Harvesting spatial-temporal load migration flexibility of data centers: A chance-constrained bi-level optimization model with endogenously formed risk-reflective locational prices

Yujian Ye, Ding Ma, Yizhi Wu, Heng Hu, Xi Zhang, Chuan Liu and Dezhi Xu

Applied Energy, 2026, vol. 402, issue PB, No S0306261925017015

Abstract: Despite data centers (DCs) exhibit significant spatial-temporal load migration flexibility potentials, adequate utilization of which necessitates efficient coordination between the operation of DCs and the power system, namely electricity-computation co-optimization (ECC). However, existing ECC studies typically adopt either a DC operator or power system perspective, overlooking their holistic operational coordination. Uncertainties stemmed from both computation workload of DCs and renewable power source (RES) and load of power systems are not fully encapsulated in the ECC model. Furthermore, neglection of uncertainties results in inadequate formation of locational prices which do not reflect operational risks, hindering effective guidance and thus exploitation of DC load spatial-temporal migration flexibility. To fill the above research gaps, this paper proposes a chance-constrained bi-level ECC model which coordinates the operator’s business model of geo-distributed DCs, and dispatch model of power system in a coupled fashion. A generic DC model is developed to account for heterogeneity in cooling methodologies, thermal power exchange, and spatial-temporal load migration flexibility for DCs. Risk-reflective locational marginal prices are endogenously formed in the ECC model by linking risk probabilities to price signals via chance constraint dual variables. The bi-level model is reformulated into a second-order conic program, transformed via Karush-Kuhn-Tucker conditions into a mathematical program with equilibrium constraints, and solved as a mixed-integer quadratic program using strong duality. Case studies on the IEEE 118-bus system quantifies the value of harvesting DC spatial-temporal load migration flexibility, demonstrating its increasing trend with the extent of operational uncertainties. In face of both DC- and grid-side uncertainties, a win-win outcome involving 8.23 % profit gain for DC operator and 27.92 % cost shaving for power system is witnessed, respectively. More efficient power system operation exploiting DC flexibility also results in alleviation of transmission congestion (and thus removal of locational price discrepancies), enhanced RES utilization and reduced carbon emissions.

Keywords: Data centers; Electricity-computation co-optimization; Spatial-temporal load migration; Bi-level optimization; Locational price formation; Chance constraints (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1016/j.apenergy.2025.126971

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