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Integrated Thermal and Power Management for Wave-Powered Subsea Data Centers via Nonlinear Model Predictive Control

Wanqun Yang, Jun Chen

arXiv:2609.34109v1eess.SYcs.SY

TL;DR

The paper addresses the challenge of coordinating flexible workloads, cooling, wave power, and battery operation in a wave-powered subsea data center. It develops an integrated model and NMPC controller, which maintains the prescribed IT temperature limit while adapting cooling and workload execution to wave availability and battery state of charge.

  • Problem

    Prior studies considered parts of data-center workload, cooling, and renewable-storage coordination, but did not simultaneously coordinate job-level flexible workloads, active cooling, renewable generation, and battery storage.

    Source: §I · p. 2

  • Method

    An integrated NMPC uses workload, thermal, cooling, wave-power, and battery models to jointly set the flexible-workload power budget and cooling command, then applies an FCFS job-admission rule.

    Source: §I · p. 2

  • Results

    The controller maintains IT temperature within its prescribed limit while adapting cooling and flexible-workload execution to wave-power availability and battery SOC.

    Source: §IX · p. 15

  • Takeaways & Limitations

    Increasing WEC units improves battery availability and reduces flexible-workload queue accumulation, but increases wave-energy curtailment; mean delayed-job delay is relatively insensitive to investigated parameters.

    Source: §IX · p. 15

Abstract

from arXiv · show

This paper develops an integrated modeling and nonlinear model predictive control (NMPC) framework for coordinating thermal management, flexible workload scheduling, wave-power utilization, and battery operation in a wave-powered subsea data center. Realistic data center workloads are constructed from job-level CPU, memory, and GPU measurements from the MIT Supercloud dataset and divided into interactive and delay-tolerant flexible jobs. Thermal behavior is represented by a three-node lumped model of the IT equipment, recirculating nitrogen, and pressure hull with surrounding seawater as the thermal boundary. The NMPC jointly optimizes the flexible workload power budget and cooling command subject to thermal, battery, and workload constraints. Closed-loop simulations under different workload, thermal, battery, and renewable-generation conditions demonstrate that the proposed framework maintains thermal safety while adapting cooling operation and flexible workload execution to wave-power availability and battery state-of-charge. The parametric studies show that battery capacity and wave-generation capacity strongly affect battery availability and flexible-workload queue accumulation, while excessive renewable generation capacity may lead to increased energy curtailment. Monte Carlo and distance-correlation analyses further show that flexible-job delay is relatively insensitive to the investigated system parameters, whereas terminal battery state-of-charge is primarily influenced by battery energy capacity and wave generation capacity.

I. Introduction

Rising computational demand increases both data-center power use and thermal-management needs, while wave variability, battery limits, cooling power, and flexible workloads create coupled control requirements. The paper develops an integrated model and NMPC framework for a wave-powered subsea data center, using job-level workload data and coordinating cooling with flexible-job execution.

I. Introduction

  • A wave-powered subsea data center uses seawater as a heat sink, but internal fans and pumps still consume power and must be controlled for thermal safety.Heat moves from IT equipment to internal gas, then through heat exchangers to seawater; some heat also passes through the pressure hull.Source: §I · p. 2
  • Wave generation varies and may not match demand, so battery storage buffers power imbalances while its available energy remains limited by state of charge.Flexible workloads can be deferred to adapt demand to renewable availability and battery condition, but they also add electrical load and heat.Source: §I · p. 2
  • The integrated NMPC coordinates flexible-workload execution and active cooling because workload, thermal dynamics, wave generation, and battery operation are coupled.Earlier studies considered parts of this problem, but not job-level flexible workload, cooling, renewable generation, and storage together.Source: §I · p. 2
  • Interactive jobs run upon arrival, while delay-tolerant flexible jobs may be deferred and admitted in strict first-come-first-served order under the NMPC power budget.Admission requires the first-step job power to fit within that budget and the battery-energy reserve condition to be satisfied.Source: §I · p. 2

II. System Overview

  • The system overview links wave-energy converters and battery storage to the data-center load, while the controller coordinates flexible-job execution with pod cooling.Electrical supply, heat rejection, and control commands connect the power and thermal sides of the system.Source: §II · p. 3

III. Subsea Data Center Workload Model

  • The workload model processes MIT Supercloud job-level CPU, memory, and GPU measurements alongside Slurm execution intervals to form a time-aligned IT power profile.CPU and memory power are estimated from utilization and resident memory; GPU power comes directly from hardware telemetry, and background loads are represented separately.Source: §III · pp. 3–4

IV. Subsea Data Center Thermal Model

The thermal model represents the subsea pod with three lumped temperature states and treats seawater temperature as a time-varying boundary. Its IT-node balance captures heat generation and exchange with recirculating nitrogen.

IV. Subsea Data Center Thermal Model

  • The three thermal states are IT equipment, recirculating nitrogen, and pressure-hull temperatures, with seawater temperature as a time-varying boundary condition.IT heat first transfers to nitrogen; some is removed by the gas-to-seawater heat exchanger, and remaining heat can transfer to the pressure hull.Source: §IV · p. 4

A. IT Temperature (TIT)

  • The IT-node energy balance accounts for IT heat generation and heat exchanged between the equipment and recirculating nitrogen.The IT thermal capacitance is calculated using rack count and effective rack thermal mass; the effective specific heat capacity is set to 600 J/(kg K).Source: A. IT Temperature (TIT) · pp. 4–5
  • The effective IT-to-nitrogen thermal conductance depends on total nitrogen mass flow and an effective heat-transfer factor.The model defines this conductance using nitrogen flow and specific heat capacity.Source: A. IT Temperature (TIT) · p. 5

B. Nitrogen Temperature (TN2)

The nitrogen node exchanges heat with the IT equipment, heat exchangers, and pressure hull. Heat-exchanger capacity is modeled using flow-dependent heat-capacity rates and an effectiveness map adapted from air-to-water data.

B. Nitrogen Temperature (TN2)

  • The nitrogen energy balance accounts for heat exchange with the IT equipment, gas-to-seawater heat exchangers, and pressure hull.The nitrogen thermal capacitance is calculated from its specific heat capacity and total pod nitrogen mass, with pod volume based on a cylindrical enclosure.Source: B. Nitrogen Temperature (TN2) · p. 5
  • The heat-exchanger model calculates conductance from the number of active units and heat-capacity rates on the nitrogen and seawater sides.The active-unit count is treated as a continuous equivalent quantity; the model limits heat transfer using the smaller side heat-capacity rate.Source: B. Nitrogen Temperature (TN2) · p. 5
  • Heat-exchanger effectiveness uses an air-to-water map as a surrogate for nitrogen-to-seawater exchange, with two-dimensional interpolation by per-unit flow rates.The stated justification is that nitrogen and air, and seawater and fresh water, have similar thermophysical properties.Source: B. Nitrogen Temperature (TN2) · p. 5

C. Pressure Hull Temperature (Th)

The pressure-hull model accounts for heat exchange with both recirculating nitrogen and surrounding seawater. A normalized cooling command sets the active cooling fraction and associated flow conditions.

C. Pressure Hull Temperature (Th)

  • The pressure hull exchanges heat with recirculating nitrogen and surrounding seawater, with hull-to-seawater transfer represented by an effective thermal conductance.The cited empirical and CFD study reports hull-to-seawater heat-transfer coefficients of approximately 360–670.5 W/(m2K).Source: C. Pressure Hull Temperature (Th) · pp. 5–6
  • Hull thermal capacitance is determined from its structural thickness, material density, and specific heat capacity.Source: C. Pressure Hull Temperature (Th) · p. 5

A. Cooling Flow Regulation

  • The normalized cooling command sets a continuous active fraction, represented as an equivalent active heat-exchanger count rather than an integer unit count.A nonzero minimum active fraction preserves baseline cooling at the minimum command.Source: A. Cooling Flow Regulation · p. 6
  • Fan speed and seawater flow through each active heat exchanger are derived from the cooling command, with seawater flow bounded by the modeled minimum and maximum.Nitrogen flow is treated at system level as the effective gas-side flow through the active heat-exchanger path.Source: A. Cooling Flow Regulation · p. 6
  • At the minimum command, cooling equipment operates at minimum flow with a nonzero active fraction; at the maximum, all units operate at maximum modeled flow.Source: A. Cooling Flow Regulation · p. 6

B. Internal Nitrogen Circulation Fan Power

Fan and pump power are modeled from cooling-system operation. Fan power uses a speed-based polynomial, while pump power uses a reference pump and centrifugal-pump affinity laws.

B. Internal Nitrogen Circulation Fan Power

  • Each running circulation fan’s power is estimated by a polynomial in rotational speed, and total fan power accounts for the active cooling fraction and fan count.The polynomial coefficients are adopted from experimental fan testing reported by Garraghan et al..Source: B. Internal Nitrogen Circulation Fan… · pp. 6–7

C. Seawater Pump Power

  • The seawater-pump model uses a representative Calpeda BNMS 40/125A pump and does not explicitly resolve hydraulic pressure losses in the seawater loop.The selected pump’s rated flow and power are taken from the manufacturer’s catalog.Source: C. Seawater Pump Power · p. 7
  • Pump power is calculated from per-pump seawater flow using affinity laws: flow scales with speed, and power scales with speed ratio cubed.The flow is compared with the selected pump’s reference flow to determine its speed ratio.Source: C. Seawater Pump Power · p. 7
  • At the maximum cooling command, modeled pump flow reaches the maximum heat-exchanger-side flow; at the minimum, pump power decreases with minimum active cooling.Source: C. Seawater Pump Power · p. 7

VI. Energy Supply Modeling

The energy-supply model combines IT and active-cooling demand with wave generation and battery storage. It estimates wave output from environmental conditions and uses the resulting generation and load profiles in the storage model.

A. Power Consumption Modeling

  • Facility demand combines IT power with active cooling power from circulation fans and seawater pumps; the heat-exchanger core affects thermal dynamics but adds no electrical power term.IT power from the workload model is also used as thermal-model heat input.Source: A. Power Consumption Modeling · p. 7
  • PUE is calculated as total load energy divided by IT energy, measuring active-cooling energy overhead relative to IT consumption.Source: A. Power Consumption Modeling · p. 7

B. Wave Power Generation

  • Wave-converter output is estimated from significant wave height, representative wave period, conversion efficiency, seawater density, gravity, and capture width, then limited by rated power.Array generation is used with the data-center load profile in the battery storage model.Source: B. Wave Power Generation · pp. 7–8
  • In the ERA5 dataset, wave activity and generated energy are generally higher in winter and lower in summer, while seawater temperature follows a seasonal trend.Figure 2 presents full-year environmental and renewable-energy conditions.Source: B. Wave Power Generation · p. 8, Figure 2 · p. 8

C. Battery Storage System

The battery model updates state of charge according to whether wave generation exceeds or falls short of data-center load. Charging and discharging are bounded by power limits and available battery energy.

C. Battery Storage System

  • Net power balance compares total wave generation with data-center load, including IT and active cooling power.Source: C. Battery Storage System · p. 8
  • When generation meets or exceeds load, surplus power charges the battery, with charging limited by battery power capacity and remaining energy capacity.The charging update accounts for charging efficiency and the maximum state of charge.Source: C. Battery Storage System · p. 8
  • When generation is below load, the battery discharges to cover the deficit, constrained by the deficit, battery power capacity, and stored energy above minimum state of charge.The discharge update accounts for discharging efficiency and the minimum state-of-charge limit.Source: C. Battery Storage System · p. 8

VII. NMPC-Based Cooling and Workload Control

The NMPC predicts thermal, battery, workload, and queue states to coordinate flexible-workload power with active cooling. Its constraints and FCFS admission process preserve operating limits while scheduling queued jobs.

VII. NMPC-Based Cooling and Workload Control

  • The normalized cooling command ranges from 0 to 1 and sets the active cooling fraction, fan speed, seawater flow, and associated power.The objective penalizes queue backlog, high cooling, low predicted SOC, temperatures near the limit, and control variation.Source: §VII · pp. 9–10
  • The controller includes remaining queued flexible-workload energy as a predicted state, accounting for arrivals and planned power available for new jobs.The queue update estimates energy removed during each prediction interval, though actual reduction may be smaller under strict FCFS scheduling.Source: §VII · p. 9
  • The NMPC jointly predicts thermal, battery, and queue dynamics to optimize flexible-workload power and cooling over a finite horizon.Only the first cooling command and first-step workload budget are applied before the optimization is repeated at the next sampling time.Source: §VII · pp. 8–9
  • Constraints bound workload power and cooling, preserve battery SOC limits, and keep IT temperature below its maximum while honoring power for committed jobs.When measured SOC is at or below the admission threshold, first-step workload power is restricted to committed jobs.Source: §VII · p. 9
  • A strict FCFS scheduler admits jobs using the optimized power budget; admitted jobs remain committed until completion and cannot be bypassed.Admission also requires sufficient battery energy above the flexible-job reserve threshold; a separate hard SOC threshold stops new admissions while committed jobs continue.Source: §VII · pp. 9–10

VIII. Results and Discussion

The results section evaluates the integrated model and controller through parametric closed-loop simulations. Simulations use an hourly control interval, an eight-hour prediction horizon, and a nine-day workload case.

VIII. Results and Discussion

  • The studies use the same three-node thermal model, wave-battery energy model, strict FCFS admission rule, and NMPC formulation across varied conditions.Only the investigated parameter or input dataset changes in each study.Source: §VIII · p. 10
  • Closed-loop simulations use a 1 h sampling interval, an 8 h prediction horizon, SQP via fmincon, and a 48 h baseline deadline.One NMPC problem is solved at each sampling time.Source: §VIII · p. 10
  • Each workload case runs for nine days, with flexible jobs arriving in the first seven days included in job-level QoS metrics.The final two days let jobs already in the system continue affecting the physical workload, battery, thermal states, and FCFS queue.Source: §VIII · p. 10

A. Impacts of Temperature Limit TIT,max

Temperature-limit and weekly-condition studies show that cooling, battery use, queue accumulation, and flexible-job service vary across operating conditions. Higher temperature limits reduce cooling demand but do not consistently improve job QoS.

A. Impacts of Temperature Limit TIT,max

  • Across temperature limits, IT temperature rises and cooling power and real-time PUE fall; battery trajectories are mostly similar and executed workload power changes little.More noticeable queue differences appear near the simulation end.Source: A. Impacts of Temperature Limit TIT,max · p. 11
  • Increasing the IT temperature limit reduces cooling demand and slightly improves battery SOC, but does not consistently improve flexible-job QoS.The 40°C case remains the baseline, with no missed jobs in any evaluated temperature-limit case.Source: A. Impacts of Temperature Limit TIT,max · p. 11, Table V · p. 11

B. Impacts of Week of Year

  • Weekly flexible-job characteristics vary substantially: Jan. 10 and Mar. 9 have shorter, lower-power jobs, while Feb. 13 and Jul. 1 have broader duration and power distributions.These differences impose different scheduling and energy-management demands.Source: B. Impacts of Week of Year · pp. 11–12, Figure 4 · p. 11
  • Across weeks, battery SOC is mostly near its upper range, but Jul. 1 and Jul. 17 show wider SOC distributions and larger reductions; IT temperature stays below 40°C.Sep. 12 has the largest integrated queue burden and maximum queue size, while Jan. 10 and Apr. 8 also show noticeable queue accumulation.Source: Figure 5 · p. 11, B. Impacts of Week of Year · p. 12, Figure 6 · p. 12
  • Sep. 12 has the largest queue burden but not the highest delayed-job percentage, so queue accumulation and delayed-job fraction do not necessarily align.Weekly conditions affect battery utilization, queue accumulation, and flexible-job service performance.Source: B. Impacts of Week of Year · p. 12, Table VI · p. 12

C. Impacts of Base-IT-Power

The base-IT-power study finds that higher continuous IT demand reduces minimum battery SOC and raises operating temperature, while flexible-job QoS and PUE change little.

C. Impacts of Base-IT-Power

  • As base IT power increases, minimum battery SOC falls and IT temperature shifts higher, while remaining below its limit in all evaluated cases.The study varies base power from 25 to 55 kW with the July 17 week and 40°C IT limit held fixed.Source: C. Impacts of Base-IT-Power · p. 12, Figure 7 · p. 12
  • Only 3.1%–3.8% of started flexible jobs are delayed across base-power cases, with no missed deadlines and no clear QoS trend as base power increases.Delayed jobs wait one or two hours; mean delays are 1.00–1.11 h and standard deviations are no greater than 0.31 h.Source: C. Impacts of Base-IT-Power · p. 12, Figure 8 · p. 12, Table VII · p. 12
  • PUE remains nearly unchanged across the evaluated base-power settings, and 45 kW is retained as the nominal setting for other studies.Overall, the higher base load mainly reduces battery-energy margin and raises IT operating temperature.Source: C. Impacts of Base-IT-Power · p. 12, Table VIII · p. 13

D. Impacts of Battery Capacity

Across the parametric studies, larger batteries and more WEC units improve battery availability and reduce flexible-job queue accumulation; Monte Carlo results find delay less parameter-sensitive than terminal battery SOC.

D. Impacts of Battery Capacity

  • 6.0/0.8 MWh/MW is the smallest evaluated battery pair with no missed jobs and the same reported QoS as larger configurations.Larger batteries also maintain higher late-period SOC, reduce queue accumulation, and support higher flexible-job power after SOC trajectories separate.Source: D. Impacts of Battery Capacity · p. 13

E. Impacts of WEC Configuration

F. Monte Carlo Simulation and Sensitivity Analysis

IX. Conclusion

  • The integrated controller keeps IT temperature within its limit while adapting cooling and flexible-workload execution to wave availability and battery SOC.The conclusion also reports that higher base IT power reduces the battery-energy margin and raises IT operating temperature.Source: §IX · p. 15
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