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A Conformal Prediction-Based Chance-Constrained Programming Approach for 24/7 Carbon-Free Data Center Operation Scheduling

Yijie Yang, Jian Shi, Dan Wang, Chenye Wu, Zhu Han

TL;DR

The paper tackles scheduling data centers to operate on 24/7 carbon-free energy under renewable uncertainty. It combines conformal prediction with chance-constrained programming to build covariate-aware, statistically valid uncertainty sets, enabling robust, low-emission operation while guaranteeing feasibility. Introducing AMV-CQR and IMV-CQR, it provides frameworks for both average and per-output reliability, and proves theoretical links between CP-derived uncertainty and CCP feasibility. Numerical results show meaningful cost and carbon reductions (up to ~6-7%) compared to covariate-independent methods, demonstrating practical potential for deploying 24/7 CFE in data centers.

Abstract

The rapid growth of AI applications is dramatically increasing data center energy demand, exacerbating carbon emissions, and necessitating a shift towards 24/7 carbon-free energy (CFE). Unlike traditional annual energy matching, 24/7 CFE requires matching real-time electricity consumption with clean energy generation every hour, presenting significant challenges due to the inherent variability and forecasting errors of renewable energy sources. Traditional robust and data-driven optimization methods often fail to leverage the features of the prediction model (also known as contextual or covariate information) when constructing the uncertainty set, leading to overly conservative operational decisions. This paper proposes a comprehensive approach for 24/7 CFE data center operation scheduling, focusing on robust decision-making under renewable generation uncertainty. This framework leverages covariate information through a multi-variable conformal prediction (CP) technique to construct statistically valid and adaptive uncertainty sets for renewable forecasts. The uncertainty sets directly inform the chance-constrained programming (CCP) problem, ensuring that chance constraints are met with a specified probability. We further establish theoretical underpinnings connecting the CP-generated uncertainty sets to the statistical feasibility guarantees of the CCP. Numerical results highlight the benefits of this covariate-aware approach, demonstrating up to 6.65% cost reduction and 6.96% decrease in carbon-based energy usage compared to conventional covariate-independent methods, thereby enabling data centers to progress toward 24/7 CEF.

A Conformal Prediction-Based Chance-Constrained Programming Approach for 24/7 Carbon-Free Data Center Operation Scheduling

TL;DR

The paper tackles scheduling data centers to operate on 24/7 carbon-free energy under renewable uncertainty. It combines conformal prediction with chance-constrained programming to build covariate-aware, statistically valid uncertainty sets, enabling robust, low-emission operation while guaranteeing feasibility. Introducing AMV-CQR and IMV-CQR, it provides frameworks for both average and per-output reliability, and proves theoretical links between CP-derived uncertainty and CCP feasibility. Numerical results show meaningful cost and carbon reductions (up to ~6-7%) compared to covariate-independent methods, demonstrating practical potential for deploying 24/7 CFE in data centers.

Abstract

The rapid growth of AI applications is dramatically increasing data center energy demand, exacerbating carbon emissions, and necessitating a shift towards 24/7 carbon-free energy (CFE). Unlike traditional annual energy matching, 24/7 CFE requires matching real-time electricity consumption with clean energy generation every hour, presenting significant challenges due to the inherent variability and forecasting errors of renewable energy sources. Traditional robust and data-driven optimization methods often fail to leverage the features of the prediction model (also known as contextual or covariate information) when constructing the uncertainty set, leading to overly conservative operational decisions. This paper proposes a comprehensive approach for 24/7 CFE data center operation scheduling, focusing on robust decision-making under renewable generation uncertainty. This framework leverages covariate information through a multi-variable conformal prediction (CP) technique to construct statistically valid and adaptive uncertainty sets for renewable forecasts. The uncertainty sets directly inform the chance-constrained programming (CCP) problem, ensuring that chance constraints are met with a specified probability. We further establish theoretical underpinnings connecting the CP-generated uncertainty sets to the statistical feasibility guarantees of the CCP. Numerical results highlight the benefits of this covariate-aware approach, demonstrating up to 6.65% cost reduction and 6.96% decrease in carbon-based energy usage compared to conventional covariate-independent methods, thereby enabling data centers to progress toward 24/7 CEF.

Paper Structure

This paper contains 24 sections, 6 theorems, 32 equations, 6 figures, 9 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation and Challenges
  3. Literature Review
  4. Our Contributions
  5. Model Formulation
  6. Data Centers Power Consumption Model
  7. Data Centers Workloads Scheduling Model
  8. ESS Model
  9. Chance-Constraints Problem Formulation
  10. Proposed Framework of Conformal Prediction-based Chance Constrained Programming
  11. Contextual Chance-Constraints Programming
  12. The RO Reformulation of the C-CCP
  13. Uncertainty Quantification and Conformal Prediction
  14. The Proposed Approach
  15. Conformal Quantile Regression
  16. ...and 9 more sections

Key Result

Theorem 1

Any feasible solution to problem RO (model:ro1) is also feasible to problem T-CCP (m1) if the following condition holds for $\mathcal{U}$:

Figures (6)

  • Figure 1: Comparison between conventional and proposed uncertainty set construction
  • Figure 2: The process getting prediction interval $C(X_{n+1})$.
  • Figure 3: The overall process
  • Figure 4: Day-ahead carbon-based energy proportion and electricity price
  • Figure 5: Pattern of different classes of workloads
  • ...and 1 more figures

Theorems & Definitions (12)

  • Theorem 1
  • proof
  • Theorem 2
  • Theorem 3
  • proof : Proof for lower bound
  • proof : Proof for upper bound
  • Theorem 4
  • proof
  • Theorem 5
  • proof
  • ...and 2 more