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

The gist The work studies the optimization of physical plant characteristics and controller parameters for sustainability in microgrid-driven data centers.

Control Co-Design Framework

The authors established a generalized, sustainability-centric control co-design (CCD) framework for energy systems to address gaps in prior research. This framework defines and categorizes sustainability metrics into three lifecycle stages: manufacturing, operation, and disposal. The total objective function is formulated as a weighted sum of these three metrics: J total = w m J m + w o J o + w d J d where the individual objectives are defined as Manufacturing (Jm), Operation (Jo), and Disposal (Jd).

Design Variables and Constraints

The CCD framework incorporates both plant design variables (θ) and controller design variables (φ) to expand the design space. Plant design variables include sizing- and topology-related parameters of the system such as PV array configuration, number of battery cells, and converter size and material selection <ref:2609.01912#pg3> while controller design variables can include control architecture settings, timesteps, predictive horizons, and gains within a control algorithm <ref:2609.01912#pg3>. The optimization problem is structured into five steps to solve the CCD problem. The constraints ensure physical and practical limitations are obeyed <ref:2609.01912#pg6> including equality constraints representing plant dynamics described by Equation (2) and inequality constraints limiting the metrics to upper bounds M max and design variable ranges.

Model Dynamics

The system model couples microgrid and data center components through algebraic relationships and thermal matching. The combined model involves several dynamic systems, including voltage bus dynamics (Equation 8), converter dynamics (Equations 9-10), PV subsystem dynamics (Equation 11), battery pack dynamics (Equations 12-14), server rack temperature dynamics (Equation 15), and various air flow CVs in the data center. The full system state vector has N=37 states, and there are N=6 control inputs representing converter duty cycles <ref:3pg13,There are Ns = 37 states of the system: Vbus1, Vbus2, T pv, SOC, Vbat volt2 to Vbat volt4, Track1 and TRack2 and TRackair1 to TRackair8 and Trackair9 to Trackair3, Xpbpk and the twelve Vin and Vout states of the converters <ref:2609.01912#pg14>.

Optimization Results

The optimization procedure uses a grid search on design variables, resulting in 166 designs tested. Sensitivity analyses reveal that the manufacturing objective function relies solely on the plant design variable when adjusting theta sh. Furthermore, battery pack size has higher impact on the production of e-waste rather than the controller design variable for the degradation objective. The comparison with a baseline design shows that the proposed has a 50% reduction over the baseline in the manufacturing objective value.

Conclusion

The CCD framework demonstrates that by prioritizing sustainability attributes, designers can achieve significant reductions in environmental impacts compared to baseline approaches. The results indicate that GHG emissions during manufacturing are the highest for the system analyzed. Compared to baseline designs that minimize power tracking error, the CCD framework can yield a 50% reduction in emissions and e-waste. The work concludes by showing that by prioritizing J1v, the baseline gets the design the furthest to the left on the Jm vs. J1v Pareto front. The CCD framework is a valuable tool for optimizing energy systems by integrating sustainability criteria across all lifecycle stages. The developed CCD-oriented model is connected to a perturb-and-observe algorithm to control the system dynamics.

How it works

The optimization problem is formulated as minimizing J total = w m J m + w o J o + w d J d. The plant dynamics are augmented by design variables using diagonal design matrices κc(θ) and κ(θ). The control algorithm uses a model-free approach, specifically Perturb and observe methods [52] to compute duty cycle values. The controller's performance is validated by testing the model under small variations in certain parameters <ref:2609.01912#pg16> and includes nine discrete modes for the controller as presented in Table 8.

Sustainability Metrics

The sustainability metrics are categorized into three distinct stages to support comparative analysis. The manufacturing objective function Jm captures impacts from net energy consumption, waste generation, and pollutants emitted during the extraction, transportation, and assembly of raw materials <ref:2609.01912#pg5> while the operation objective function Jo accounts for electricity consumption, resource use, control strategies, heat generation, and noise production <ref:2609.01912#pg6>. The disposal objective function Jd agglomerates metrics related to improper waste disposal, inadequate recycling, and increased demand for new resources <ref:2609.01912#pg6>.

Pareto Front Analysis

The analysis involves constructing 2D Pareto fronts from the Pareto-optimal solutions to compare competing sustainability objective functions. The comparison between Jm and Jo shows that the operation objective is more sensitive to changes in the plant design variable over the controller design variable. The analysis of Jd versus design variables shows that generated e-waste is more heavily influenced by theta sh as compared to phi1 for this subset of designs. The threshold value c dEphi = 5.33 provides guidance for engineers on how to balance waste heat or GHG emissions against e-waste <ref:6pg22,With w m = 0, w o = 1, w d = c dEphi/365.25 to convert into kg per day, Equation (1) is calculated twice: for the leftmost design (Jd = 7.424 × 10 cubed and Jo = 42.

1. Bold plant design variables to optimize manufacturing emissions: The framework allows optimization of plant design variables, including battery pack size (scaling factor thetaଵ) and rack height (scaling factor thetaଶ), which directly correlate with sustainability metrics such as the manufacturing objective function, The functionJ௠ captures all sustainability metrics relating to the manufacturing of components for, and the construction of, the energy system.

2. Bold controller design variables to optimize operational waste heat: The control co-design (CCD) framework optimizes controller design variables (scaling factor phiଵ), which influence the operation objective functionJ௢ accounts for environmental impacts relating to the operation of the energy system, thereby minimizing waste heat generation.

3. Bold disposal metrics to inform end-of-life decisions: The framework categorizes sustainability into three lifecycle stages, including Disposal: The objective functionJௗ agglomerates sustainability metrics categorized by the ending lifecycle stage for plant components, electronic devices, and other pieces of the system, enabling optimization based on e-waste generation.

4. Implement a multi-objective trade-off analysis: By constructing 2D Pareto fronts comparing objectives like manufacturing emissions and operation costs, designers can determine which design variable should be the focus to improve sustainability by analyzing sensitivity terms, such as the comparison of terms related to plant versus controller design variables.

5. Integrate model-free control for real-time adaptation: The system uses a model-free approach with Perturb and observe methods [52] especially appropriate to compute duty cycle values, allowing the AI system to dynamically adjust converter duty cycles based on real-time measurements, such as SOCI, T௦,ଵ and T௦,ଶ.

6. Develop predictive load tracking capability: The controller is validated by demonstrating that it can track the reference power to the servers for at least 20 hours, which is crucial for maintaining system functionality under dynamic conditions.