⚡ electrical engineering

Distributionally robust low-carbon dispatch of multi-data-center integrated energy systems considering user response uncertainty

This paper proposes a distributionally robust low-carbon dispatch framework for multi-data-center integrated energy systems that leverages spatiotemporally transferable computing loads and shared hydrogen storage to effectively manage source-load uncertainties while minimizing operational costs and constraint violation risks.

Original authors: Xiangqing Liu, Yanbo Che, Xiao Guo

Published 2026-09-17

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Xiangqing Liu, Yanbo Che, Xiao Guo

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the modern world, the invisible engine of our digital lives is the data center. These vast facilities, filled with rows of humming servers, process everything from streaming movies to complex artificial intelligence calculations. However, this digital convenience comes with a heavy physical cost: data centers consume enormous amounts of electricity and generate significant carbon emissions. As the demand for computing power explodes, the challenge is no longer just about building more servers, but about powering them cleanly and efficiently. The solution lies in a concept known as an integrated energy system, where electricity, heat, cooling, and even computing tasks are managed together rather than in isolation. Imagine a network of data centers spread across different regions, each connected not just by fiber-optic cables, but by a shared energy grid that includes wind turbines, solar panels, and hydrogen storage. The goal is to balance the fluctuating supply of renewable energy with the variable demand of computing work, all while minimizing the carbon footprint and cost.

The core difficulty in managing such a system is uncertainty. The wind does not always blow, the sun does not always shine, and the users of the data centers do not always behave exactly as predicted. If a system is designed based on perfect predictions, it risks failure when reality deviates. If it is designed to be overly cautious, it becomes prohibitively expensive. Researchers at Tianjin University have tackled this problem by developing a new method for dispatching, or scheduling, these multi-data-center systems. They created a sophisticated planning tool that accounts for the unpredictable nature of both the weather and human behavior. By treating the uncertainty of wind and solar power alongside the uncertainty of how much computing work users will actually shift in response to price changes, the researchers built a model that is both robust against surprises and economical in its operation.

The researchers focused on a network of three data centers, each with its own mix of renewable energy and computing needs. One center was rich in renewable power, another was balanced, and the third relied more on traditional sources. To connect them, they introduced two powerful tools: the ability to move computing tasks between locations and a shared hydrogen storage system. The first tool works by recognizing that some computing jobs can be delayed or moved. If a data center in a windy region has excess electricity, the system can encourage users to send their computing tasks there, or shift tasks from a busy time to a time when the wind is blowing harder. The second tool involves hydrogen. When there is too much renewable electricity, the system uses it to split water and create hydrogen, which is then stored in a large, shared tank. This hydrogen can later be converted back into electricity or used as fuel when the wind stops blowing. This shared storage acts as a long-term battery, allowing energy produced in one place to be used in another, days later.

To manage the unpredictability of this system, the researchers moved beyond traditional planning methods. Older approaches often assumed that the wind and user behavior would follow a predictable average, or they assumed the worst-case scenario for everything, which led to overly expensive and conservative plans. Instead, the team used a data-driven approach that looks at historical patterns of wind and user behavior to create a "cloud" of possible futures. This method, known as distributionally robust optimization, allows the system to prepare for a wide range of outcomes without panicking over the most extreme possibilities. It essentially asks, "What is the most likely set of bad days we might face, and how do we prepare for those?" This approach proved to be far more efficient than previous methods. In their simulations, the new method reduced the cost of being prepared for uncertainty by more than half compared to older techniques that relied on simple averages. It also dramatically improved reliability, cutting the chance of the system failing to meet its energy needs from nearly two percent down to a fraction of a percent.

The study revealed that the two main tools—moving computing tasks and sharing hydrogen storage—work in different but complementary ways. Moving computing tasks was found to lower the overall cost of running the system by about 3.6 percent, primarily by ensuring that computing work happens when and where renewable energy is cheapest and most abundant. The shared hydrogen storage had an even larger impact, reducing costs by about 5.5 percent. More importantly, the hydrogen storage provided a crucial safety net. It allowed the system to handle unexpected drops in wind or solar power without needing to buy expensive backup power or shut down services. Without this shared storage, the system would have needed to keep much larger reserves of backup power, making the entire operation significantly more expensive and less flexible.

The researchers also tested how their system would perform under different conditions, such as changes in carbon prices or the amount of renewable energy available. They found that the system remained effective and stable even when these factors changed significantly. The method successfully translated policy signals, like a higher price on carbon emissions, into real-world actions, such as using more wind power and less fossil fuel. As the amount of historical data used to train the system increased, the plans became even more accurate and less expensive, demonstrating that the approach gets better with time and more information. The study concludes that by combining the flexibility of computing tasks with the long-term storage capability of hydrogen, and by planning for uncertainty in a smart, data-driven way, it is possible to run a network of data centers that is both low-carbon and economically viable. This approach offers a clear path forward for the energy-intensive digital infrastructure of the future, turning the challenge of uncertainty into an opportunity for efficiency.

Technical Summary: Distributionally Robust Low-Carbon Dispatch of Multi-Data-Center Integrated Energy Systems

Problem Statement
The rapid expansion of data centers (DCs) has led to a significant increase in electricity consumption and carbon emissions, complicating the transition to carbon neutrality. While integrating renewable energy and utilizing the spatiotemporal flexibility of computing loads offer pathways for low-carbon operation, current approaches often treat these elements in isolation. Specifically, existing studies frequently:

Model computing load flexibility and hydrogen storage separately for single facilities rather than across geographically distributed multi-DC systems.
Treat renewable generation as deterministic or rely on moment-based ambiguity sets that fail to capture the joint uncertainty of both source-side (wind/PV output deviations) and load-side (user response uncertainty) variations.
Lack a unified dispatch framework that coordinates computing task migration, shared hydrogen storage, and stepwise carbon trading under a rigorous uncertainty quantification method.

This disconnect leads to dispatch decisions that either underestimate operational risks or yield overly conservative and economically suboptimal solutions.

Methodology
The paper proposes a distributionally robust low-carbon dispatch framework for a multi-data-center Integrated Energy System (IES) that couples electricity, gas, heat, cooling, and computing power. The methodology is structured in three layers:

System Architecture and Modeling:
- Multi-DC IES: The system consists of $N$ geographically distributed DCs connected via a distribution network and a shared hydrogen storage station. Each DC is equipped with combined heat and power (CHP) units, gas boilers, fuel cells, electrolyzers, and thermal storage.
- Computing Load Response: Deferrable loads are modeled via temporal shifting within a delay window, while interactive loads are modeled via cross-site migration. User participation is guided by optimized selling prices, introducing response uncertainty.
- Shared Hydrogen Storage: Hydrogen production (via electrolysis using surplus renewables), storage, and utilization (via fuel cells or methanation) are decoupled. The shared station allows hydrogen produced at renewable-rich sites to be stored and dispatched to renewable-poor sites, facilitating long-duration regulation.
- Stepwise Carbon Trading: A mechanism is incorporated where carbon trading costs increase in steps as emissions exceed free quotas, incentivizing low-carbon operation.
Distributionally Robust Optimization (DRO) Formulation:
- Uncertainty Characterization: A joint uncertain vector is defined comprising deviations in computing user response degrees and wind/PV output deviations.
- Wasserstein Ambiguity Set: Instead of moment-based sets, a data-driven ambiguity set based on the Wasserstein metric is constructed. This set forms a ball around the empirical distribution of historical samples, containing all distributions within a specific radius. This approach adapts conservativeness to the amount of available data.
- Two-Stage Decision: The problem is formulated as a two-stage model. The first stage determines device outputs, energy purchases, and scheduled computing transfers before uncertainty realization. The second stage re-adjusts deferrable computing responses and utilizes reserved hydrogen stocks to balance realized deviations.
- Reformulation: The resulting min-max-min problem is reformulated into a tractable convex Second-Order Cone Program (SOCP) using duality theory, allowing for efficient solution via interior-point conic solvers.
Objective:
The model minimizes the total daily operation cost, which includes energy purchase, water consumption, stepwise carbon trading, renewable curtailment penalties, and computing response compensation, subject to multi-energy balance, computing task balance, and device constraints.

Key Contributions
The paper identifies three primary contributions:

Unified Operation Framework: It establishes a multi-DC IES framework that couples spatiotemporal computing load transfer with shared hydrogen storage. This allows for regulation on both the load side (computing transfer) and source side (hydrogen storage), with mechanisms shown to reduce costs by 3.58% and 5.54%, respectively.
Low-Carbon Economic Dispatch Model: It formulates a dispatch model that integrates computing task balance and shared hydrogen storage with stepwise carbon trading across multiple DCs. The model minimizes costs while guiding computing demand toward high-renewable periods.
Data-Driven Robust Dispatch: It develops a DRO model that jointly characterizes source-load dual uncertainty using a Wasserstein ambiguity set. This approach balances robustness and economy, reformulating the problem into a convex SOCP.

Results
Case studies on a representative three-DC test system demonstrate the effectiveness of the proposed method:

Risk Reduction: Compared to a deterministic schedule, the proposed method reduces the constraint violation probability from 1.77% to 0.12% (a 93.0% reduction) while lowering the out-of-sample cost by 3.10%.
Economic Efficiency of Uncertainty Modeling: Compared to a moment-based ambiguity set, the proposed Wasserstein-based approach reduces the "price of robustness" (robustness adjustment cost) by 50.1% while maintaining comparable reliability. Compared to a box set, the reduction is 88.5%.
Mechanism Value:
- Removing computing spatiotemporal transfer increases out-of-sample costs by 3.58% and emissions by 8.56%.
- Removing shared hydrogen storage increases out-of-sample costs by 5.54% and robustness adjustment costs by 42.0%.
Scalability: The direct conic solve method achieves the optimum in 4.31 seconds, significantly faster than Column-and-Constraint Generation (10.1x longer) and Benders Decomposition (19.2x longer).
Sensitivity: The advantages of the data-driven set and the hedging mechanisms persist and even widen under perturbations of renewable capacity, price spreads, carbon prices, and deviation levels.

Significance and Claims
The paper claims that its primary significance lies in providing a unified, tractable framework for the low-carbon dispatch of multi-DC systems that explicitly addresses the joint uncertainty of renewable generation and user response. By utilizing a data-driven Wasserstein ambiguity set, the method avoids the excessive conservatism of moment-based or box-based approaches, achieving lower operational costs without compromising reliability. Furthermore, the study highlights the complementary nature of computing load flexibility and shared hydrogen storage, demonstrating that their combined use is essential for fully exploiting the regulation potential of distributed data centers under uncertainty. The authors note that the current study is limited to a single-day horizon and continuous server modeling, suggesting future work will address seasonal storage values and discrete server commitment.

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