Two-stage robust optimization strategy for spatially-temporally correlated data centers with data-driven uncertainty sets

Abstract

Data center buildings (DCBs) in data center parks consume significant and ever-growing amounts of electric power for processing tremendous data workloads in a modern city. The workloads are divided into two types: interactive workloads (IWs) with spatially transferrable characteristics and batch workloads (BWs) with temporally shiftable characteristics. The unique spatially-temporally workloads show great demand response capability, enabling reducing the electricity cost of DCBs. However, the source-load uncertainties such as the number of arriving workloads, and photovoltaic output affect the cost-efficient operation of DCBs in the electricity market. Inadequate server numbers during worst-case scenarios may result in the inability to fulfill user contracts. This paper presents a model for DCBs that incorporates battery energy storage systems, photovoltaic generation, and electrical loads for processing spatially-temporally correlated workloads. Considering multiple uncertainties, a two-stage robust optimization strategy is proposed to coordinate workload and power for DCBs. To accurately determine the boundaries of the uncertainty sets, a data-driven method using the 1-Wasserstein metric is adopted. This method is reformulated into a distributionally robust chance-constrained programming model. The nested column-and-constraint generation (C&CG) method is used to resolve the established two-stage robust optimization problem with mixed-integer recourse. Finally, case studies verify the effectiveness of the proposed method.