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Data Center Chiller Plant Optimization via Mixed-Integer Nonlinear Differentiable Predictive Control

Ján Boldocký, Cary Faulkner, Elad Michael, Martin Gulan, Aaron Tuor, Ján Drgoňa

Abstract

We present a computationally tractable framework for real-time predictive control of multi-chiller plants that involve both discrete and continuous control decisions coupled through nonlinear dynamics, resulting in a mixed-integer optimal control problem. To address this challenge, we extend Differentiable Predictive Control (DPC) -- a self-supervised, model-based learning methodology for approximately solving parametric optimal control problems -- to accommodate mixed-integer control policies. We benchmark the proposed framework against a state-of-the-art Model Predictive Control (MPC) solver and a fast heuristic Rule-Based Controller (RBC). Simulation results demonstrate that our approach achieves significant energy savings over the RBC while maintaining orders-of-magnitude faster computation times than MPC, offering a scalable and practical alternative to conventional combinatorial mixed-integer control formulations.

Data Center Chiller Plant Optimization via Mixed-Integer Nonlinear Differentiable Predictive Control

Abstract

We present a computationally tractable framework for real-time predictive control of multi-chiller plants that involve both discrete and continuous control decisions coupled through nonlinear dynamics, resulting in a mixed-integer optimal control problem. To address this challenge, we extend Differentiable Predictive Control (DPC) -- a self-supervised, model-based learning methodology for approximately solving parametric optimal control problems -- to accommodate mixed-integer control policies. We benchmark the proposed framework against a state-of-the-art Model Predictive Control (MPC) solver and a fast heuristic Rule-Based Controller (RBC). Simulation results demonstrate that our approach achieves significant energy savings over the RBC while maintaining orders-of-magnitude faster computation times than MPC, offering a scalable and practical alternative to conventional combinatorial mixed-integer control formulations.

Paper Structure

This paper contains 16 sections, 12 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. System Model
  4. Optimal Control Problem
  5. Rule-Based Control
  6. Methodology
  7. Problem Reformulation
  8. Differentiable Rounding
  9. Binary-Variance Regularization
  10. Mixed-Integer Policy Optimization
  11. Numerical Experiments
  12. Experimental Setup
  13. Computational Scalability
  14. Performance Comparison
  15. Practical Challenges and Limitations
  16. ...and 1 more sections

Figures (6)

  • Figure 1: Schematic of a multiple-chiller plant arranged in a parallel configuration.
  • Figure 2: Conceptual diagram of the mixed-integer differentiable predictive control for nonlinear chiller plant optimization. Green dashed arrows represent the forward pass, while red dashed arrows represent the backward pass.
  • Figure 3: Effect of binary-variance regularization on relaxed integer values, showing switching behavior under a step change in cooling load from 150.0kW to 500.0kW occurring at time $k\!=\!20$ (setup from Sec. \ref{['sec:experiments']}, $N\!=\!20$). The dotted black line indicates the rounding threshold.
  • Figure 4: Computational scalability of MI-DPC across different number of chillers ($M$) and horizon lengths ($N$). The top panel illustrates the total training time (TT), while the bottom panel reports the mean inference time (MIT).
  • Figure 5: Closed-loop simulation results of a chiller plant ($M\!=\!3$, $Q_{\max}\!=\!1$ MW) with MI-DPC and RBC policies, highlighting the importance of predictive action for stable operation, when considering cooling ramp-rate constraints.
  • ...and 1 more figures