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A Control Co-Design Framework to Optimize Sustainability with Application to Microgrid-Driven Data Centers

Tania Rifat Jahan, Donald J. Docimo

arXiv:2609.01912v1eess.SY

TL;DR

Data-center and microgrid design rarely optimizes plant and controller features together while treating sustainability as central. The paper develops a lifecycle-based sustainability-centric CCD framework, applies it to a microgrid-driven data center, and reports improved sustainability outcomes, including a 50% reduction in emissions and e-waste relative to baseline designs.

  • Problem

    Limited studies simultaneously optimize data-center and microgrid plant and controller features, and few make quantified sustainability criteria the focus of optimization.

  • Method

    The paper develops a sustainability-centric CCD framework that uses lifecycle-stage metrics as primary objectives and applies it to a microgrid-driven data-center model.

  • Results

    Compared to baseline designs minimizing power tracking error, the CCD framework can yield a 50% reduction in emissions and e-waste.

  • Takeaways & Limitations

    The framework shows that sustainability-focused CCD can identify designs with improved environmental sustainability across the analyzed microgrid-driven data-center system.

  • Takeaways & Limitations

    Validation is limited to a small set of designs, with hardware-in-the-loop validation left for future work.

Abstract

from arXiv · show

This work studies the optimization of physical plant characteristics and controller parameters for sustainability. Environmental sustainability is strongly correlated with the development and operation of energy systems, with data centers as the preeminent modern example. Data centers, and the grid technologies that provide their power, consume nonnegligible amounts of global energy and pose a risk to increase greenhouse gas (GHG) emissions and electronic waste. Addressing such issues requires improved plant design and control strategies, often approached through optimization-based methods. However, there are noticeable gaps regarding data center and microgrid design: (i) simultaneous optimization of plant and controller features is rarely explored, and (ii) sustainability criteria are not emphasized. This work addresses these gaps by establishing a generalized, sustainability-centric control co-design (CCD) framework for energy systems. Uniquely, the CCD framework defines and categorizes sustainability metrics into three lifecycle stages - manufacturing, operation, and disposal - supporting optimization and comparative analysis of the metrics for different design options. To exemplify its use, the CCD framework is applied to a microgrid-driven data center system, providing a family of sustainability metrics correlated to plant and controller parameters. The analysis enabled by the framework provides insights into the CCD of microgrids and data centers, such as that GHG-equivalent emissions from manufacturing of components can dwarf those generated during operation of the system. The system designs identified by the proposed framework show substantial improvements to environmental sustainability categories as compared to designs identified through baseline procedures.

1. INTRODUCTION

Data-center and microgrid sustainability depends on jointly considering plant design and control, but prior work rarely optimizes both while making sustainability central. This paper addresses those gaps with a sustainability-centric CCD framework and a microgrid-driven data-center application.

  • Motivation: Data centers consume 2% of the world’s net generated electricity per year, while AI and cloud use are driving that share upward.
  • Research gap: Prior studies broaden plant or controller design spaces, but limited work simultaneously optimizes both plant and controller parameters through CCD.
  • Research gap: Few studies quantify sustainability as a primary optimization focus, leaving environmental impacts of microgrid-driven data centers insufficiently addressed.
  • Contributions: The paper develops a sustainability-centric CCD framework and applies it to a novel microgrid-powered data-center representation.
  • Contributions: The application produces correlations between plant and controller parameters and sustainability metrics, alongside Pareto-optimal designs and baseline comparisons.

2. SUSTAINABILITY-CENTRIC CONTROL CO-DESIGN FRAMEWORK

The framework co-optimizes plant and controller variables under system constraints while making sustainability objectives explicit across the component lifecycle. It solves and analyzes a multi-objective CCD problem to identify designs and lifecycle-stage trade-offs.

  • Framework structure: The five-step framework defines design variables, objectives, constraints, the multi-objective problem, and its solution and outcome analysis.
  • Design variables: Plant variables cover sizing and topology, while controller variables include architecture settings, timesteps, predictive horizons, and algorithm gains.
  • Sustainability objectives: Manufacturing accounts for impacts from component production, operation covers environmental effects during system use, and disposal captures e-waste and resource impacts.
  • Analysis: Categorizing metrics enables comparison of designs and identification of the lifecycle stage producing the primary negative sustainability impacts.
  • Optimization formulation: The CCD formulation couples plant dynamics and controller inputs, enforces performance and design bounds, and supports multiple control-algorithm implementations.
  • Sustainability objectives: Sustainability objectives are organized into manufacturing, operation, and disposal lifecycle stages.

3. MODEL DYNAMICS

The model combines a renewable microgrid, battery storage, power converters, and a data center represented through coupled electrical and thermal dynamics.

  • The full system combines renewable generation and battery storage with a data center whose servers and cooling subsystems consume energy.
  • Microgrid components: Five electrical component types model microgrid dynamics: voltage buses, boost and buck converters, PV subsystems, and battery packs.
  • Microgrid components: Voltage bus 1 connects generation and storage, while voltage bus 2 bridges the microgrid and data center.
  • Microgrid components: The PV subsystem models temperature effects from irradiance, ambient temperature, and electrical power output, while the battery captures state of charge and relaxation voltages.
  • Data center components: Data-center dynamics represent server-rack heating, server-room air circulation, cooling-control-unit air, plenum air, and vapor-compression cooling.
  • Data center components: Thermal control-volume equations account for air flows, convection, thermal capacitance, and cooling effects across the server room and cooling system.

3.3 Combined Microgrid and Data Center Model

The combined model couples the microgrid and data-center electrical, thermal, and electro-thermal component models. It represents the resulting system in a graph-based energy-dynamics format with defined states, inputs, and power flows.

  • Model coupling: The model couples individual microgrid and data-center component models into one combined system.Electrical components are connected through algebraic relationships, while thermal models are connected by matching appropriate temperatures.
  • Model coupling: The VCS and server racks are connected through power-flow relationships that represent electro-thermal coupling.The VCS power is computed from converter output voltage and current, while rack powers are defined similarly and summed into total rack load.
  • System representation: The combined system contains 37 states, including electrical, battery, thermal, VCS, and converter states.The listed states include bus voltages, battery and PV variables, temperatures, VCS state, and converter input/output voltage states.
  • System representation: The model has 6 converter duty-cycle control inputs and 2 exogenous inputs: solar irradiance and ambient temperature.The control vector contains D₁ through D₆, while the exogenous-input vector contains G and T∞.
  • System representation: The energy dynamics use a graph-based model containing a capacitance matrix, an incidence matrix, nonlinear power flows, and sink states.This format supports the CCD representation of the coupled system.

4. CONTROL ALGORITHM & VALIDATION

The controller uses a model-free perturb-and-observe strategy to manipulate converter duty cycles under operating constraints. Validation across parameter variations shows reference-power tracking and battery-protection behavior, with thermal response depending on rack geometry.

  • Control algorithm: The controller uses nine discrete modes determined by battery SOC and server-rack temperatures.The modes modify the αᵢ and βᵢ expressions while respecting state and input bounds.
  • Control modes: In normal operation, the PV boost converter maximizes PV power while converters 5 and 6 track the electrical power demands of the two server racks.The remaining converter duty cycles are held constant in this mode.
  • Control modes: When battery SOC exceeds its upper bound, the controller cuts off PV input and drives the battery toward a safer charge level.The VCS converter is set high to assist battery discharge, while the server-rack converters continue tracking their power references.
  • Validation: All three tested parameter sets track server reference power for at least 20 hours and stop battery charging when SOC reaches its maximum.PV energy is curtailed to avoid overcharging; the lowest-capacity battery eventually reaches SOC_min and forces rack power shutdown.
  • Validation: Validation uses three plant-parameter sets under a 24-hour simulation with sinusoidal irradiance peaking at 1000 W/m^2 for 12 daylight hours.The tests use ∆u = 0.01, ∆t = 60 s, and initial battery SOC and rack temperatures of 0.5 and 18°C.
  • Validation: Increasing rack height lowers rack temperature by increasing vertical surface area and distributing the same input power across more servers.The comparison between parameter sets 2 and 3 identifies an inverse relationship between rack height and rack temperature.

5. APPLICATION OF PROPOSED CCD FRAMEWORK TO THE CANDIDATE SYSTEM

The proposed CCD framework applies lifecycle sustainability objectives to jointly vary plant and controller design variables for the microgrid-driven data center. It evaluates manufacturing emissions, operational waste heat, disposal impacts, and power-tracking feasibility across candidate designs.

  • CCD formulation: Plant design variables scale the number of Li-ion cells and server-rack height, while a controller variable sets the common duty-cycle perturbation magnitude.The augmented plant dynamics incorporate design matrices, and the controller constraint matches the plant model with the control policy.
  • Sustainability objectives: The framework defines sustainability objectives for manufacturing, operation, and disposal and combines them into a total objective.Manufacturing covers component GHG emissions, operation covers waste heat, and disposal covers annual e-waste from component replacement.
  • Sustainability objectives: Manufacturing emissions quantify GHG equivalents from microgrid and data-center components, including battery cells and servers.The manufacturing objective is expressed in kilograms of CO2 equivalent and correlates component sizing with emissions.
  • Sustainability objectives: The operation objective integrates waste heat released by the microgrid and data-center halves while delivering server power.Separate microgrid and data-center waste-heat terms are converted into kg of CO2 equivalent using the specified coefficients.
  • Sustainability objectives: The disposal objective estimates e-waste from battery and server replacement using battery degradation and processor-transistor thermal-cycling failure models.Battery end of life occurs after 20% nominal-capacity loss, while server lifetime depends on MTTF as a function of rack and ambient temperatures.
  • CCD formulation: Power tracking is imposed as a key inequality constraint, with additional constraints limiting plant and controller design variables.The traditional tracking objective is instead constrained below μ₁,max = 5.3 × 10^10 for the sustainability-focused optimization.

6. RESULTS AND DISCUSSION

The analysis maps sustainability objectives against plant and controller variables, constructs Pareto fronts, and compares a sustainability-centric design with a power-tracking baseline. Manufacturing impacts can dominate operational impacts, while modest power-tracking sacrifice yields substantial environmental reductions.

  • Analysis procedure: The grid search relates design variables to sustainability objectives, and Pareto fronts expose trade-offs among manufacturing, operation, and disposal impacts.Designs are also compared with one selected through a baseline procedure.
  • θ₁ and ϕ₁ relationships: Three designs with θ₁ < 200 violate the power-tracking error constraint μ₁,max and are classified as unacceptable.
  • θ₁ and ϕ₁ relationships: Manufacturing depends solely on θ₁, while the operation objective depends on both θ₁ and ϕ₁ and is more sensitive to θ₁.The normalized sensitivity ∂Jₒ/∂ϕ₁ is 0.3318, and changes in θ₁ become more impactful as waste-heat generation increases.
  • Design-variable comparisons: Generated e-waste is more strongly influenced by θ₁ than ϕ₁, while θ₂ has greater impact than ϕ₁ on e-waste in the second design subset.For θ₂, the controller variable does not affect manufacturing, and rack height minimally affects operation except at high ϕ₁; ∂Jₒ/∂θ₂ peaks at 162.0.
  • Design-variable comparisons: Increasing battery-cell count raises degradation, whereas increasing server count lowers average server temperature and degradation.Higher degradation leads to more e-waste or earlier component replacement.
  • Sustainability-centric Pareto fronts: For operation of 16.7 years or less, the rightmost design prioritizes minimizing manufacturing emissions, while longer operation favors the leftmost design to reduce waste heat.Components may require replacement within 16.7 years, creating another manufacturing instance.
  • Sustainability-centric Pareto fronts: At c_d,o = 5.33, the extreme designs have equal environmental impact; below it, the leftmost design is preferred, while above it, the rightmost is preferred.The threshold balances waste heat against e-waste when no accepted conversion rate is available.

7. CONCLUSION

The paper develops a sustainability-focused CCD framework for microgrid-driven data centers by jointly considering plant and controller variables across component lifecycle stages. Manufacturing emissions are highest for the analyzed system, and the framework improves environmental outcomes over power-tracking baselines.

  • Existing plant and controller optimization studies overlook sustainability impacts, motivating a sustainability-focused CCD framework for microgrid-driven data centers.
  • The framework combines plant variables, controller variables, and manufacturing, operation, and disposal objectives in a microgrid-driven data-center model.Plant variables include battery-pack size and rack height; controller variables include duty-cycle perturbation.
  • Manufacturing GHG emissions are highest for the analyzed system.
  • Compared with power-tracking baseline designs, the CCD framework can yield a 50% reduction in emissions and e-waste.
  • Hardware-in-the-loop validation and comparison of design options are identified for future work.

A.1 Model Parameters and Maps

The appendix specifies model inputs and parameter maps for the battery and data-center subsystems. These include battery voltage as a function of state of charge and thermal properties for server racks.

  • The model uses microgrid, data-center simulation, and experimental-data parameters together with battery-cell and reference-power maps.
  • The battery open-circuit voltage OCV_Li is represented as a function of state of charge.
  • A scaled rack power profile represents data-center server demand.
  • The server rack is modeled as a single control volume using air and aluminum properties, including specific heat and mass.For selected server sections, thermal capacitance is defined as C_sr = m_a,1 c_p,a.

A.2 Model Coupling

The appendix defines electrical and thermal coupling terms connecting converters, buses, batteries, photovoltaic sources, and loads. Tables instantiate the general equations for individual server racks and control volumes.

  • Coupling terms connect the component subsystems through converter and bus currents.
  • The bus-current relations identify converter input and output currents, with negative terms denoting current drawn from a bus.
  • Converter load resistance captures conversion of electrical energy into power for the respective loads.
  • Converter voltages are connected to battery and PV voltages to complete the electrical coupling equations.
  • Tables specify mass-flow rates and map general coupling terms to the individual server racks and control volumes.

A.3 Controller Map

The controller map presents nine discrete modes for the model-free controller and organizes supporting component and dynamic-variable information across Tables 3–8.

  • Nine discrete modes are provided for the model-free controller.The modes are shown in Table 8.
  • Table 3 presents component-wise mass flow rates.
  • Tables 4–7 define dynamic variables and parameters for servers, server-room air control volumes, CCU air control volumes, and plenum air control volumes.
  • The controller modes include high, acceptable, and low Li-ion battery state-of-charge conditions.
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