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DC-TORQ: Fast Assessment of Data Center-Induced Generator Torsional Oscillation Risk Quantification

Yingyi Tang, Bin Wang, Junbo Zhao, Qiang Zhang, Pradip Vijayan, Xiaochuan Luo, Tongxin Zheng

arXiv:2610.22572v1eess.SYcs.SY

TL;DR

Periodic data-center power fluctuations can excite turbine-generator torsional modes, while assessing frequency-dependent shaft-torque responses across buses with EMT scans can be computationally demanding. The paper develops a coupled analytical model with transfer functions and torque-based power limits; its case studies report rapid frequency-sweep evaluation and frequency-specific admissible-load limits.

  • Problem

    Assessing how data-center oscillations couple through the network to generator shaft torque requires frequency-dependent analysis, but repeated EMT scans across frequencies and load locations can be computationally demanding.

    Source: §I · p. 1

  • Method

    A coupled generator–network model derives transfer functions from data-center power perturbations to generator states and shaft torques, then uses harmonic superposition and admissible torque limits to assess periodic loads.

    Source: §I · p. 2

  • Results

    The proposed method swept 565 frequency points over 15–35 Hz in 0.83 s, compared with 349.27 min for a sequential PSCAD sweep of 101 points; the admissible amplitude minimum was 1.17 MW at 22.39 Hz.

    Source: 1) Generator terminal active power… · p. 6, 3) Data center active power… · p. 8

  • Takeaways & Limitations

    Frequency-dependent shaft-torque limits provide a quantitative criterion for screening candidate data-center connection buses against admissible torque amplitudes.

    Source: §I · p. 2, §VI · p. 10

Abstract

from arXiv · show

The periodic power demand of large data centers can introduce forced oscillations into the power system. When these oscillations contain frequency components near a turbine-generator torsional mode, they may excite sustained shaft torque oscillations with amplitudes exceeding the allowable cyclic torque limits. Characterizing the impact of data center power oscillations on generator shaft torque requires accounting for frequency-dependent network coupling among the data center, the transmission network, and the generators. Although electromagnetic transient (EMT) simulations can capture these interactions in detail, repeated simulations across excitation frequencies and load locations can be computationally demanding. This paper proposes an analytical framework for data center induced torsional oscillations that retains the coupled electrical and shaft dynamics. A detailed generator-network model is established, and closed-form transfer functions that map data center power perturbations to the torque in each shaft section are derived. Admissible shaft torque amplitudes are then translated into frequency-dependent limits on data center power oscillations. The proposed framework enables fast assessment of the shaft torque response while accounting for network dynamics and provides a quantitative screening criterion for candidate data center connection buses. The framework is validated on the IEEE benchmark model and applied to the IEEE 39-bus system.

I. INTRODUCTION

Periodic data-center demand can excite turbine-generator torsional modes, while frequency-dependent network coupling makes shaft-torque risk costly to assess through repeated EMT scans. The paper develops a coupled analytical model, derives load-to-torque transfer functions, and converts allowable torque amplitudes into frequency-dependent screening limits.

I. INTRODUCTION

  • Demand fluctuations near a turbine-generator torsional mode may excite sustained shaft oscillations, amplify alternating stress, and contribute to fatigue or shaft damage under unfavorable conditions.Synchronized AI computing tasks can leave repeated power fluctuations visible after aggregation across servers and racks.Source: §I · p. 1
  • Repeated EMT frequency scans can capture coupled load-to-generator responses, but their computational burden grows when many load locations and network configurations must be evaluated.Existing interaction-factor and short-circuit-based screening measures are efficient but require further consideration of coupled electrical and shaft dynamics for frequency-dependent responses.Source: §I · p. 2
  • The framework establishes a coupled generator–network model that captures multi-mass shaft and network dynamics, including black-box IBRs through terminal admittances.This modeling choice extends the generality of the model.Source: §I · p. 2
  • Transfer functions map a data-center power perturbation at a candidate bus to generator states and shaft torques, with harmonic superposition handling arbitrary periodic load profiles.The framework thereby analytically assesses oscillations without relying on repeated EMT simulations.Source: §I · p. 2
  • Admissible shaft-torque amplitudes are translated into frequency-dependent limits on data-center power oscillations for screening sustained oscillation risk.The assessment can be made for arbitrary data-center connection buses.Source: §I · p. 2

A. Electrical Model With Stator-Flux Dynamics

  • The generator electrical model retains stator-flux linkage dynamics to include the impact of DC-offset torque components.These dynamics distinguish the model from GENROU and other standard stability models.Source: A. Electrical Model With Stator-Flux… · p. 2

B. Multi-Mass Shaft Model

Each turbine-generator is represented as rotating masses connected by shaft sections, with states and parameters defining the mechanical dynamics and section torques.

B. Multi-Mass Shaft Model

  • Generator k has n_k rotating masses connected by n_k−1 shaft sections, with rotor angles and per-unit speed deviations collected as vectors.The model uses an incidence matrix to represent shaft connections.Source: B. Multi-Mass Shaft Model · pp. 2–3
  • Shaft-section torques are calculated from shaft stiffnesses and the incidence matrix applied to rotor angles.The model defines the stiffness matrix as diagonal in the section stiffnesses.Source: B. Multi-Mass Shaft Model · p. 3
  • Each mass is characterized by inertia and self-damping, while section torque follows the stiffness times the angle difference between adjacent masses.The stated sign convention is T_s,k,ℓ = K_k,ℓ(θ_k,i − θ_k,i+1).Source: B. Multi-Mass Shaft Model · p. 3

C. Small-Signal Model

The generator model stacks electrical and mechanical states, expresses terminal currents as outputs, and is linearized around an operating point for small-signal analysis.

C. Small-Signal Model

  • Electrical and mechanical states of all generators are stacked to form the coupled generator-state representation.The model also stacks terminal voltages and injected currents in the common network xy frame.Source: C. Small-Signal Model · p. 3
  • The nonlinear generator equations are linearized around the operating point to obtain the small-signal generator model.The linearization is applied to the stacked state and terminal-current equations.Source: C. Small-Signal Model · p. 3
  • With zero initial perturbations, the small-signal representation is expressed in the Laplace domain.Source: C. Small-Signal Model · p. 3

III. DERIVATION OF THE GENERATOR RESPONSE MODEL TO DATA CENTER DEMAND

The data-center demand model represents active power as a steady component plus periodic harmonics and assumes constant power factor. Its linearized terminal-current perturbation depends on both demand and terminal-voltage changes.

A. Periodic Data Center Demand Model

  • Data-center active power is modeled as a steady-state demand plus a periodic perturbation represented by harmonics.The representation covers sinusoidal forcing and periodic workload profiles with specified harmonics.Source: A. Periodic Data Center Demand Model · p. 3
  • The model assumes constant power factor, with the reactive-to-active-power ratio setting reactive demand and zero ratio corresponding to unity power factor.Source: A. Periodic Data Center Demand Model · p. 3
  • The change in data-center terminal current is determined by both active-power demand variation and the corresponding terminal-voltage variation.The current perturbation is represented in the Laplace domain.Source: A. Periodic Data Center Demand Model · p. 3

B. Consideration of Network Dynamics

The section models the transmission network dynamically because its frequency-dependent coupling affects how data-center disturbances reach generator terminals. The resulting network equations provide a mapping from a load-power perturbation to generator states.

B. Consideration of Network Dynamics

  • The network is modeled in the synchronous xy frame with branch and shunt blocks that depend on the perturbation-frequency variable s.The formulation includes ordinary loads represented by fixed RLC elements.Source: B. Consideration of Network Dynamics · p. 3
  • The nodal equation places data-center and generator current perturbations at their respective buses through selection matrices.The network voltage response is then expressed using the generator-terminal impedance matrix and a load-power-to-terminal-voltage mapping.Source: B. Consideration of Network Dynamics · p. 4
  • Combining the network relation with the generator model defines a transfer function from data-center active-power oscillations to all generator states.Source: B. Consideration of Network Dynamics · p. 4

C. Extension to Black-Box IBR Models

Black-box IBRs can be incorporated through terminal admittance models fitted from their frequency responses. This extension retains their terminal dynamics in the propagation of data-center oscillations and generator shaft-torque responses.

C. Extension to Black-Box IBR Models

A. Torsional Modes and Shaft Torque Response

The section derives shaft-torque responses from generator angle states and models torsional modes within the coupled generator-network system. It uses harmonic response to assess torque levels against admissible limits.

A. Torsional Modes and Shaft Torque Response

  • The coupled-system torsional modes are shaped by electromagnetic torque feedback, which links shaft motion to electrical dynamics and modifies modal frequencies and damping.The network dynamics are retained through W(s).Source: A. Torsional Modes and Shaft Torque… · p. 4
  • The transfer function maps data-center power perturbations at Bus j to the shaft torques of generator k, with each row specifying one shaft section.It combines the mapping from load perturbation to system states with the generator angle-to-torque relation.Source: A. Torsional Modes and Shaft Torque… · pp. 4–5
  • For a stable operating point, each demand harmonic produces a shaft-torque amplitude set by the transfer-function magnitude at that harmonic frequency and its demand amplitude.The total steady-state response is obtained by superposing the harmonic responses.Source: A. Torsional Modes and Shaft Torque… · p. 5
  • A demand harmonic can strongly excite a lightly damped torsional mode when its frequency approaches the modal frequency.The response depends on both system modes and the data-center oscillation.Source: A. Torsional Modes and Shaft Torque… · p. 5
  • Torque can exceed a shaft section’s material-endurance limit even at a stable operating point, and the derived relations enable fast planning-stage assessment of multiharmonic fluctuations.Source: A. Torsional Modes and Shaft Torque… · p. 5

B. Torque-Based Data Center Power Oscillation Limits

Admissible shaft-torque amplitudes are converted into frequency-dependent limits on data-center power oscillations, with a conservative system-wide limit taken across generators. Benchmark comparisons report close agreement in modal quantities, torque amplitudes, and transient waveforms.

B. Torque-Based Data Center Power Oscillation Limits

  • A shaft section’s admissible alternating-torque threshold is translated into a frequency-dependent admissible data-center power-oscillation amplitude for each generator.The threshold can come from a material endurance limit when geometry, stress concentrations, and mean-stress effects are known, or from a prescribed fatigue limit.Source: B. Torque-Based Data Center Power… · p. 5
  • The conservative periodic-load limit requires the harmonic torque contributions to remain within each shaft section’s admissible threshold for every generator.The bus-level system limit is obtained by taking the minimum across generators.Source: B. Torque-Based Data Center Power… · p. 5
  • The bound limits peak alternating shaft torque; cumulative fatigue damage requires a separate assessment of loading history and material fatigue properties.Source: B. Torque-Based Data Center Power… · p. 5

1) Validation:

  • The proposed framework closely matches benchmark modal quantities, torque amplitudes, and transient waveforms in validation against the IEEE second benchmark system.The validation reproduces Case 1A, including a three-phase fault cleared after 0.017 s.Source: 1) Validation · p. 5, Table I · p. 5

2) Response to Data Center Power Oscillations:

The analytical framework is compared with EMT simulations for a benchmark generator and for a data center connected to Bus 17 of the IEEE 39-bus system. The comparisons report close agreement in frequency and transient responses, while revealing network-mediated interactions among generators and torque peaks that may occur at another machine’s dominant mode.

2) Response to Data Center Power Oscillations:

1) Generator terminal active power oscillation:

2) Shaft torque response:

  • The framework and EMT agree across units, shaft sections, and forcing frequencies over a torque-response range spanning six orders of magnitude.Unit 3 machines show GEN–EXC features at Unit 1 and Unit 2 modal frequencies, and the reciprocal responses also occur through network-mediated inter-machine interaction.Source: 2) Shaft torque response · pp. 7–8, Figure 8 · p. 7
  • Thirteen modes span 15–35 Hz; generator participation varies by mode, and damping ranges from 0.003% to 0.2%.Unit 3 modes are shared among machines, while Unit 2 modes are localized; the least-damped 30 Hz modes produce narrow peaks.Source: Table II · p. 6, Figure 9 · p. 7, 2) Shaft torque response · p. 8
  • 3.4122 p.u. analytical peak-to-peak torque for G30’s M3–M4 section agrees closely with EMT during forcing at 22.39 Hz.The analytical and EMT times to reach 99% amplitude are 19.61 s and 19.14 s; their times to fall to 0.1 p.u. after disconnection are 15.03 s and 14.35 s.Source: Figure 10 · p. 7, 2) Shaft torque response · p. 8
  • For G32, G38, and G39, maximum torque is 1.2 to 2.1 times the torque at each machine’s own dominant mode when another same-type machine’s mode dominates.Thus, evaluating only at each machine’s own dominant modal frequency would underestimate its maximum torque.Source: 2) Shaft torque response · p. 8, Table III · p. 8

3) Data center active power oscillation limit:

The system-wide admissible data center power-oscillation amplitude is the lower envelope of the individual generator limits and varies sharply with frequency. Resonant minima make a single frequency-independent limit potentially too restrictive off resonance or too permissive near modes.

3) Data center active power oscillation limit:

  • 1.17 MW is the band-wide minimum system-wide admissible amplitude at 22.39 Hz, governed by the M3–M4 section of G30.Comparable minima occur near 19.08 Hz, set by the GEN–EXC section of G35, and 30.05 Hz, set by the M5–M6 section of G31.Source: 3) Data center active power… · p. 8
  • The system-wide admissible amplitude spans about two and a half orders of magnitude over 15–35 Hz, recovering to hundreds or thousands of megawatts away from resonances.G30 sets the lower envelope over most of the band.Source: 3) Data center active power… · p. 8
  • A frequency-independent limit set at the resonant minimum would be roughly two orders of magnitude too restrictive over most of the band, while an off-resonance limit would allow torques beyond endurance limits at modes.Source: 3) Data center active power… · p. 8

4) Impact of data center locations:

The location scan shows that maximum shaft torque and its governing machine vary by connection bus. With G34 replaced by a black-box IBR, the remaining system response stays close to the original, and the conclusion presents the framework as a computationally efficient alternative to EMT torsional screening.

4) Impact of data center locations:

C. Application to the IEEE 39-Bus System with IBRs

  • Replacing G34 with a black-box IBR removes its two dominated torsional modes; eleven modes remain with frequency shifts of at most about 0.02 Hz.The G37 mode at 21.67 Hz loses about 17% of its damping, with σm changing from −0.087 to −0.073 s−1.Source: Table IV · p. 9, C. Application to the IEEE 39-Bus… · p. 9
  • The IBR smooths Bus 34 power response, while the framework using its fitted admittance agrees with EMT across the band and the remaining machines’ torque envelope stays close to the original.The main envelope change is near 21.7 Hz, where the G34 mode has been removed.Source: C. Application to the IEEE 39-Bus… · p. 9, Figure 14 · p. 10

VI. CONCLUSION

  • The framework combines multi-mass shaft dynamics, network electromagnetic dynamics, and black-box IBR terminal admittances in transfer functions for arbitrary periodic loads.Harmonic superposition yields shaft responses, and frequency-dependent power limits screen candidate connection buses.Source: §VI · p. 10
  • IEEE SSR benchmark validation and IEEE 39-bus case studies support a reliable, computationally efficient alternative to EMT for torsional screening; future work targets critical network impedance and black-box multi-mass shaft models.Source: §VI · p. 10
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