AI Training Power Swings, Grid Oscillations and BESS Sizing

Workload and spectrum. The synchronized site swing is $\Delta P=N(P_\mathrm{compute}-P_\mathrm{idle})/\eta_\mathrm{chain}$, with floor $P_\mathrm{other}+NP_\mathrm{idle}/\eta_\mathrm{chain}$ and mean $P_\mathrm{floor}+d\Delta P$. Harmonic $n$ has peak amplitude $2\Delta P|\sin(n\pi d)|/(n\pi)$ at $n/T$. This follows the BSP pulse representation in Chaudhary et al., arXiv:2606.22096, p. 2. Sixty harmonics are retained for the spectrum, RMS period sweep and amplitude-sum frequency screen.

Time-domain source. With $x=\Delta f/f_0$, per-unit load perturbation $u=(P-P_\mathrm{mean})/P_\mathrm{base}$ and angle $\delta$, the implemented equations are

An island has $K=0$, $G=1/R$ and entered $D$. A grid-mode equivalent has $G=0$, $K=2H\omega_k^2/\omega_0$ and $D=4H\zeta_k\omega_k$. Grid damping includes the dynamics already represented by that mode. These state equations and their transfer function are derived here; they are not a detailed gas-engine or multi-bus model. Each constant or linear-load interval is propagated with an augmented matrix exponential. Every compute edge, barrier edge and BESS ramp corner is an integration boundary. This solves the linear ODE without smoothing the raw pulses or truncating them to harmonics. Within each interval, each relevant state is a linear particular solution plus the two-pole homogeneous response. All stationary points are located continuously: derivative zeroes are analytic for an unshifted modal response; for a ramp-driven response, analytic derivative turning points bracket each zero for bisection. The real-pole and repeated-pole limits are included. Frequency, mechanical-power and grid-angle extrema therefore do not depend on the plot grid or the simulation horizon's sample spacing. The characteristic poles are rates in s⁻¹; only the modal oscillation frequency is converted to Hz by dividing its imaginary rate by 2π.

The frequency transfer gain is

The period chart shows $\sqrt{\sum_n|F_n|^2/2}$; the arithmetic amplitude sum is a conservative bound for the retained harmonics only. The frequency-only accelerator bound uses that sum and does not include voltage, engine headroom or startup.

Voltage. On the same source base, solve the high-voltage root of $V^4-[E^2-2(rp+x_\mathrm{th}q)]V^2+|z|^2(p^2+q^2)=0$. Engine impedance uses entered transient reactance; grid impedance uses $|z|=P_\mathrm{base}/(\mathrm{SCR}\,S_\mathrm{site,peak})$. Each alternative's fixed internal EMF is set to give unity bus voltage at its own mean load. Voltage extrema and feasibility are evaluated on both sides of every pulse edge and at all ramp corners, requiring positive discriminant and positive squared-voltage root. The BESS supplies active power only, so raw reactive-load pulses remain. Dummy kernels have the entered site power factor.

Buffer and gap filling. Source demand is the causal box average of raw load over $w=\Delta P/\dot P_\mathrm{limit}$, plus a constant loss-replenishment bias. This guarantees the ramp bound even when the averaging window spans several periods. Its harmonic filter is $\sin(\pi fw)/(\pi fw)$. Brent iteration finds the bias that balances $\int P_\mathrm{dis}/\eta_b\,dt=\int P_\mathrm{chg}\eta_b\,dt$. Exact piecewise-linear power areas give inverter extrema and pack energy; zero crossings are included. Nameplate energy is the larger of cyclic excursion/usable SOC and internal pack power/entered C-rate. These sizes apply to this controller and are not a global optimum. Mean dummy power is $\alpha(1-d)\Delta P$; its added energy and the BESS replenishment energy are multiplied by job runtime. The gap-fill mechanism is supported by Ardestani et al., arXiv:2605.24461, pp. 9–10.

• One deterministic, fully synchronized job, rectangular compute/barrier phases and steady non-GPU load. All accelerator and supply efficiencies are constant. The 700 W / 100 W / 0.90 defaults follow the H100 illustration in arXiv:2606.22096; source, impedance and battery defaults are illustrative user parameters.
• $H$ must be expressed on the chosen power base: preserve $H P_\mathrm{base}$ when changing base. The grid mode is a calibrated equivalent coordinate; SCR does not identify its inertia, frequency or damping.
• Frequency starts at zero deviation with mechanical power dispatched to each alternative's mean load. The BESS has periodic workload history and adequate initial charge. Enabling/disabling the buffer or dummy kernels and their mean-power pickup are not simulated.
• Constant-PQ load at lagging PF, fixed source EMF during the trace, no active/reactive coupling through AVR or volts-per-hertz controls. The source must support the dummy load's higher mean.
• Ideal, immediate bidirectional inverter tracking; equal one-way charge/discharge efficiency. The entered C-rate applies to repeated charging as well as discharging; no degradation, auxiliaries, standby losses or temperature derating.

Use the source model for small frequency and equivalent-angle excursions with an unsaturated governor. Conditions flag a raw excursion above 5% frequency, a grid-mode angle above 0.3 rad, engine mechanical power outside 0…rated power, an OEM load-step exceedance, or loss of the high-voltage constant-power solution. The governor is linear: a flagged saturation requires an equipment model rather than extrapolation.

Voltage is a time-varying algebraic RMS envelope at fixed EMF, not an AVR transient prediction. Engine excitation, turbocharger/fuel/air limits, secondary frequency restoration, UPS current limiting and converter controls are excluded. A weak-grid study can require several modes and location-dependent participation; one equivalent mode cannot represent wide-area dynamics generally.

The raw pulse waveform and continuous linear source dynamics are retained between breakpoints. Continuous stationary-point searches determine the extrema independently of horizon length and display resolution. Reported peaks include a conservative numerical allowance. An unconverged search or frequency allowance above 1 µHz blocks a passing assessment and raises a condition. Time plots evaluate the interval solution at 1,801 display points; playback uses shape-preserving interpolation. A short transient can be visually undersampled in a long trace even though the reported peak includes it; do not read protection timing from the plot. Battery areas include exact sign crossings; the energy curve has about 800 samples per period.

The spectrum and period map stop at harmonic 60. The retained-harmonic sum is not a certified all-frequency bound, and the RMS period map is a steady-state screen, whereas reported transient peaks include startup and only the entered iteration count. Increase that count for lightly damped build-up. The plotted period maximum is a sampled maximum over 0.2…10 s.

ISO 8528-5:2025 (sixth edition) is a performance context, not a load-acceptance curve implemented here. Use the gas-engine manufacturer's agreed constant-power load-step/ramp data and check against the standard in force. No standard tables or performance-class limits are reproduced.