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Grid-Mode-Aware Model Predictive Control of Hybrid Energy Storage Systems for AI Data Center Power Smoothing

Xin Chen

arXiv:2609.04398v1eess.SYcs.SY

TL;DR

Highly variable AI data center loads can challenge grid stability by exciting vulnerable oscillatory modes, motivating control that accounts for more than overall load variation. The paper coordinates BESS and SC through grid-mode-aware MPC with embedded band-pass filtering. Simulations show that explicitly suppressing vulnerable-mode power components matters: overall smoothing alone can leave larger frequency oscillations.

  • Problem

    Existing HESS control methods may not flexibly account for grid requirements or vulnerable oscillatory modes, although load components near those modes can drive grid oscillations.

    Source: §I · p. 1

  • Method

    The G-MPC coordinates a BESS and SC over a receding horizon, embedding band-pass filter dynamics to constrain and penalize grid-side power components associated with vulnerable modes.

    Source: §I · p. 2

  • Results

    Case 3 produced larger frequency oscillations than Cases 1 and 2, although all three reduced frequency deviations versus raw data center demand; Case 2 attenuated the 0.5 Hz component effectively.

    Source: C. Grid Frequency Response and… · p. 8

  • Takeaways & Limitations

    The simulations indicate that explicitly attenuating power near a vulnerable grid mode is important for reducing frequency oscillations, beyond reducing overall power fluctuations.

    Source: C. Grid Frequency Response and… · p. 8

    The current G-MPC models do not explicitly regulate terminal energy or SOC deviations, so stored energy may drift toward its limits during extended operation.

    Source: D. Terminal Energy Conditions for BESS… · p. 8

Abstract

from arXiv · show

To facilitate the grid-friendly integration of highly variable AI data center loads, this paper proposes a grid-mode-aware model predictive control (G-MPC) framework for managing a hybrid energy storage system (HESS) to smooth grid-side power demand. The framework optimally coordinates a battery energy storage system (BESS) and a supercapacitor (SC) by solving a multi-step optimization problem in a receding-horizon manner. In particular, band-pass filter dynamics are directly embedded in the G-MPC formulation to extract and suppress grid-side power components associated with vulnerable grid oscillatory modes, thus mitigating load-induced grid oscillations. The resulting G-MPC optimization jointly minimizes violations of grid-side power-envelope, ramp-rate, and modal-power requirements and the degradation and power-ramping costs of the BESS and SC, while satisfying power limits, state-of-charge limits, and other operational constraints. To enable real-time implementation, a fix-and-re-optimize algorithm is developed to solve each G-MPC problem efficiently while preventing simultaneous charging and discharging. Extensive simulations demonstrate the effectiveness, flexibility, and computational efficiency of the proposed framework. The results also highlight the importance of explicitly suppressing power components associated with vulnerable grid modes, rather than merely reducing overall load variations, to effectively mitigate grid oscillations.

I. INTRODUCTION

Highly variable AI data center loads can challenge grid stability, including by exciting poorly damped oscillatory modes. This section motivates combining BESS and SC in a grid-mode-aware controller that accounts for grid requirements and storage operating constraints.

I. INTRODUCTION

  • BESS and SC offer complementary capabilities: the BESS handles slower, energy-dominant variations, while the SC absorbs fast, frequent, power-dominant variations.The combination can reduce battery cycling stress while providing power and energy capabilities for AI data center smoothing.Source: §I · p. 1
  • Existing HESS controls may smooth overall load variations without accounting for vulnerable grid modes, even though near-mode power components can produce larger grid oscillations.The introduction identifies this gap as especially important when storage capacity is limited, because storage may otherwise be spent on dynamically benign variations.Source: §I · p. 2
  • The proposed G-MPC coordinates BESS and SC over a receding horizon, embedding band-pass filter dynamics to constrain and penalize grid-side power components near vulnerable modes.It jointly considers power-envelope, ramp-rate, and modal-power requirements alongside storage degradation and power-ramping costs and operational constraints.Source: §I · p. 2
  • The paper frames its contribution as a flexible G-MPC interface that can adapt to evolving interconnection requirements by changing objective terms and constraints.The introduction also identifies mode suppression and an efficient fix-and-re-optimize solution algorithm as contributions.Source: §I · p. 2

A. Hybrid Energy Storage System in AI Data Center

  • The grid-side objective is to keep AI data center demand within an admissible power envelope, limit upward and downward ramp rates, and suppress components near poorly damped modes.Periodic or quasi-periodic demand near vulnerable frequencies can continuously excite the corresponding grid mode.Source: A. Hybrid Energy Storage System in AI… · p. 3

B. Power Mode Extraction of AI Data Center Load

The power mode extraction model uses a band-pass filter centered on each identified vulnerable grid mode. Its dynamics provide a grid-side power component that the controller can constrain or penalize.

B. Power Mode Extraction of AI Data Center Load

  • For each vulnerable grid mode identified by an operator or measurement-based modal estimation, a second-order band-pass filter extracts the grid-side power component around that mode.The mode frequency sets the filter center, while ζ_m determines the width of the frequency band of interest.Source: B. Power Mode Extraction of AI Data… · p. 3
  • The continuous-time mode extraction dynamics are discretized using sampling interval Δt for implementation in discrete-time MPC.The resulting discrete-time dynamics are given by equation (12).Source: B. Power Mode Extraction of AI Data… · p. 3
  • The extracted component z_m,k represents grid-side data center power within the frequency band surrounding vulnerable mode ω_m.Penalizing or constraining z_m,k lets the controller suppress power variations that can excite the corresponding poorly damped mode.Source: B. Power Mode Extraction of AI Data… · p. 3

C. Control Design Problem

The control design uses a higher-level controller to set BESS and SC power references, with lower-level converters tracking them. G-MPC optimizes over a multi-step horizon and implements only the first action before replanning.

C. Control Design Problem

  • The HESS uses higher-level coordination of BESS and SC power references, while lower-level converter controllers track those references.The lower level operates on millisecond-to-tens-of-milliseconds timescales, while the higher level operates over hundreds of milliseconds or seconds.Source: C. Control Design Problem · pp. 3–4
  • The control-design objective is to choose BESS and SC power-reference trajectories to smooth AI data center demand.The section introduces the optimization models and solution algorithm for coordinating the two storage devices.Source: C. Control Design Problem · p. 4, §III · p. 4

III. GRID-MODE-AWARE MODEL PREDICTIVE CONTROL FOR HYBRID ENERGY STORAGE SYSTEM

  • At each step, G-MPC optimizes BESS and SC power trajectories over an N-step horizon using predicted data center demand, implements the first action, then shifts the horizon and replans.The procedure adapts control actions to evolving load fluctuations and operating conditions.Source: §III · p. 4

A. Energy Storage Dynamics and Constraints

The storage model tracks BESS and SC energy and constrains their charging, discharging, and state of charge. Preventing simultaneous charging and discharging introduces binary constraints that make the optimization nonconvex.

A. Energy Storage Dynamics and Constraints

  • The model represents BESS and SC stored-energy dynamics using charging and discharging powers, efficiencies, and initial stored energy.Their energy states are subject to state-of-charge limits and charging and discharging power limits.Source: A. Energy Storage Dynamics and… · p. 4
  • The BESS has larger energy capacity than the SC, which typically has a small energy capacity because of its low energy density and high capital cost.The BESS is assigned the role of compensating for sustained power variations.Source: A. Energy Storage Dynamics and… · p. 4
  • Binary constraints prevent simultaneous charging and discharging by the BESS or SC, but make the optimization nonconvex and substantially increase computational complexity.The paper introduces a tailored solution algorithm to address this issue.Source: A. Energy Storage Dynamics and… · p. 4

B. Grid-Side Power Requirements

Grid-side power-envelope, ramp-rate, and vulnerable-mode requirements are incorporated as soft constraints, while the G-MPC objective balances their violations against HESS operating costs. The HESS-side costs combine throughput-related degradation and power-ramping penalties to guide BESS-SC allocation.

B. Grid-Side Power Requirements

  • Soft power-envelope, ramp-rate, and modal-power constraints use penalized slack variables to preserve optimization feasibility when requirements cannot be met.The modal-power bound is specified by the grid operator; violations are discouraged through the objective.Source: B. Grid-Side Power Requirements · p. 4

C. Definition of G-MPC Objective

  • The G-MPC objective combines grid-side requirement-violation costs with HESS operating costs.The two objective components are elaborated as grid-side and HESS-side objectives.Source: C. Definition of G-MPC Objective · p. 4

1) Grid-side Objective:

  • Three grid-side objective terms penalize violations of power-envelope, ramp-rate, and grid-mode suppression requirements, with quadratic penalties making larger violations increasingly costly.The corresponding coefficients are cp,k, cr,k, and cm,k.Source: 1) Grid-side Objective · pp. 4–5

2) HESS-side Objective:

  • HESS operating costs account for BESS and SC energy-throughput degradation and penalize power ramps, with the larger BESS ramp penalty steering fast fluctuations toward the SC.The BESS ramping penalty is stated to be much larger than the SC penalty; this allocation avoids predefined frequency separation.Source: 2) HESS-side Objective · p. 5

D. Complete G-MPC Models and Solution Algorithm

The complete G-MPC model is an MIQP whose binary operating constraints complicate efficient real-time solution. A relaxed QP followed, when needed, by status fixing and re-optimization provides a computationally efficient approach that avoids simultaneous charging and discharging.

D. Complete G-MPC Models and Solution Algorithm

  • The complete model is an MIQP, and its nonconvexity and computational burden challenge efficient real-time HESS control.The binary constraints give rise to the MIQP formulation.Source: D. Complete G-MPC Models and Solution… · p. 5
  • Relaxing binary constraints yields a convex QP that standard QP solvers can efficiently solve, although its solution may include simultaneous charging and discharging.The relaxation replaces binary constraints with continuous ones.Source: D. Complete G-MPC Models and Solution… · p. 5
  • When the relaxed solution has simultaneous charging and discharging, the algorithm recovers operating status from net energy changes and power outputs, fixes the statuses, and re-solves the QP.Small tolerances are used to avoid numerical ambiguity when net energy change or net power is close to zero.Source: D. Complete G-MPC Models and Solution… · p. 5
  • At most two QPs are solved per MPC step; soft grid-side constraints preserve feasibility, and the relaxed and fixed-status solutions provide bounds on the original problem’s objective and optimality gap.If no simultaneous charging and discharging occurs, the relaxed solution is also optimal for the original model.Source: D. Complete G-MPC Models and Solution… · pp. 5–6

IV. NUMERICAL SIMULATIONS

The paper evaluates the proposed G-MPC-based HESS control algorithm through simulations of AI data center power smoothing and grid oscillation mitigation.

IV. NUMERICAL SIMULATIONS

  • Simulations are conducted to evaluate G-MPC-based HESS control for AI data center power smoothing and grid oscillation mitigation.Source: §IV · p. 6

A. Simulation Setup and Parameter Settings

The simulations represent the grid with aggregate synchronous-generator frequency dynamics and evaluate the HESS controller using a constructed AI data center load profile. Three cases compare joint grid requirements, mode suppression alone, and grid requirements without explicit mode suppression.

1) Aggregate Power Grid Dynamic Model:

  • The grid model uses linearized swing and governor equations, with one targeted oscillatory mode set to the grid’s natural frequency of 0.5 Hz.The modal filter damping ratio is set to 0.1.Source: 1) Aggregate Power Grid Dynamic Model · p. 6

2) AI Data Center Load Profile and HESS Configuration:

  • The test load combines measured GPU training demand scaled to 100 MW, a constant 50 MW auxiliary load, and a 20 MW sinusoid at the grid’s natural frequency.The HESS comprises a 40-MW/40-MWh BESS and a 20-MW/0.3-MWh SC, each operated within a 10%-90% energy window; the controller uses a 0.25-second sampling interval and a 50-second prediction window.Source: 2) AI Data Center Load Profile and… · p. 6
  • The three comparison cases test the complete model, mode suppression alone, and power-envelope and ramp-rate requirements without explicit mode suppression.Additional evaluations cover terminal conditions that restore initial SOC and computational efficiency.Source: 2) AI Data Center Load Profile and… · p. 6

B. Performance of the Proposed G-MPC Framework

In Case 1, G-MPC keeps grid-side demand within [120, 130] MW for most of the simulation by coordinating the SC’s rapid response with the BESS’s slower, sustained compensation. The BESS and SC satisfy their SOC constraints, and the targeted-mode suppression cost quickly falls to nearly zero.

1) Data Center Load and HESS Power Outputs:

  • The grid-side load stays within [120, 130] MW for most of Case 1, while the SC responds to rapid variations and the BESS compensates for slower, sustained changes.Temporary envelope violations occur during very large demand excursions when both storage systems reach their power limits.Source: 1) Data Center Load and HESS Power… · p. 7, Figure 2 · p. 7

2) HESS Energy Trajectories and Re-Optimization:

  • Both storage systems satisfy their SOC constraints, and the fix-and-re-optimize step is not invoked because the relaxed QP solution avoids simultaneous charging and discharging.The re-optimization indicator remains inactive throughout this simulation.Source: 2) HESS Energy Trajectories and… · p. 7, Figure 3 · p. 7

3) Objective Values:

  • The targeted-mode suppression cost rapidly falls to nearly zero, while grid-side regulation remains close to zero except during a 190–220 s envelope violation at the storage power limits.Figure 4 reports the objective costs incurred by the control action implemented at each MPC step.Source: 3) Objective Values · p. 7, Figure 4 · p. 7
  • The HESS ramping cost occasionally spikes, primarily from fast BESS power changes, while its degradation cost remains relatively small throughout the simulation.The reported ramping-cost spikes occur as the BESS accommodates rapid load variations.Source: 3) Objective Values · p. 7, Figure 4 · p. 7

C. Grid Frequency Response and Oscillation Suppression

Across Cases 1–3, HESS-filtered loads reduce frequency deviations versus raw data center demand, but Case 3’s smoother overall load still produces larger oscillations than Cases 1 and 2. The results associate better mitigation with suppressing the component near the grid’s 0.5-Hz natural frequency; Case 2 has the lowest reported HESS operating cost.

Grid-side load profiles

  • Case 3 keeps grid-side load mainly within [120, 130] MW, whereas Case 2 retains relatively large variations, particularly during the 190–220 s low-load period.Case 2 targets the oscillation-mode component; Case 3 targets power-envelope and ramp-rate requirements.Source: C. Grid Frequency Response and… · pp. 7–8, Figure 5 · p. 8

Grid frequency response

  • All three cases substantially reduce frequency deviations versus raw demand, but Case 3 produces larger oscillations than Cases 1 and 2 despite smaller overall power variations.The grid-frequency response comparison is shown for the raw-demand baseline and filtered loads in Cases 1–3.Source: C. Grid Frequency Response and… · p. 8, Figure 6 · p. 8

Targeted oscillation suppression

  • Raw demand contains an approximately 20 MW component at 0.5 Hz; Cases 1 and 2 eliminate it, while Case 3 retains a noticeable component despite attenuating low-frequency components.The five dominant frequency components were identified using FFT analysis.Source: C. Grid Frequency Response and… · p. 8, Figure 7 · p. 8

Operational cost

  • Case 2 incurs the lowest HESS operational cost at $72.39 over 300 seconds, with oscillation mitigation comparable to Case 1 and superior to Case 3.The reported costs for Cases 1–3 are $99.48, $72.39, and $74.17, respectively.Source: C. Grid Frequency Response and… · p. 8

D. Terminal Energy Conditions for BESS and SC

The complete G-MPC framework coordinates BESS and SC operation to suppress vulnerable grid-mode power components, and the conclusion reports that this matters beyond reducing overall power variations. In Case 4, anticipatory storage operation kept both stores near their initial energy levels while meeting terminal constraints; the fix-and-re-optimize algorithm had a small objective gap and the optimization met the reported solution-time limits.

D. Terminal Energy Conditions for BESS and SC

  • Without explicit terminal-energy regulation, stored energy can drift toward its bounds and reduce the margin available for future load increases or decreases.The paper identifies a terminal penalty or hard terminal-energy constraints as ways to discourage drift or restore terminal energy to its initial level.Source: D. Terminal Energy Conditions for BESS… · p. 8
  • During the predicted load reduction, the BESS and SC discharged in advance and then charged during the low-load period, leaving both energy levels close to their initial values.Figures 8 and 9 show the grid-side load and storage outputs, and the stored-energy trajectories, respectively.Source: D. Terminal Energy Conditions for BESS… · p. 9, Figure 8 · p. 9, Figure 9 · p. 9
  • The relative objective value gap reached a maximum of 0.55% and averaged 0.4% across re-optimized instances, indicating near-optimal final control decisions.Figure 10 presents the relative objective value gap.Source: D. Terminal Energy Conditions for BESS… · p. 9, Figure 10 · p. 9

E. Computational Efficiency

V. CONCLUSION

  • Simulations show that G-MPC smooths variable AI data center demand and suppresses vulnerable grid-mode components; ablations show that reducing overall variations alone does not necessarily mitigate grid oscillations.The framework coordinates the complementary power and energy capabilities of the BESS and SC.Source: §V · p. 9
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