Limiting the Impact of AI Data Centers on Fatigue Life of Thermal Turbine Generators in the Grid: A Frequency-Domain Approach

Abstract: A framework is established that assesses the impact of variations in AI data center (DC) loads on the fatigue damage of steam/gas turbines of the synchronous generators (SGs) from torsional oscillations. Next, a simple three-step process that is supported by frequency-domain analysis is laid out to quantify the limits on fluctuations in AI DC loads. In the first step, the maximum allowable variation in electrical power output at each SG terminal is independently determined from the first principles. This step needs only a lumped multi-mass model of the mechanical side of the SG. In the second step, we propose a new approach that relies on load flow to determine the so-called algebraic `interaction factor' that maps the change in AI DC load at a given bus to the corresponding change in each of the SG power outputs. In the third step, we propose a screening method to rank the candidate buses to site AI DCs and solve an optimization problem to determine the optimal allowable fluctuations in the AI DCs. We demonstrate the applicability of the proposed approach through frequency-domain and time-domain analyses in the modified IEEE 4-machine and IEEE-68 bus systems using a dynamic phasor framework. Finally, we demonstrate the scalability of the proposed approach on the synthetic 2000-bus Texas system.

• The paper introduces a frequency-domain framework that converts turbine-shaft fatigue and blade-vibration constraints into enforceable limits on subsynchronous AI data-center power fluctuations.
• The method combines multi-mass turbine modeling, load-flow interaction factors, and linear programming to allocate safe fluctuation limits across multiple data centers while accounting for generator coupling.
• Case studies show that uncoordinated fluctuations can exceed shaft-fatigue limits and cause predicted failure, whereas optimized allocations keep stresses and frequency deviations safe and scale to a 2,000-bus system.

Motivation and problem statement

AI data centers (DCs) exhibit large, persistent power fluctuations during training cycles—power draw can rise by up to 70% of rated capacity at the start of a training cycle, followed by sustained variations. The North American Electric Reliability Corporation (NERC) has flagged these fluctuations as a bulk-system reliability concern, and prior literature has examined their excitation of electromechanical modes and IBR-induced subsynchronous oscillations (SSO). What has not been addressed is the consequence for turbine-generator shaft fatigue life: poorly damped torsional oscillations (damping time constants of 4–30 s) driven by forced oscillations from large loads can consume fatigue life of steam/gas turbine shafts. This paper fills that gap by proposing a first-principles, frequency-domain framework to quantify how much fluctuation AI DC loads may inject into a grid without endangering the fatigue life of any synchronous generator (SG) turbine shaft.

The regulatory context motivates the work. Utilities have proposed ad hoc limits—ERCOT's 10 MW change per 5 s sliding window, LIPA's 3.5 MW limit on adjacent FFT bins in the 5–55 Hz band, AESO's 16 kW/100 ms variability cap, ATC's 25 MW over 5 s for loads above 200 MW—but none provides technical justification. The paper's stated gaps are: no solid quantitative basis behind utility limits; ESIG's study-based and approximation-based recommendations lack any proposed method; and no method exists to optimize allowable fluctuations when multiple AI DCs are present simultaneously.

Fatigue assessment framework

The mechanical side of each SG is modeled as a lumped multi-mass system (HP/IP/LP turbine stages, generator rotor, exciter) connected by elastic shaft sections, capturing subsynchronous torsional modes—the range where electrical-mechanical interaction problems are concentrated. For each shaft section, maximum tensile stress under pure torsion is computed from the twist angle via $\sigma_r = \frac{GR_r}{l_r}(\theta_{r+1}-\theta_r)$, and the transfer function $G_r(s)$ between shear stress and SG electrical power output $P_e$ is derived by linearizing the multi-mass model.

Fatigue safety is assessed against two criteria:

• Torsional fatigue: the stress amplitude must remain below the high-cycle fatigue limit (HCFL) $S_e$ of AISI 4130 steel; nonzero mean stress reduces the allowable amplitude via the augmented modified Goodman diagram.
• Blade vibrational fatigue: off-nominal frequency operation is bounded by requiring frequency deviation within $\Delta f^{max} = 1.5$ Hz, per IEEE C37.106-2003.

A key modeling assumption is that generator controls (including PSS) contribute no negative damping to torsional modes—standard practice, but a dependency nonetheless. The framework also assumes supersynchronous load fluctuations are attenuated before reaching SG terminals, so the analysis is restricted to $\omega_i < \omega_s$.

Three-step procedure for determining allowable DC fluctuations

Step 1 — Terminal power variation limits. For single-frequency perturbations, the maximum allowable $P_e$ amplitude at frequency $\omega_i$ is $$P_{ei}^{max} = \min\{P_{ei,tor}^{max}, P_{ei,vib}^{max}\}$$, where the torsional bound is $\sigma_{ra0}^{max}/G_{ri}$ minimized over all $G_r(s)$0 shaft sections. For multi-frequency content, H\"older's inequality yields the sufficient condition that the sum of amplitudes of all subsynchronous components satisfies $G_r(s)$1, where $G_r(s)$2 is the infimum of the single-frequency bounds. This is conservative but simple and enforceable via FFT on measured power.

Step 2 — Algebraic interaction factors (IFs). A new load-flow-based method computes $G_r(s)$3, mapping a change in real power at load bus $G_r(s)$4 to the change in output of SG $G_r(s)$5. Internal SG voltages are computed behind subtransient impedance $G_r(s)$6, held constant (justified by the constant flux linkage theorem and rotor inertia), and all internal buses are designated slack buses so transmission losses are shared among generators rather than assigned to one slack. The method avoids decoupled-load-flow assumptions and handles constant-power and constant-impedance loads, and requires only standard load-flow tooling—an important scalability property.

Step 3 — Screening and LP optimization. Candidate siting buses are ranked by $G_r(s)$7, where $G_r(s)$8 is conservatively taken as 25% of the DC rating based on NERC training-cycle profiles. With multiple DCs, an iterative linear program maximizes total allowable fluctuation subject to $G_r(s)$9 for every relevant SG, with an iteratively relaxed lower-bound parameter ensuring feasibility. Buses yielding overly restrictive limits are discarded and the LP rerun.

Dynamic phasor validation

The approach is validated using a dynamic phasor (DP) framework: network, loads, and SGs modeled in the $P_e$0 domain ($P_e$1 DPs), multi-mass mechanics at $P_e$2, and GFL IBRs in the $P_e$3 frame ($P_e$4). On the IEEE First Benchmark Model for SSR, eigenvalues of the linearized DP model match published results essentially exactly (e.g., torsional mode $P_e$5), and time-domain responses to an LLL-G fault closely match a Simscape EMT model—establishing confidence in the validation platform.

Case studies

In the modified IEEE 4-machine system (G3, G4 with multi-mass turbines; two GFL IBRs replacing G1, G2), the multi-frequency terminal limits are 1.17% and 1.02% of the G3 and G4 ratings, respectively—a strikingly tight bound illustrating how restrictive torsional fatigue constraints are. Algebraic IFs give conservative estimates of $P_e$6: 32.39 MW vs. an actual 71.37 MW at bus 9, and 11.47 MW vs. 74.46 MW at bus 7. The bus-7 result is notably over-conservative, attributed to the nearby GFL IBRs being treated as PV rather than slack buses in the load flow—an acknowledged limitation of the IF estimation. Time-domain simulation with a deliberate worst-case 20 Hz component (coinciding with a torsional mode) at the allowed amplitude confirms stresses and frequency deviations stay within Goodman-derived limits.

The modified IEEE-68 bus case demonstrates both the necessity of the LP and its effectiveness. Allowing each of twelve NETS candidate buses to fluctuate up to its individual $P_e$7 causes the aggregate weighted sum at G7 to reach 55.62 MW versus a terminal limit of 18.76 MW; the resulting stress in G7's IP-LPA shaft section permanently exceeds the safe limit, and Rainflow counting plus the Palmgren-Miner rule predicts shaft breakage. Solving the LP instead allocates much smaller per-bus limits (6–13 MW across the twelve buses), and time-domain simulation confirms all transient peak stresses and frequency deviations across eight SGs remain within safe bounds. The interaction-factor heatmap also shows low coupling between NYPS load buses and NETS generators, supporting the practical conclusion that a regional study area suffices rather than whole-interconnection analysis.

Scalability is demonstrated on the synthetic 2000-bus Texas system (485 generators, 1123 loads): screening reduced 39 candidate buses in Zone 1 to 14 (discarding those below a 10 MW threshold), and the LP yielded permissible fluctuations above 10 MW for 13 of them.

Limitations and open questions

Several assumptions bound the applicability of the results. The algebraic IFs are static sensitivities; they are provably conservative relative to the true frequency-dependent ground truth, but the degree of conservatism varies widely (ratios of estimated-to-actual $P_e$8 ranged from roughly 0.45 at bus 7 in the 4-machine case to 0.75–1.0 in the 68-bus case), and the treatment of IBRs as PV buses during load flow degrades accuracy near converter-dominated areas. The frequency-domain bounds are steady-state and conservative; transient overshoots in shear stress are argued to be limited by ramp-rate constraints and norm-inequality slack, with confirmation only through exhaustive simulation rather than a formal guarantee. The framework assumes controls do not negatively damp torsional modes, assumes supersynchronous DC fluctuations are attenuated upstream, and restricts attention to subsynchronous frequencies valid for lumped-mass models. Blade-vibration effects are handled only through the aggregate 1.5 Hz frequency-deviation criterion rather than detailed bladed-disk analysis, despite the authors' own recent work showing speed fluctuations induce time-varying mistuning effects. Open questions include whether tighter, less conservative multi-frequency bounds than the sum-of-amplitudes condition can be certified, and how IF accuracy can be improved in systems with high IBR penetration.

Conclusion

This paper establishes a defensible, first-principles basis for limiting AI DC load fluctuations to protect thermal turbine-generator fatigue life, addressing a gap left open by current utility interconnection requirements. Its three-step pipeline—terminal power limits from multi-mass models and Goodman-based fatigue criteria, load-flow-derived algebraic interaction factors, and LP-based allocation across multiple DCs—is computationally light, scales to a 2000-bus system, and produces enforceable compliance metrics via FFT on measured DC power. The demonstrated failure case without coordinated optimization underscores that per-bus individual limits are insufficient when multiple large fluctuating loads coexist.