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Forced Oscillations in Power Systems Induced by Data Centers Hosting AI Workloads

Jovan Krajacic, Georgia Pierrou, Maitraya Desai, Gabriela Hug, Gustavo Valverde

arXiv:2609.27698v1eess.SYcs.SY

TL;DR

Periodic AI-workload fluctuations in large data centers can excite poorly damped power-system modes and produce sustained oscillations. The paper analyzes these risks with analytical methods and time-domain simulations, finding that large fluctuations can drive small-signal-stable systems to unbounded oscillations and identifying distinct instability mechanisms.

  • Problem

    AI-workload fluctuations can excite poorly damped power-system modes, while prior studies provide limited analysis of load patterns and critical grid locations for known DTC sources.

    Source: §I · p. 1

  • Method

    The paper develops an analytical framework for forced oscillations, analyzes load profiles and grid locations, and verifies the framework with time-domain simulations in three test systems.

    Source: §I · pp. 1–2

  • Results

    Large DTC load fluctuations can drive a small-signal-stable system to unbounded oscillations; Floquet multipliers detect saddle-node bifurcations, while Jacobian singularity detects impasse-surface encounters.

    Source: §V · pp. 9–10

  • Takeaways & Limitations

    Transfer-function magnitude can identify critical DTC locations, while phase can indicate whether multiple facilities’ oscillations reinforce or partially cancel.

    Source: §V · p. 10

Abstract

from arXiv · show

Power swings in large Data Centers (DTCs) running Artificial Intelligence (AI) workloads can excite poorly damped modes in power systems. The resulting forced oscillations can lead to flicker, equipment disconnection, or blackouts. This paper investigates the risks of such load fluctuations for different system strengths and damping conditions. Using an analytical approach based on transfer functions, we identify critical DTC locations in the power grid at which load fluctuations could induce the largest forced oscillations and further characterize the harmonic spectrum of the resulting system response. Depending on the frequency and magnitude of the DTC load fluctuations, forced oscillations can become unbounded. The underlying instabilities are classified into saddle-node bifurcations of the forced periodic response and impasse-surface encounters, using Floquet multipliers and the minimum singular value of the algebraic Jacobian. Furthermore, the impact of different duty cycles and harmonic components beyond the fundamental oscillation frequency in square-wave load profiles is analyzed. Finally, the interaction of two oscillating DTCs is investigated for different locations and forcing frequencies, considering both synchronized and unsynchronized operation. The findings can help system operators to define new regulations on the maximum load fluctuations permitted for DTC facilities at specific grid locations, without negatively affecting the stability and operation of the system.

I. INTRODUCTION

Large AI data-center loads can fluctuate periodically and excite poorly damped power-system modes, risking sustained oscillations. The paper develops and validates analytical tools to assess these risks across load conditions, grid locations, and interacting data centers.

I. INTRODUCTION

  • AI-training DTC loads can fluctuate between operational and almost-idle power, creating periodic demand changes that may excite poorly damped modes and produce large sustained oscillations.Modern facilities are described as tens to hundreds of megawatts, with one- or two-gigawatt facilities expected in the near future.Source: §I · p. 1
  • Oscillation severity depends on system damping, load-fluctuation magnitude and frequency, and DTC location; multiple facilities may produce swings of tens or hundreds of megawatts.DTCs cannot be disconnected, and sustained oscillations may reduce transfer capability, disconnect equipment, or cause blackouts.Source: §I · p. 1
  • Prior AI-workload studies did not assess different load patterns or identify critical grid locations, while predefined-bus simulations can become computationally demanding at large scale.This paper instead targets analytical characterization of response harmonics and critical locations for known DTC sources.Source: §I · pp. 1–2
  • The proposed analytical framework evaluates forced oscillations from AI workloads and is verified with time-domain simulations in three test systems.Its contributions include harmonic-response analysis, critical-location identification, instability classification, and assessment of multiple oscillating DTCs.Source: §I · p. 2
  • The analysis evaluates system strength, duty cycles, and higher harmonics, and identifies DTC fluctuation magnitudes that can produce unbounded oscillations in small-signal-stable systems.Instabilities are classified as saddle-node bifurcations of the forced periodic response or impasse-surface encounters using Floquet multipliers and the algebraic Jacobian’s minimum singular value.Source: §I · p. 2
  • The paper derives harmonic-component amplitudes in system quantities and validates them against time-domain simulations, while identifying critical DTC locations in the grid.It also assesses interactions between multiple DTCs under synchronized and unsynchronized workload oscillations.Source: §I · p. 2

II. DATA CENTER LOAD PROFILES AND MODELING

The paper focuses on low-frequency AI-training load fluctuations that can excite electromechanical modes. It characterizes representative profiles and uses filtered traces to retain the dominant variations relevant to power-system simulations.

A. Load Profile Analysis

  • Thousands of GPUs can vary demand together during training phases or while waiting for checkpoints or communications, producing sustained square-wave fluctuations of tens of megawatts at 0.05–1 Hz.Servers account for 60% to 90% of a DTC’s electricity consumption.Source: A. Load Profile Analysis · p. 2
  • The duty cycle is defined using active duration Ton and total cycle duration Tf; training cycles may also contain 5–30 Hz fluctuations during Ton.Inference workloads distributed among fewer synchronized servers may have smaller load fluctuations.Source: A. Load Profile Analysis · p. 2
  • The study focuses on low-frequency training-load fluctuations and illustrates synchronization dips, GPU burst cycles, and step-pulse profiles using real-world and filtered traces.The filtered traces retain dominant low-frequency variations relevant to phasor-domain simulations, while the real-world traces include high-frequency fluctuations.Source: A. Load Profile Analysis · p. 2, Figure 1 · p. 2

B. Load Profile Modeling

The filtered step-pulse IT load is modeled as a square wave with adjustable duty cycle, represented by a Fourier series. The model assumes active-power variation at unity power factor and accounts for the duty-cycle-dependent mean load and harmonic components.

B. Load Profile Modeling

  • The filtered step-pulse profile is modeled as a square-wave load varying between 50% and 100% of rated load at 1.0 Hz, with unity power factor assumed.The paper also notes reported demand variations ranging from 10% to 100% of rated load.Source: B. Load Profile Modeling · p. 2
  • The square wave has duty cycle D and period Tf = 1/ff, with load P0+Pf during the on interval and P0−Pf during the remainder.Pf is half the peak-to-peak IT-load swing and ωf = 2πff; the term −Pf(1−2D) shifts mean load relative to P0.Source: B. Load Profile Modeling · p. 3
  • Its Fourier series represents the load profile through harmonic amplitudes and phases, while D = 0.5 makes mean DTC consumption equal P0.For other duty cycles, the mean-load shift is captured by −Pf(1−2D).Source: B. Load Profile Modeling · p. 3

C. Data Center Model and Grid Interconnection

The DTC model combines a pulsing IT load, an UPS, and an induction-motor representation of cooling. Its interconnection has two IT-load supply modes, while cooling remains grid-connected in both.

C. Data Center Model and Grid Interconnection

  • The modeled DTC includes an UPS, an induction motor representing cooling, and a pulsing IT load representing AI-workload transients.The IT load is supplied directly from the grid in Eco mode or through the UPS in UPS mode; cooling remains directly connected to the grid unless otherwise stated.Source: C. Data Center Model and Grid… · p. 3
  • The UPS uses two average-value converters linked by a common DC link, with a first-order approximation for load-side converter dynamics.The grid-side converter regulates active-power exchange through d-axis current control and reactive power through q-axis current control; its current-control dynamics use first-order low-pass filters.Source: C. Data Center Model and Grid… · p. 3
  • In Eco mode, S1 connects the IT load directly to the grid and bypasses the UPS; in UPS mode, S2 routes IT power through the AC/DC–DC/AC conversion stage.The cooling load stays grid-connected in both modes.Source: Figure 2 · p. 3

A. Power System Modeling

The analysis linearizes a differential-algebraic power-system model and uses transfer functions to relate DTC load fluctuations to selected outputs. It then evaluates resonant harmonic responses and how multiple DTC responses combine.

A. Power System Modeling

  • The power system is represented by differential and algebraic equations, then linearized around an operating point to obtain state-space matrices and a SISO transfer function for filtered IT-load input.The state, algebraic, input, and output vectors are x, y, u, and z; the filtered input assumption makes D = 0.Source: A. Power System Modeling · p. 3
  • The transfer-function residues depend on the input and output vectors, so DTC location affects system impact and the chosen output determines how strongly an excited mode appears.Outputs can include voltage magnitude or machine speed, and other physical quantities representable as system outputs may also be used.Source: A. Power System Modeling · p. 3
  • For a square-wave cyclic load, steady-state response is the sum of responses to individual harmonics, whose output amplitudes depend on system gain at each harmonic frequency.The h-th harmonic input has amplitude Ah and phase θh.Source: A. Power System Modeling · p. 3
  • Resonance occurs when a load harmonic frequency hωf is near a mode's damped natural frequency; nonlinearities can shift the response frequency, especially at larger Pf and low damping.Higher harmonics can also excite modes, though their input amplitudes decrease with harmonic order; some higher-order sub-synchronous excitation is outside the study's scope.Source: A. Power System Modeling · pp. 3–4
  • For synchronized identical DTC loads, the total h-th harmonic response combines their individual transfer-function responses, reinforcing for phase differences from −90° to 90° and partially cancelling over part of the remaining range.Cancellation yields a smaller amplitude than a single DTC only under the stated condition in the paper.Source: A. Power System Modeling · p. 4
  • For unsynchronized DTCs, a relative time offset changes phase difference by −hωfΔt, while loads with different forcing frequencies are treated separately.Source: A. Power System Modeling · p. 4

B. Stability Analysis of Periodic Solutions

The sustained response to cyclic load is a forced limit cycle assessed with Floquet multipliers and a separate algebraic-Jacobian criterion. Increasing forcing can cause either a dynamic loss of periodic-orbit stability or an impasse-surface encounter that ends the solution.

B. Stability Analysis of Periodic Solutions

  • A cyclic load produces a sustained periodic DAE response with forcing period Tf, called a forced limit cycle, whose stability is assessed with Floquet theory.The variational equation tracks small perturbations along the orbit; hard control limits require saltation-matrix corrections when they engage.Source: B. Stability Analysis of Periodic… · p. 4
  • Floquet multipliers are eigenvalues of the monodromy matrix mapping infinitesimal perturbations over one forcing period, and the orbit is stable when all lie inside the unit circle.For time-varying A(t), frozen-time eigenvalues do not establish stability; multipliers must be computed from the monodromy matrix.Source: B. Stability Analysis of Periodic… · p. 4
  • As forcing amplitude increases, a real Floquet multiplier crossing +1 marks a saddle-node bifurcation where stable and unstable limit cycles collide and disappear.Crossings at −1 or through a complex-conjugate pair instead indicate period-doubling or Neimark-Sacker bifurcations, respectively.Source: B. Stability Analysis of Periodic… · p. 4
  • An impasse surface occurs where the algebraic Jacobian gy becomes singular, and a trajectory reaching it loses its periodic solution because the algebraic equations no longer admit a solution.The minimum singular value of gy over one period approaches zero at the impasse surface, providing a detection criterion separate from Floquet multipliers.Source: B. Stability Analysis of Periodic… · pp. 4–5
  • A saddle-node bifurcation sets the maximum forcing amplitude the system can sustain, whereas an impasse-surface encounter produces abrupt voltage collapse through a distinct mechanism.A singularity-induced bifurcation is associated with an eigenvalue diverging to infinity and instantaneous loss of stability.Source: B. Stability Analysis of Periodic… · pp. 4–5

IV. RESULTS

The simulations use three test systems to examine DTC-induced forced oscillations under different grid conditions.

IV. RESULTS

  • The first test system assesses DTC impact across system strengths and illustrates two instability mechanisms.The second and third systems examine frequency shifts, duty cycles, higher harmonics, critical DTC locations, and interactions between synchronized and unsynchronized DTCs.Source: §IV · p. 5
  • The second test system examines nonlinear frequency shifts, square-wave duty cycles, and third- and fifth-harmonic effects.The third system identifies high-impact DTC locations and studies synchronized and unsynchronized operation across locations and forcing frequencies.Source: §IV · p. 5
  • The third test system identifies the DTC locations with the highest grid impact and analyzes interactions between DTCs at different locations and forcing frequencies.Both synchronized and unsynchronized jobs are considered.Source: §IV · p. 5

A. Four-Bus Test System

The four-bus simulations show that DTC forcing can destabilize the weakest grid, with instability mechanisms distinguishable through Floquet multipliers and the algebraic Jacobian. Analytical harmonic estimates track simulated responses, while system strength and forcing conditions shape the response.

A. Four-Bus Test System

  • Across the SCC range, analytical harmonic responses closely follow FFT values, and all three harmonic amplitudes decrease as SCC increases, with the fundamental remaining dominant.At Pf = 0.8 p.u., the 2000 MVA case underestimates amplitudes by about 3.3% when field-limiter saturation is absent from the linearized model; at Pf = 0.4 p.u., errors are about 2% for all SCCs.Source: A. Four-Bus Test System · p. 5
  • At 1000 MVA SCC, increasing Pf from 0.7 to 0.8 p.u. causes growing voltage oscillations and instability despite a 24.54% damping ratio for the corresponding small-signal mode.The periodic orbit approaches algebraic singularity before the final disturbance step, indicating impasse-surface instability rather than a Floquet multiplier crossing the unit circle.Source: A. Four-Bus Test System · pp. 5–6
  • With damping reduced to 10% of its original value, the dominant Floquet multiplier rises from 0.979 to 1.012 and crosses unity, identifying a saddle-node bifurcation while the algebraic Jacobian remains nonsingular.The voltage response grows cycle by cycle after the final Pf step.Source: A. Four-Bus Test System · p. 6
  • Forcing frequencies 10% below and above the critical frequency sustain oscillation magnitudes of 0.746 p.u. and 1.363 p.u., respectively, with saddle-node and impasse-surface mechanisms, respectively.The instability mechanism depends on the forcing frequency and operating conditions.Source: A. Four-Bus Test System · p. 6

B. Two-Area Test System

The two-area simulations show that nonlinear frequency shifts move peak responses away from the critical eigenfrequency as forcing grows. Duty cycle and higher harmonics also affect voltage response, including spikes and resonance-driven oscillations.

B. Two-Area Test System

  • As Pf increases, peak-response frequencies shift from 0.6211 Hz at 0.25 p.u. to 0.6024 Hz at 0.50 p.u. and 0.5714 Hz at 0.75 p.u.; at 0.75 p.u., a frequency-driven saddle-node jump leads to a new stable orbit.The critical eigenvalue frequency is 0.6244 Hz.Source: B. Two-Area Test System · p. 7, Figure 8 · p. 7
  • At D = 75% and 25%, shorter forcing intervals produce narrow voltage spikes opposite in sign to the corresponding power deviations, potentially posing risks to voltage-sensitive devices.For D = 50%, the voltage completes a swing during each half-cycle; in UPS mode, total DTC demand does not retain the IT load’s ideal square-wave profile.Source: B. Two-Area Test System · p. 7, Figure 9 · p. 7
  • When the third or fifth load harmonic coincides with the 0.6024 Hz resonant frequency, DTC fluctuations induce large system oscillations, though amplitudes are smaller than when ff = fr.The tested load frequencies are 0.2008 Hz and 0.1205 Hz, respectively.Source: B. Two-Area Test System · pp. 7–8, Figure 10 · p. 7

C. Longitudinal Test System

Transfer-function responses identify where DTC fluctuations most stress the longitudinal grid, while the phase and frequency of two DTCs shape their combined voltage impact.

C. Longitudinal Test System

  • The longitudinal test system is a 50-Hz, five-area network with 14 synchronous generators, five SVCs, and loads modeled as constant current for active power and constant impedance for reactive power.Generator, excitation-system, and PSS models are also specified.Source: C. Longitudinal Test System · p. 8
  • DTCs at Buses 504, 507, and 508 produce the greatest generator-speed oscillations, while voltage impacts are strongest at Bus 502 and also affect Bus 311.The location ranking follows transfer-function magnitude responses; the authors relate the Area 3 impact to its electrical proximity to Area 5.Source: C. Longitudinal Test System · p. 8, Figure 12 · p. 8, Table I · p. 8
  • The largest bounded fluctuations are 1.61, 2.17, and 0.62 p.u. at Buses 508, 507, and 504, respectively, corresponding to 31.3%, 32.3%, and 32.8% of local active power.The relative fluctuation the system can sustain is smaller at the more critical location.Source: C. Longitudinal Test System · p. 9
  • Two same-area DTCs oscillating in phase approximately double the Bus 502 voltage variation, whereas a half-cycle offset reduces it to about 3% of the single-DTC response.In the out-of-phase case, the contributions oppose and the stated amplitude condition is satisfied.Source: C. Longitudinal Test System · p. 9, Figure 13 · p. 9
  • For DTCs in different areas, a roughly 152° transfer-function phase difference partially cancels their contributions, while a roughly 57° difference reinforces them.The interaction varies across system outputs, producing different spatial patterns of constructive and destructive effects.Source: C. Longitudinal Test System · p. 9, Figure 14 · p. 9
  • When the two DTCs oscillate at the two most critical modal frequencies, their voltage impact is smaller than when both oscillate at the most critical frequency.The comparison is for voltage magnitude at Bus 502.Source: C. Longitudinal Test System · p. 9

V. CONCLUSION

The conclusion shows how DTC load fluctuations can drive a small-signal stable system to unbounded oscillations and summarizes analytical tools for evaluating bounded responses. It also identifies how forcing frequency, duty cycle, location, and coordination affect the oscillations.

V. CONCLUSION

  • Large DTC load fluctuations can drive a small-signal stable system outside its region of attraction, causing unbounded oscillations.Floquet multipliers detect saddle-node bifurcations of the forced response, while the minimum singular value of the algebraic Jacobian detects impasse-surface encounters that the multipliers do not warn of.Source: §V · pp. 9–10
  • For bounded oscillations, derived equations enable harmonic analysis of the forced response using a linearized model without time-domain simulations.The conclusion distinguishes this analytical approach from the instability indicators used for unbounded responses.Source: §V · p. 10
  • As fluctuations grow, the peak response shifts away from the modal frequency; among tested duty cycles, 50% produces the largest oscillations, and higher harmonics can also cause large responses.The largest fluctuation considered exhibits a jump phenomenon.Source: §V · p. 10
  • Transfer-function magnitudes identify critical DTC locations, while their phases govern whether multiple DTC contributions reinforce or partially cancel, suggesting workload scheduling as a possible mitigation.Same-area synchronized DTCs at critical buses can nearly double oscillations, while a half-cycle offset can nearly cancel them.Source: §V · p. 10
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