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Trajectory Sensitivity-Based Dynamic Assessment of an AI Data Center Under Contingencies
Arnav Bagga, Saskia A. Putri, Abhishek Banerjee, Xiaofan Wu
TL;DR
Detailed AI data-center models make repeated nonlinear time-domain simulation costly across outages, workload variations, and parameter perturbations. The paper computes disturbance-conditioned trajectory sensitivities for a self-contained data center and uses them to estimate perturbed responses. The estimates closely track nonlinear simulations, while new responses can be computed in milliseconds once sensitivities are available.
Problem
Repeated nonlinear time-domain simulations for each outage, load realization, and parameter perturbation are computationally burdensome for detailed AI data-center models.
Source: §I · p. 1Method
The framework computes trajectory sensitivities for disturbances in a self-contained AI data center and uses them to estimate trajectories under simultaneous parameter perturbations.
Source: §I · pp. 1–2Results
TS-predicted trajectories closely match full nonlinear ODE responses under studied disturbances, and a new perturbed trajectory takes 25 ms, about 400× faster than full nonlinear simulation.
Source: C. Validation With Simultaneous… · p. 5, D. Computational Advantage · p. 5Takeaways & Limitations
The approach is suited to rapid post-disturbance screening when many parameter sets, outage combinations, or workload realizations must be evaluated.
Source: §V · p. 5
Abstract
from arXiv · showhide
Artificial Intelligence (AI) data centers are emerging as converter-dominated, parameter-rich electrical systems whose dynamic response depends on fast workload-driven demand variations, tightly regulated data-hall converters, and coordinated on-site sources. Assessing such systems by repeatedly solving nonlinear time-domain models for every outage, load realization, and parameter perturbation is computationally expensive and provides limited insight into response sensitivity. This paper presents a trajectory sensitivity (TS)-based dynamic assessment framework for a self-contained AI data center supplied by a 2 kV DC microgrid with a grid-tied interface. The model includes time-varying data-hall load profiles, a voltage source converter (VSC), battery energy storage systems (BESS) units, supercapacitors, and synchronous-generation-side sources. For each disturbance, firstly, TS are computed along the nonlinear disturbance trajectory, capturing the local effect of source trips, data-hall outages, converter controls, and load ramps. Later, the computed TS data is used to estimate system trajectories under simultaneous parameter perturbations. Validation against full nonlinear ODE simulations with $\pm 15\%$ perturbations shows close agreement. In addition, the TS-based approach reduces computational time of dynamic-response evaluations from seconds to milliseconds, demonstrating its potential as a scalable screening tool for AI data center dynamics.
I. Introduction
Detailed AI data-center dynamics make repeated nonlinear simulations burdensome, while trajectory sensitivity analysis offers a way to assess disturbance responses along their evolving trajectories. The paper applies this approach to a self-contained, time-varying AI data-center model and evaluates its use for estimating perturbed responses.
I. Introduction
- Each outage, data-hall trip, load ramp, controller setting, or uncertain parameter may require a separate nonlinear simulation, motivating a faster assessment approach.AI data centers combine tightly regulated power-electronic interfaces, hierarchical controls, storage, backup sources, and rapidly changing demand, which can interact during disturbances.Source: §I · p. 1
- Trajectory sensitivity analysis linearizes the nonlinear response along a simulated trajectory, rather than around an equilibrium point.Its application to AI data-center dynamic assessment remains largely unexplored.Source: §I · p. 1
- The framework studies a self-contained AI data center supplied through a 2 kV DC microgrid, with time-varying loads, storage, a grid-tied converter, and synchronous-generation-side sources.The paper identifies this as a first application of trajectory sensitivity to an AI data-center model with time-varying data-hall profiles and ramps rather than fixed demand or a single operating point.Source: §I · pp. 1–2
- The work lays a foundation for using trajectory sensitivity as a dynamic assessment tool for AI data centers with detailed converter-interfaced source and load models.The introduction frames the approach as a way to assess dynamic responses without repeatedly solving the full nonlinear model for every perturbation.Source: §I · pp. 1–2
- Disturbance-conditioned sensitivities are computed for data-hall outages and source-side trips, then used to estimate trajectories under simultaneous parameter perturbations and validated against nonlinear ODE simulations.The estimates support assessment of DC-bus voltage, source currents, data-hall converter states, and grid-interface variables during high-impact disturbances.Source: §I · p. 2
II. AI Data Center System Description
The system description models a 2 kV DC microgrid linking a grid interface, on-site sources, and two converter-fed data halls. Its controls coordinate grid support and source-specific voltage-droop roles around a shared DC bus.
System architecture
- The 2 kV common DC bus connects the utility-grid VSC, four synchronous-generator sources, two supercapacitors, four BESS units, and two independently varying data halls.Each hall is supplied through a tightly regulated 800 V buck converter; the grid interface connects to a 25 kVac grid through an impedance, filter, and transformer.Source: §II · p. 2
Grid-interface control
- The grid-tied VSC supplies scheduled base power and supplementary voltage support, while its outer DC-voltage loop sets grid-to-DC power and PI terms provide corrective regulation.Positive grid-to-DC power denotes import from the AC grid into the DC bus.Source: §II · p. 2
On-site source control
- On-site BESS, supercapacitor, and generator sources use a common voltage-restoration signal with source-specific virtual droop, represented through equivalent series R–L branches.BESS virtual impedance supports medium-frequency balancing, supercapacitor capacitive droop provides fast transient support, and generator resistive droop supports base-load sharing.Source: §II · p. 2
Data-hall loads
- Each data hall is modeled as a constant-power load with a time-varying demand profile and averaged buck-converter dynamics for load-side voltage and current.The profiles are curated to reflect rapid load ramps and high noise amplitude reported for large-scale data-center demand.Source: §II · p. 3, Figure 2 · p. 3
DC-bus model
- The common DC-bus voltage is modeled by an equivalent-capacitance current balance combining BESS, supercapacitor, generator-side, and grid-interface currents.The bus capacitance is Ceq, and the current terms represent outputs from the respective source classes and the grid-tied VSC.Source: §II · p. 3
III. Trajectory Sensitivity-based Method
The method builds a disturbance-conditioned, trajectory-local linear representation of the nonlinear system response. Once sensitivities are computed, it uses them to estimate trajectories under simultaneous parameter changes and checks those estimates against nonlinear simulations.
III. Trajectory Sensitivity-based Method
- The method represents each disturbance response as a nonlinear flow map from the initial condition and parameter vector to monitored system trajectories.The nominal parameter vector defines the reference trajectory for each disturbance scenario.Source: §III · p. 3
- Sensitivities are computed numerically by perturbing one candidate parameter at a time and comparing trajectories from the same warm-start initial condition.Each parameter perturbation is 2% of its nominal value.Source: §III · p. 3
- For each contingency, the workflow simulates the nonlinear model at nominal parameters, perturbs only one parameter at a time, assembles TS tensors, predicts a simultaneous-perturbation trajectory, and compares it with nonlinear simulation.Source: §III · p. 4
- After the disturbance-conditioned TS database is available, matrix-vector operations estimate perturbed responses without another full nonlinear simulation.The representation is built around the actual pre- and post-disturbance trajectory.Source: §III · pp. 3–4
- A close match between TS estimates and independent nonlinear simulations verifies sensitivity accuracy for the selected disturbance and checks the approximation’s useful linear range.Validation uses larger simultaneous parameter perturbations than those used to compute TS.Source: §III · p. 4
IV. Numerical Results
The numerical study uses six-second simulations with a 1 ms time step and applies contingencies at three seconds. The section identifies the disturbance scenarios and candidate-parameter table scopes.
IV. Numerical Results
- The simulation horizon is 6 s with a 1 ms time step, covering pre-, during-, and post-disturbance responses.Contingencies are applied at t = 3 s.Source: §IV · p. 4
- Table I identifies the disturbance scenarios used for TS generation, while Table II identifies the candidate parameters used.Source: Table I · p. 4, Table II · p. 4
- The simulations use MATLAB’s variable-step stiff solver ode15s with relative tolerance 10^-5 and absolute tolerance 10^-6.Source: §IV · p. 4
A. Disturbance Scenarios and Recorded States
The study constructs TS for five disturbances, comprising one data-hall-side event and source-side outages. It records 51 dynamic states and selects parameters spanning physical and control subsystems.
A. Disturbance Scenarios and Recorded States
- Five disturbance scenarios are used: one data-hall-side disturbance and four source-side outages.Tripped source current decays with a 1 ms time constant to emulate fast disconnection while avoiding numerical discontinuities.Source: A. Disturbance Scenarios and Recorded… · p. 4
- Each contingency records 51 dynamic states, including DC-link voltage, source currents and internal states, CPL converter states, the secondary-control integrator, and grid-interface dq states.Source: A. Disturbance Scenarios and Recorded… · p. 4
- Candidate parameters span storage-source dynamics, source and secondary-voltage controllers, grid-interface and CPL controls, and line parameters.Source: A. Disturbance Scenarios and Recorded… · p. 4
B. Trajectory Sensitivity Generation
For each disturbance, the study constructs trajectory sensitivities from one nominal run and individual parameter perturbations. The resulting profiles vary over time and capture disturbance and post-disturbance effects.
B. Trajectory Sensitivity Generation
- Each disturbance uses one nominal simulation and 35 one-at-a-time simulations, with each candidate parameter perturbed by 2% from the same warm-start initial condition.Sensitivities are calculated from the difference between perturbed and base trajectories divided by the parameter perturbation magnitude.Source: B. Trajectory Sensitivity Generation · pp. 4–5
- The TS tensor has dimensions 6001 × 51 × 35 for time samples, monitored states, and candidate parameters, respectively.Source: B. Trajectory Sensitivity Generation · p. 5
- The study computes 1,785 sensitivity profiles per disturbance and 8,925 across five disturbances; plotted examples show sensitivities changing through disturbance and post-disturbance conditions.Even the pre-disturbance operating condition includes consistent load variation.Source: B. Trajectory Sensitivity Generation · p. 5
C. Validation With Simultaneous Parameter Perturbations
The TS-based predictions closely match independent nonlinear ODE trajectories when all 35 candidate parameters are perturbed simultaneously by ±15%, with errors bounded across pre- and post-disturbance intervals.
C. Validation With Simultaneous Parameter Perturbations
- All 35 candidate parameters were perturbed simultaneously by ±15% for each of the five disturbance scenarios during validation.TS generation instead perturbed one parameter at a time by 2%.Source: C. Validation With Simultaneous… · p. 5
- The TS-predicted trajectories closely match independent nonlinear ODE simulations across the studied cases, with relative errors bounded over pre- and post-disturbance intervals.The error is evaluated pointwise as the percentage deviation between the nonlinear response and its first-order sensitivity-based approximation.Source: C. Validation With Simultaneous… · p. 5
D. Computational Advantage
Once the TS tensor is available, the framework estimates new perturbed trajectories much faster than full nonlinear simulations, supporting repeated-response screening while the study remains limited to two varying data-hall units.
D. Computational Advantage
- The TS approach complements expensive nonlinear simulations with an offline data-driven framework for estimating new perturbed trajectories from the available TS tensor.The update uses a linearized TS operation.Source: D. Computational Advantage · p. 5
- 25 ms per perturbed trajectory yields an approximately 400× speed-up relative to full nonlinear simulation in this case study.A full nonlinear 6 s simulation sampled at 1 ms resolution required approximately 10 s of wall-clock time.Source: D. Computational Advantage · p. 5
- The case study includes only two varying data-hall units, while the authors identify larger planning and screening studies as a setting where computational gains can become significant.Such studies may evaluate many parameter combinations, operating conditions, and disturbance scenarios.Source: D. Computational Advantage · p. 5
V. Conclusion and Future Work
Across the studied disturbances, TS estimates closely track nonlinear ODE responses under simultaneous parameter perturbations, and precomputed sensitivities recover new responses in milliseconds. Future work proposes broader assessment uses and larger system studies.
V. Conclusion and Future Work
- Across the studied data-hall and source-side disturbances, TS trajectory estimates closely tracked nonlinear ODE responses under simultaneous parameter perturbations.New perturbed responses can be recovered from the precomputed TS tensor in milliseconds.Source: §V · p. 5
- Future work proposes using TS for parameter estimation and model calibration, identifying influential or poorly observable parameters, guiding sensor placement, and prioritizing model fidelity.The target includes model-heavy data centers with uncertain or vendor-limited parameters.Source: §V · p. 5
- The authors also propose adaptive TS database updates for materially changed workload trajectories and studies of larger multibus campuses with AC-side contingencies.Source: §V · p. 5