time-invariant positive-sequence representation so that it can be combined with phasor-domain grid models and reduced to a small-signal state-space model. The scripts in this repository support the main numerical workflows in the paper:

• equilibrium computation of the nonlinear data-center/grid model,
• bandwidth-based PI-controller tuning,
• comparison between full three-phase and reduced positive-sequence/QSS models,
• eigenvalue and participation-factor analysis,
• power oscillation amplification (POA) analysis from server-load disturbance to grid-visible active power, and
• time-domain simulations driven by sinusoidal or GPU-workload load variations.

Repository layout

TPWRS_DataCenter_SupplementalCode/
├── README.md
├── .gitignore
├── .gitattributes
└── src/
    ├── case9/
    │   ├── case9.m
    │   ├── datacenter_init_from_pf_qss.m
    │   ├── datacenter_port_model.m
    │   ├── default_datacenter_params.m
    │   ├── gfl_init_from_pf_qss_newton.m
    │   ├── gfl_port_model.m
    │   ├── gfm_init_from_pf_qss_newton.m
    │   ├── gfm_port_model.m
    │   ├── sm_init_from_pf_fsolve.m
    │   └── sm_port_model.m
    └── sdcib/
        ├── SDCIB.m
        ├── SDCIB_simplified_eigs_step.m
        ├── ModelValidation.m
        └── gpu_load_response.m

Code-to-paper map

Paper component	Main script(s)	Description
Component-level data-center model	src/sdcib/SDCIB.m, src/case9/datacenter_port_model.m	Implements the reduced positive-sequence data-center power-delivery model with AFE, DC link, VSI, PSU, and downstream DC-DC/load states.
Model validation in the SDCIB case	src/sdcib/ModelValidation.m	Compares the full cascaded three-phase representation with the reduced QSS/positive-sequence model under a load step. This corresponds to the validation study in the SDCIB section of the paper.
SDCIB modal, participation, and POA analysis	src/sdcib/SDCIB.m	Computes the equilibrium, linearizes the model, evaluates eigenvalues and participation factors, computes POA curves, and performs parameter scans over controller bandwidth, load level, and grid strength.
Simplified SDCIB load-step example	src/sdcib/SDCIB_simplified_eigs_step.m	Provides a compact eigenvalue/participation-factor workflow and a reduced load-step response example.
Realistic GPU-load time-domain response in SDCIB	src/sdcib/gpu_load_response.m	Uses an external GPU-load trace to simulate workload-induced propagation from server load to PCC power and to compute FFT spectra.
Modified 3-machine 9-bus grid-integration case	src/case9/case9.m	Builds the modified 9-bus system with a synchronous machine, a grid-forming inverter, a grid-following inverter, and the data-center load at Bus 8; then performs modal/POA analysis and GPU-load time-domain simulation.
SM/GFM/GFL/data-center dynamic port models	src/case9/*_port_model.m, src/case9/*_init_*.m	Initialization and dynamic port-equation routines used by the 9-bus study.

Main workflows

1. Single-data-center infinite-bus case

The SDCIB scripts study the intrinsic oscillatory behavior of the data-center power-delivery chain when the data center is connected to an infinite bus through a Thevenin impedance. This workflow is useful for isolating data-center internal modes before coupling the model to a larger grid.

Recommended run order:

cd src/sdcib
ModelValidation
SDCIB_simplified_eigs_step
SDCIB

ModelValidation.m compares the full three-phase model and the reduced QSS positive-sequence model. SDCIB.m then computes eigenvalues, participation factors, POA curves, controller/load/grid-strength sensitivity scans, and sinusoidal load-response examples.

2. Realistic GPU-workload response

Two scripts use a time-varying GPU-load trace:

cd src/sdcib
gpu_load_response

cd src/case9
case9

These scripts require an external file named GPU_data.csv in the current MATLAB working directory. The expected columns are:

t_seconds,P_gpu_W

The raw workload trace is not included in this code-only release. When using your own trace, keep the same column names or modify the corresponding readtable section in the scripts.

3. Modified 3-machine 9-bus case

The 9-bus workflow is implemented in:

cd src/case9
case9

This script:

1. solves the power flow of the modified 9-bus system,
2. performs Kron reduction for the retained dynamic ports,
3. initializes the synchronous-machine, GFM, GFL, and data-center port models,
4. forms the reduced small-signal model,
5. computes eigenvalues and modal participation/coupling information,
6. computes POA transfer gains from data-center load variation to multiple grid-side ports, and
7. runs a GPU-load-driven time-domain simulation when GPU_data.csv is available.

In the included setup, the data-center load is connected at Bus 8. The three dynamic generation units are represented by a synchronous-machine model, a grid-forming inverter model, and a grid-following inverter model.

MATLAB requirements

Recommended environment:

• MATLAB R2022b or newer.
• Optimization Toolbox, required for fsolve and optimoptions.

The scripts also use standard MATLAB functionality including ode15s, readtable, writetable, eig, fft, plotting routines, and script-local functions. No Simulink model or third-party package is included.

This repository was prepared as a clean code release. The numerical cases were not re-run during packaging.

Generated files

The following files may be generated when running the scripts and are ignored by Git:

eigvals_sorted.csv
participation_abs_norm.csv
*.fig
*.png
*.pdf
*.asv

If exact figure reproduction is needed, run the scripts from their respective folders and save the generated figures manually.

Notes on modifying experiments

Common parameters are defined near the beginning of each main script. Useful entries include:

• p.p_load0, p.p_load1, and p.sin_amp in the SDCIB scripts,
• controller bandwidth targets in the tg structure of SDCIB.m,
• grid impedance or SCR-related parameters in SDCIB.m,
• scale_lev and Bus 8 data-center loading in case9.m, and
• the parameter structure returned by src/case9/default_datacenter_params.m.

For a new workload trace, place the data in GPU_data.csv or adjust the file name and column names in the scripts that call readtable.

Citation

If this code is used in academic work, please cite the associated manuscript:

@article{zhao2026datacenter,
  title   = {Dynamic Modeling of Data-Center Power Delivery for Power System Resonance Analysis},
  author  = {Zhao, Xingyu and Zhao, Junbo},
  journal = {arXiv preprint arXiv:2604.06624},
  year    = {2026}
}

License

No license file is included in this packaged code release. Add a LICENSE file before making the repository public if a specific open-source license is intended.